Springer Series in Optical Sciences 127
Dominik Gerhard Rabus
Cinzia Sada
Integrated Ring
Resonators
A Compendium
Second Edition
Springer Series in Optical Sciences
Volume 127
Founding Editor
H.K.V. Lotsch, Nußloch, Baden-Württemberg, Germany
Editor-in-Chief
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Japan
Theodor W. Hänsch, Max Planck Institute of Quantum Optics, Garching b.
München, Bayern, Germany
Ferenc Krausz, Max Planck Institute of Quantum Optics, Garching b. München,
Bayern, Germany
Barry R. Masters, Cambridge, MA, USA
Katsumi Midorikawa, Laser Tech Lab, RIKEN Advanced Science Institute,
Saitama, Japan
Herbert Venghaus, Fraunhofer Institute for Telecommunications, Berlin, Germany
Horst Weber, Berlin, Germany
Harald Weinfurter, München, Germany
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Japan
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Philadelphia, PA, USA
Springer Series in Optical Sciences is led by Editor-in-Chief William T. Rhodes,
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Dominik Gerhard Rabus Cinzia Sada
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Integrated Ring Resonators
A Compendium
Second Edition
With 328 Figures and 15 Tables
123
Dominik Gerhard Rabus
Department of Applied Chemistry, Process
Analysis and Technology (PA&T)
Reutlingen University
Reutlingen, Germany
Cinzia Sada
Department of Physics and Astronomy
“Galileo Galilei”
University of Padova
Padua, Italy
ISSN 0342-4111
ISSN 1556-1534 (electronic)
Springer Series in Optical Sciences
ISBN 978-3-030-60130-0
ISBN 978-3-030-60131-7 (eBook)
https://doi.org/10.1007/978-3-030-60131-7
1st edition: © Springer-Verlag Berlin Heidelberg 2007
2nd edition: © Springer Nature Switzerland AG 2020
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar
methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publication does not imply, even in the absence of a specific statement, that such names are exempt from
the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authors or the editors give a warranty, expressed or implied, with respect to the material contained
herein or for any errors or omissions that may have been made. The publisher remains neutral with regard
to jurisdictional claims in published maps and institutional affiliations.
This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Inspiration
“Progress is a never-ending spiral toward the future.
When looked from one side, it can seem either a ring or a line.
Its real natural evolution can be seen, loved, and appreciated only by changing the
viewing angle thus the perspective.”
The Authors
v
Preface
This book is all about integrated ring resonators made out of optical waveguides in
various materials for different applications. Integrated ring resonators are used to
build optical filters, lasers, sensors, modulators, dispersion compensators, just to
name a few. The book covers the range from simulation of various ring resonator
configurations to the fabrication processes currently used, to the description of the
application of integrated ring resonator in various fields. The book presents a
summary of the activities in this field from the past to the current state of the art
giving several examples. It has been written for students, graduates, professionals,
academics and industry alike, working in this exciting and ever thriving field.
The examples in literature used in this book have been collected over the last 20
years, categorizing the different examples into what are now the chapters of this
book.
Integrated ring resonators have been and still are a fascinating class of devices.
Since the beginning they have gained great attention from the integrated optics
community, especially in the frantic search to optimize their performances and win
the competition to be the first to get the smallest device dimensions. This race has
brought to the surface several astonishing results, later interpreted as new paths for
outstanding applications even outside the mere integrated optics field. Those
technologies that have been initially addressed as too much complicated to be of
real practical interest, have become progressively available. As a consequence, a
new inspiring light and weight have been implied to re-read and re-interpret the
results published since the nineties, at that time mainly classified as pure academic
achievements. Nowadays integrated ring resonators can therefore proudly boast to
be the pulsing heart in new sensing approaches which are of great interest surely in
biology, medicine and chemistry but not limited to these application fields. The
huge advances in the fabrication technologies have covered the gap to match the
micrometer/sub-micrometer scales needed for integrated ring resonators with the
endless power of dreaming visioners in search of progress and improvement. It is in
this frame of reference and mindset that the authors have come to this new version
of the compendium on Integrated Ring Resonators.
vii
viii
Preface
Due to high demand and continued interest in the topic, the first version from
2007 is upgraded in this second edition considering the progress made in the field
and extending the fabrication material range to polymers, crystals and hybrids
which had been briefly discussed in the first edition and have now received a major
upgrade in Chap. 3. Among others, Lithium Niobate has been introduced into the
second edition reflecting the growing interest and achievements in Chap. 3.9. In
Chap. 4, on building blocks for ring resonators, a brief overview on gratings for
light in- and outcoupling is presented, making this chapter now updated with some
of the most recent achievements. Chapter 5 has been “enriched” with interesting
results on modulators and a short introduction on ring resonator switching in
telecom operations. Chapter 6 on sensors has been upgraded to reflect the advances
in biosensing and opto-microfluidics as both research fields have reached a considerable maturity state with direct impact on implementation of future applications
with a clear path to productization. Chapter 7 on whispering gallery mode ring
resonators has received an extension as well to serve even more as an introduction
into this topic from a material science point of view.
The authors are grateful to the entire integrated ring resonator community for
providing exciting and cutting-edge research material which enabled the writing of
this book. Due to the enormous amount of publications in this attractive field, we
hope, that we were able to refer to most of the work done so far and would be
thankful if we are made aware of any “undiscovered” work.
As research on integrated ring resonators is ongoing, we would be more than
happy to receive material for our growing database which can then of course be
included in further editions.
Reutlingen, Germany
Padua, Italy
Dominik Gerhard Rabus
Cinzia Sada
Contents
1 Introduction
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3 Materials, Fabrication and Characterization Methods . . . . . . .
3.1 Wafer Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Bonding with Intermediate Layer . . . . . . . . . . . . . .
3.1.2 Bonding Without Intermediate Layer . . . . . . . . . . .
3.1.3 Benzocyclobutene Wafer Bonding . . . . . . . . . . . . .
3.2 Dry Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Si-Based Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Ring Resonators Based on Si–SiO2 . . . . . . . . . . . .
3.3.2 Ring Resonators Based on Ta2O5–SiO2 . . . . . . . . .
3.3.3 Ring Resonators Based on SiN, SiON, and Si3N4 . .
3.3.4 Ring Resonators Based on SiO2–GeO2 . . . . . . . . .
3.4 III–V Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 The Quaternary Semiconductor Compound GaInAsP
3.4.2 The Semiconductor Compound AlGaAs . . . . . . . . .
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2 Ring Resonators: Theory and Modeling . . . . . . . . .
2.1 Single Ring Resonators . . . . . . . . . . . . . . . . . .
2.1.1 Ring Structure . . . . . . . . . . . . . . . . . . .
2.1.2 Racetrack Shaped Resonators . . . . . . . .
2.2 Double Ring Resonators . . . . . . . . . . . . . . . . . .
2.2.1 Serially Coupled Double Ring Resonator
2.2.2 Parallel Coupled Double Ring Resonator
2.3 Multiple Coupled Resonators . . . . . . . . . . . . . . .
2.3.1 Serially Coupled Ring Resonators . . . . .
2.3.2 Parallel Coupled Ring Resonators . . . . .
2.4 Microring Resonator Based Electro-optic Effect .
2.5 Microring Resonator Modulator . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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ix
x
Contents
3.4.3 Lateral Coupling in GaInAsP/InP . . . . . . . . . . . . .
3.4.4 Vertical Coupling in GaInAsP/InP . . . . . . . . . . . . .
3.4.5 Lateral Coupling in AlGaAs/GaAs . . . . . . . . . . . . .
3.4.6 Vertical Coupling in AlGaAs/GaAs . . . . . . . . . . . .
3.4.7 Implementation of Gain in Ring Resonators . . . . . .
3.5 Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Conventional Fabrication Techniques . . . . . . . . . . .
3.5.2 Replication and Nanoimprinting . . . . . . . . . . . . . .
3.5.3 Novel Polymer Devices . . . . . . . . . . . . . . . . . . . . .
3.6 Temperature Insensitivity . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Polarization Independence . . . . . . . . . . . . . . . . . . . . . . . .
3.8 Characterization Methods . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.1 Conventional Characterization . . . . . . . . . . . . . . . .
3.8.2 Optical Low Coherence Reflectometry . . . . . . . . . .
3.8.3 Evanescent Field Measurement Methods . . . . . . . .
3.9 Lithium Niobate and Hybrid Solutions . . . . . . . . . . . . . . .
3.9.1 Ring Resonators Based on Lithium Niobate . . . . . .
3.9.2 Ring Resonators Based on Lithium Niobate
on Insulators (LNOI) . . . . . . . . . . . . . . . . . . . . . .
3.9.3 Ring Resonators Based on Lithium Niobate
on Insulators in Hybrid Configuration with Nitrides
and Semiconductors . . . . . . . . . . . . . . . . . . . . . . .
3.9.4 Microring Modulators Based on Lithium Niobate
and Chalcogenide Glasses on Silicon . . . . . . . . . . .
3.10 Microring Modulators in LN, LNOI and Hybrids:
Limits and Improvements . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4 Building Blocks of Ring Resonator Devices . . . . . . . . .
4.1 Couplers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Directional Couplers . . . . . . . . . . . . . . . . .
4.1.2 Multimode Interference Couplers . . . . . . . .
4.1.3 Y-Couplers . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Spot Size Converters for Light in- and Outcoupling
4.4 Gratings for Light in- and Outcoupling . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5 Devices . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Filters . . . . . . . . . . . . . . . . . . . .
5.1.1 Passive Devices . . . . . . .
5.1.2 Devices with Gain Section
5.2 Tunability Methods . . . . . . . . . .
5.2.1 Wavelength Tuning . . . .
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Contents
xi
5.2.2 Center Wavelength Trimming . . . . . . . . . . .
5.2.3 Tunable Couplers in Ring Resonators . . . . .
5.3 Dispersion Compensators . . . . . . . . . . . . . . . . . . . .
5.4 Mach–Zehnder Interferometers Combined with Ring
Resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Modulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1 All Active Lasers . . . . . . . . . . . . . . . . . . . .
5.6.2 Devices with Gain Section . . . . . . . . . . . . .
5.6.3 Passive Ring Resonator Coupled Lasers . . . .
5.7 Wavelength Converters . . . . . . . . . . . . . . . . . . . . .
5.8 Optical Signal Processing . . . . . . . . . . . . . . . . . . . .
5.8.1 Logic Gates . . . . . . . . . . . . . . . . . . . . . . . .
5.8.2 Switching . . . . . . . . . . . . . . . . . . . . . . . . . .
5.8.3 Telecom Operations . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 232
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7 Whispering Gallery Mode Devices . . . . . . . . . . . . . . . . . . . . . . . .
7.1 Whispering Gallery Modes (WGM) . . . . . . . . . . . . . . . . . . .
7.2 WGM Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 WGM Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 WGM Microresonators in LN: Recent Advances in Dielectric
Crystalline Configurations . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 Sensors . . . . . . . . . . . . . . .
6.1 Microfluidics . . . . . . .
6.2 Optofluidic Resonators
6.3 Biosensors . . . . . . . .
References . . . . . . . . . . . . .
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8 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
Abbreviations
x
η
j
C
K
a
an
h
b
K
C/
Dk
U(x)
Dxn
k0
e0
acoupling
kg
ainsertion
/k
wk
apropagation
xRn
ut
ath
1/s
2dk
A(z)
AFM
APF
Angular frequency
Coupling efficiency to the fundamental waveguide mode
Coupling parameter
Gain of the filter
Length of waveguide segment
Loss coefficient of the ring (zero loss: a = 1)
Absorption coefficient
Phase
Propagation constant
Wavelength
Complex angular propagation constant
Free spectral range (see also FSR)
Phase shift
Complex frequency deviation
Center wavelength of the passband
Permittivity of free space
Fiber–chip coupling losses
Bandgap wavelength
Insertion loss
Coupling angle
Phase shift
Intrinsic losses
Resonant frequency of ring resonator n
Phase of the coupler
Coefficient of thermal expansion
Amplitude decay time constant
3 dB bandwidth
Polynomial
Atomic force microscope
All-pass filter
xiii
xiv
ASE
B
B(z)
BCB
BH
BHF
BPF
BW
c
c0
CAIBE
Cn
Cp
CROW
CTE
CVD
cw
DEMUX
DFB
DGD
DI
dk
DR-RCL
DTFT
DUT
E
e(t)
E(t)
E-beam
ECL
ECR-CVD
EIM
EO
F
FHD
FSK
FSR
FWHM
FWM
GRIN
h(n)
HEMT
I
ICP-RIE
Abbreviations
Amplified spontaneous emission
Intensity enhancement or buildup factor
Polynomial
Benzocyclobutene
Buried heterostructure
Buffered hydrofluoric acid
Bandpass filter
Modulation bandwidth
Phase velocity of the ring mode (c = c0/neff)
Vacuum speed of light
Chemically assisted ion beam etching
Auger recombination coefficient
AUGER recombination coefficient
Coupled resonator optical waveguides
Coefficient of thermal expansion
Chemical vapor deposition
Continuous wave
Demultiplexer
Distributed feedback
Differential group delay
Deionized
Length of the ring waveguides
Double ring resonator coupled lasers
Discrete-time Fourier transform
Device under test
Complex mode amplitude
Energy amplitude
Time-dependent mode amplitude
Electron beam
External cavity laser
Electron cyclotron resonance chemical vapor deposition
Effective index method
Electro-optic
Finesse
Flame hydrolysis deposition
Frequency-shift keying
Free spectral range
Full width at half maximum
Four wave mixing
Gradient index
Impulse response of a filter
High-electron-mobility transistors
Intensity/current
Inductively coupled plasma reactive ion etching
Abbreviations
IPA
K
k
L
LC
lk
LN
LPCVD
m
MBE
MEMS
mh
ml
MIBK
mlp
MMI
mn
mo
MOVPE
MQW
mt
MUX
MZI
neff
ng
NMP
NSOM
OEC
OLCR
OSA
OSP
P
P(t)
p(t)
PBS
PD
PECVD
PhC
PIC
PLC
PMD
PMMA
pn
PRRM
xv
Isopropanol or 2-propanol
Contrast/confinement factor
Vacuum wavenumber
Circumference of the ring/optical output
Lattice constant
Length of the coupler (note: this is not the coupling length)
Lithium niobate
Low-pressure chemical vapor deposition
Integer
Molecular beam epitaxy
Microelectromechanical system
Effective hole masses
Effective electron masses
Methyl isobutyl ketone
Effective hole masses
Multimode interference
Mode number
Mode order
Metal organic vapor-phase epitaxy
Multiple quantum well
Effective electron masses
Multiplexer
Mach–Zehnder interferometer
Effective refractive index
Group refractive index
n-methyl-2-pyrrolidone or C5H9NO
Near-field scanning optical microscopy
Optimum end-fire coupling
Optical low-coherence reflectometry
Optical spectrum analyzer
Optical signal processing
Transmission power
Time-dependent power
Total energy stored in the ring
Polarization beam splitter
Photodiode
Plasma-enhanced chemical vapor deposition
Photonic crystal
Photonic integrated circuit
Polarization controller
Polarization mode dispersion
Polymethylmethacrylate
Poles of H(z)
Pulse repetition rate multiplication
xvi
PSTM
Q
QC
QCSE
QW
R
r
RF
RIBE
RIE
RPM
RTFT
RW
RZ
S
SAMOVPE
SCCM
SCISSORS
SE
SEBL
SEM
SM
SMSR
SNOM
SOA
SOG
SOI
SPM
STM
STP
T
t
TE
Tg
TIR
TM
TN(x)
TO
UMatrix
vg
w
WDM
WGM
x0
xC
Abbreviations
Photon scanning tunneling microscope
Quality factor
Quantum cascade
Quantum-confined Stark effect
Quantum wells
Effective radius of curvature/end-face reflectivity
Radius
Radio frequency
Reactive ion beam etching
Reactive ion etching
Rounds per minute
Real-time Fourier transformation
Ridge waveguide
Return-to-zero
Optical path length
Selective area metal-organic vapor-phase epitaxy
Standard cubic centimeters per minute
Side-coupled, integrated, space sequence of resonators
Switching element
Scanning electron-beam lithography
Scanning electron microscope
Switching module
Side-mode suppression ratio
Scanning near-field optical microscopy
Semiconductor optical amplifier
Spin on glass
Silicon on insulator
Scanning probe microscopy
Scanning tunneling microscopy
Standard temperature and pressure
Characteristic matrix/temperature/tuning enhancement factor
Coupling parameter/time
Transverse electric
Glass transition temperature
Total internal reflection
Transverse magnetic
Nth-order Chebyshev polynomial
Thermo-optic
Unit matrix
Group velocity
Width
Wavelength division multiplexing
Whispering gallery mode
3 dB cutoff frequency
Center frequency
Abbreviations
xn
xP
xS
zm
xvii
Vector
Changeover region on the passband
Changeover region on the stopband
Zeros of H(z)
Chapter 1
Introduction
Integrated ring resonators have emerged in the last years in integrated optics and have
found their way into many applications and are still highly relevant both in applied
and advanced research. Integrated ring resonators do not require facets or gratings
for optical feedback and are thus particularly suited for monolithic integration with
other components. The wavelength and thus frequency response from coupled ring
resonators can be custom designed by the use of different coupling configurations.
In this way for example, the response from ring resonator filters can be designed to
have a flat top and steep roll of. Other coupling configurations lead for example to a
ring resonator reflector device, which can be used on one side or on both sides of an
integrated semiconductor optical amplifier serving as a laser. Numerous examples
of ring resonator applications exist and several of them are highlighted in this book,
demonstrating their unique use.
Ring resonators do not only find applications in optical networks, they have
recently been demonstrated to be used as sensors and biosensors.
The book is organized as follows: Chap. 2 covers the main aspects of ring resonator
theory. Chapter 3 gives an overview of the various fabrication methods and material
systems. Chapter 4 serves as a brief introduction into the building blocks of ring
resonator devices like couplers and bends. Chapter 5 describes the numerous applications of fabricated ring resonator devices. Chapter 6 highlights sensors and related
applications whilst Chap. 7 provides a short introduction into whispering gallery
mode resonators. The book ends with an outlook given in Chap. 8.
The intention of the authors is to provide the reader with a comprehensive starting
point into this hot topic of integrated ring resonators fulfilling the requirement of a
true compendium.
© Springer Nature Switzerland AG 2020
D. G. Rabus and C. Sada, Integrated Ring Resonators, Springer Series
in Optical Sciences 127, https://doi.org/10.1007/978-3-030-60131-7_1
1
Chapter 2
Ring Resonators: Theory and Modeling
One of the first papers to deal about the simulation of an integrated ring resonator
for a bandpass filter has been published in 1969 by E. A. Marcatili. The layout of the
channel dropping filter which he proposed is shown in Fig. 2.1. This can be regarded
as the standard configuration for an integrated ring resonator channel dropping filter.
Two straight waveguides also known as the bus or the port waveguides are coupled
either by directional couplers through the evanescent field or by multimode interference couplers to the ring resonator. A simpler configuration is obtained, when the
second bus or port waveguide is removed. Then the filter is typically referred to as
“notch” filter because of the unique filter characteristic. In the following chapter, the
ring resonator simulation model is described beginning with the basic notch configuration and adding more bus waveguides and ring resonators to eventually build a
multiple coupled ring resonator filter. Different types of ring resonator simulation
models will be explained, so as to be able to chose from a range of models which
best suit the need.
2.1 Single Ring Resonators
2.1.1 Ring Structure
The Basic Configuration
The basic configuration, which consists of unidirectional coupling between a ring
resonator with radius r and a waveguide, is described in Fig. 2.2, based on Yariv
(2000, 2002).
Defining that a single unidirectional mode of the resonator is excited, the coupling
is lossless, single polarization is considered, none of the waveguide segments and
coupler elements couple waves of different polarization, the various kinds of losses
occurring along the propagation of light in the ring resonator filter are incorporated
© Springer Nature Switzerland AG 2020
D. G. Rabus and C. Sada, Integrated Ring Resonators, Springer Series
in Optical Sciences 127, https://doi.org/10.1007/978-3-030-60131-7_2
3
4
2 Ring Resonators: Theory and Modeling
Fig. 2.1 Ring resonator channel dropping filter
Fig. 2.2 Model of a single ring resonator with one waveguide
in the attenuation constant, the interaction can be described by the matrix relation:
E t1
E t2
=
t κ
−κ ∗ t ∗
E i1
E i2
(2.1)
The complex mode amplitudes E are normalized, so that their squared magnitude
corresponds to the modal power. The coupler parameters t and κ depend on the
2.1 Single Ring Resonators
5
specific coupling mechanism used. The * denotes the conjugated complex value of
t and κ respectively.
The matrix is symmetric because the networks under consideration are reciprocal.
Therefore:
2 2
κ + t = 1
(2.2)
In order to further simplify the model, E i1 is chosen to be equal to 1. Then the
round trip in the ring is given by:
E i2 = α · e jθ E t2
(2.3)
where α is the loss coefficient of the ring (zero loss: α = 1) and θ = ωL/c, L being
the circumference of the ring which is given by L = 2π r, r being the radius of
the ring measured from the center of the ring to the center of the waveguide, c the
phase velocity of the ring mode (c = c0 /neff ) and the fixed angular frequency ω =
kc0 , c0 refers to the vacuum speed of light. The vacuum wavenumber k is related to
the wavelength λ through: k = 2π /λ. Using the vacuum wavenumber, the effective
refractive index neff can be introduced easily into the ring coupling relations by:
β = k · n eff =
2π · n eff
λ
(2.4)
where β is the propagation constant. This leads to:
θ=
kc0 L
r
2π · n eff · 2πr
ωL
=
= k · n eff · 2πr =
= 4π 2 n eff
c
c
λ
λ
(2.5)
From (2.1) and (2.3) we obtain:
E t1 =
−α + t · e− jθ
−αt ∗ + e− jθ
(2.6)
E i2 =
−ακ ∗
−αt ∗ + e− jθ
(2.7)
−κ ∗
1 − αt ∗ e jθ
(2.8)
E t2 =
This leads to the transmission power Pt1 in the output waveguide, which is:
Pt1 = |E t1 |2 =
α 2 + |t|2 − 2α|t| cos(θ + ϕt )
1 + α 2 |t|2 − 2α|t| cos(θ + ϕt )
(2.9)
where t = |t| exp( jϕt ), |t| representing the coupling losses and ϕ t the phase of the
coupler.
6
2 Ring Resonators: Theory and Modeling
The circulating power Pi2 in the ring is given by:
Pi2 = |E i2 | =
α 2 1 − |t|2
2
1 + α 2 |t|2 − 2α|t| cos(θ + ϕt )
(2.10)
On resonance, (θ + ϕ t ) = 2π m, where m is an integer, the following is obtained:
Pt1 = |E t1 |2 =
(α − |t|)2
(1 − α|t|)2
(2.11)
and
Pi2 = |E i2 | =
2
α 2 1 − |t|2
(1 − α|t|)2
(2.12)
A special case happens when α = |t| in (2.11), when the internal losses are equal
to the coupling losses. The transmitted power becomes 0. This is known in literature
as critical coupling, which is due to destructive interference.
In using the above equations, it is possible to get a good idea of the behavior of a
simplified basic ring resonator filter configuration consisting of only one waveguide
and one ring. The wavelength dependent filter characteristic for a ring resonator
configuration with a radius of r = 148 µm with matched coupling and loss coefficient,
derived using (2.1)–(2.11), is shown in Fig. 2.3.
This model can be extended to suit the requirement of various types of ring
resonator configurations.
The next configuration which is discussed is the basic ring resonator add-drop
configuration, consisting of one input, one output waveguide and the ring resonator.
The four ports of the ring resonator are referred to in the following as input port,
throughput port, drop port and add port (Fig. 2.4).
Fig. 2.3 Notch type ring
resonator filter characteristic
2.1 Single Ring Resonators
7
Fig. 2.4 Model of a basic add-drop single ring resonator filter
The ring resonator simulation model has been updated according to Fig. 2.4. For
simplification E i1 is as defined before equal to 1. The throughput mode amplitude in
the first waveguide is given by:
E t1 = t1 +
2
e jθ
−κ1 κ1∗ t2∗ α1/2
2
1 − t1∗ t2∗ α1/2
e jθ
|t1 |2 +|κ1 |2 =1
=
2
t1 − t2∗ α1/2
e jθ
2
1 − t1∗ t2∗ α1/2
e jθ
=
t1 − t2∗ αe jθ
1 − t1∗ t2∗ αe jθ
(2.13)
In this calculation, α 1/2 and θ 1/2 are used which are the half round trip loss and
2
and θ = 2θ 1/2 .
phase respectively. It is α = α1/2
Now, the mode amplitude in the ring has to pass the second coupler as can be seen
from the schematic to become the new dropped mode amplitude E t2 . The dropped
mode amplitude in the second waveguide is then given by:
E t2 =
−κ1∗ κ2 α1/2 e jθ1/2
1 − t1∗ t2∗ αe jθ
At resonance, the output power from the drop port is given by:
Pt2-Resonance =
(2.14)
8
2 Ring Resonators: Theory and Modeling
|E t2-Resonance | =
2
1 − |t1 |2 · 1 − |t2 |2 · α
(1 − α|t1 t2 |)2
(2.15)
The throughput port mode amplitude E t1 (2.13) will be zero at resonance for
identical symmetrical couplers t 1 = t 2 if α = 1, which indicates that the wavelength on
resonance is fully extracted by the resonator. The value of α = 1 can only be achieved
by the implementation of gain incorporated in the ring resonator to compensate the
waveguide losses. The value of the loss coefficient α is fixed in a purely passive ring
resonator. A possibility of achieving minimum intensity (Pt1 = 0) at resonance of the
output transmission Pt1 at the throughput port is to adjust the coupling parameters
t 1 , t 2 to the loss coefficient α. From (2.13) we obtain:
t1 (2.16)
α = t2
If the ring resonator is lossless (α = 1), then the couplers have to be symmetric
in order to achieve minimum intensity. The transmission of a lossless ring resonator
add drop filter with radius of r = 148 µm is shown in Fig. 2.5.
There are different kinds of requirements on the simulation of various kinds of
ring resonator configurations. Starting of with the given equations satisfies most basic
models. The ring model can for example be divided into more segments to account
for different materials or modified waveguide paths. Examples of calculated models
can be found in Rabus (2002) and Michelotti et al. (2004).
Ring Resonator Parameters
Ring resonator filters can be described by certain figures of merit which are also
generally used to describe optical filters. One important figure is the distance between
Fig. 2.5 Add drop ring resonator filter characteristic
2.1 Single Ring Resonators
9
resonance peaks, which is called the free spectral range (FSR). A simple approximation can be obtained for the FSR by using the propagation constant from (2.4),
neglecting the wavelength dependency of the effective refractive index.
β
∂n eff
β
∂β
=− +k
≈−
∂λ
λ
∂λ
λ
(2.17)
This leads to the FSR λ, which is the difference between the vacuum wavelengths
corresponding to two resonant conditions.
FSR =
2π
λ=−
L
∂β
∂λ
−1
≈
λ2
n eff L
(2.18)
Note that (2.18) is for the resonant condition next to a resonance found for the
used propagation constant.
If the wavelength dependence of the effective index can not be neglected, it can
be incorporated in the following way to obtain a modified version of (2.17).
∂β
k
= − ng
∂λ
λ
(2.19)
where ng is the group refractive index, which is defined as:
n g = n eff − λ
∂n eff
∂λ
(2.20)
The group refractive index can be used instead of the effective index whenever
appropriate avoiding the approximation and obtaining more accurate values.
The modified FSR λ is then given by:
FSR =
λ=
λ2
ng L
(2.21)
The next parameter of importance is the resonance width which is defined as
the full-width at half-maximum (FWHM) or 3 dB bandwidth 2δλ of the resonance
lineshape. Using the expressions for the drop port (2.14, 2.15):
∗
2
2
−κ1 κ2 α1/2 e jθ1/2 2
= 1 |κ1 | |κ2 | α
1 − t ∗ t ∗ αe jθ 2 (1 − α|t1 t2 |)2
1 2
(2.22)
Assuming that the coupling coefficients are real, lossless and without a phase
term, (2.22) can be written as:
2
κ1 κ2 α1/2
2
1 κ1 κ2 α1/2
=
2 (1 − t1 t2 α)2
1 − 2t1 t2 α cos(θ ) + (t1 t2 α)2
(2.23)
10
2 Ring Resonators: Theory and Modeling
Then:
2(1 − t1 t2 α)2 = 1 − 2t1 t2 α cos(θ ) + (t1 t2 α)2
(2.24)
For small θ, using the real part of the series expansion of the Euler formula:
θ2
2
(2.25)
(1 − t1 t2 α)2
t1 t2 α
(2.26)
cos(θ ) = 1 −
Therefore:
θ2 =
This equation can further be simplified if the loss in the ring is negligible and the
coupling is symmetric (t = t 1 = t 2 ) to:
θ=
2
1 − t2
1 − t2
=
t2
t
(2.27)
Using (2.5) and (2.17) to translate into the wavelength domain:
2δλ =
λ2 1 − t 2
π Ln eff t
(2.28)
The expression which is commonly used can be obtained by assuming weak
coupling and λ δλ:
FWHM = 2δλ =
κ 2 λ2
π Ln eff
(2.29)
Another parameter which can now be directly calculated from the parameters in
the previous chapter is the finesse F of the ring resonator filter. It is defined as the
ratio of the FSR and the width of a resonance for a specific wavelength (FWHM):
F=
λ
t κ1 π
FSR
=
=π
≈ 2
FWHM
2δλ
1 − t2
κ
(2.30)
A parameter which is closely related to the finesse is the quality factor Q of a
resonator, which is a measure of the sharpness of the resonance. It is defined as the
ratio of the operation wavelength and the resonance width:
Q=
n eff L t
n eff L
λ
=π
F
=
2δλ
λ 1 − t2
λ
(2.31)
2.1 Single Ring Resonators
11
The quality factor can also be regarded as the stored energy divided by the power
lost per optical cycle.
The intensity in the ring resonator can be much higher than that in the bus waveguides, as the traveling wave in the ring resonator interferes constructively at resonance
with the input wave and thus the amplitude builds up. In addition to this intensity
increase, the field also experiences a phase-shift of an integral multiple of 2π in
one round trip. The intensity enhancement or buildup factor B is given by (for a
configuration shown in Fig. 2.2):
2
E i2 2 −ακ ∗
=
B=
∗
−
jθ
E i1
−αt + e (2.32)
For a configuration like Fig. 2.4, the buildup factor is given by:
2 2
−κ1∗
=
1 − t ∗ t ∗ αe jθ i1
1 2
Er
B = E
(2.33)
On resonance, the intensity enhancement factor is:
−κ1∗ 2
B = 1 − t1∗ t2∗ α (2.34)
For a lossless resonator and setting κ 1 = κ 2 = κ which is 1, B can be written
as:
B=
1 (2.30) F
−−−→
κ2
π
(2.35)
This equation directly relates the intensity enhancement factor B to the finesse F.
For the all-pass configuration and on resonance, the buildup factor is given by (t 1
= t 2 = t):
B=
1+t
1−t
(2.36)
Ring resonators can be used for nonlinear optical devices since the intensity in
the resonator can be much higher than in the bus waveguide. Examples of devices
utilizing nonlinearities in ring resonators are given in Sects. 5.7 and 5.8.
Loss in Ring Resonator
In the previous sections, losses are basically included by insertion of the parameter α
in the formulas. They can originate either from light scattering, material absorption
or bending losses. The first two causes are well known in light propagation in straight
waveguides and, consequently will not further discussed in this chapter (the reader is
referred to Hunsperger 2002 for details). In curved waveguides, instead, the effective
12
2 Ring Resonators: Theory and Modeling
index decreases as light propagates radially away from the ring-center, due to the
increase in the phase velocity. As a consequence, light radiates at a certain (caustic)
point, corresponding to the condition of matching between the waveguide effective
index and ring cladding’ refractive index respectively. When the refractive index
contrast n = nc − ns between the ring (nc ) and the surrounding (ns ) is high, the
caustic point is moved far away from the ring core leading to radiation losses. Being
connected to the curvature of the waveguide, they are referred to bending losses
α bend . In case of planar/channel waveguides they scale with the curvature radius r
with a complex expression that can be approximated by semi-empirical relations:
αbend |planar
αbend |channel
Prad
= − ln
Pinc
∼ α0 e
− 23 · 2π
λ r
√
3
2
n c −n 2s
n c2
− 1 · 2π ·r n s 3
4π
∼ 0.72 (n c − n s )10 7.6 λ
λ
n 2c −n 2s
n 2s
(2.37)
where Prad is the radiated power due to the bend, Pinc in the incident power, α 0
is a constant depending on the waveguide thickness. It clearly emerges that low
losses can be achieved by higher refractive index contrast n and larger curvature
radius. In Fig. 2.6 an typical example of the dependence of r respect the nc value is
reported at the wavelength λ = 1.55 µm, assuming the ring embedded in a material
with refractive index ns = 1.55 and a reference radius r 0 = 12 µm. A microring
with radius 12 µm requires a material with refractive index ∼2 for bending losses
<2 dB/cm. If higher losses can be accepted, nc must be higher than 1.9 and hence
n ≈ 0.35 in order to have an acceptable performance.
The Time Dependent Relations
Before going on to extend the previous model incorporating additional ring
resonators, the time dependent relations are adapted from Little et al. (1997) for
the basic ring resonator add-drop configuration. Like in the previous model, it is
assumed that the ring supports a traveling wave of amplitude E(t), P(t) represents
Fig. 2.6 Refractive index of
the microring material
against the ring radius,
yielding bending losses of 2
and 100 dB/cm, respectively
for λ = 1.55 µm and ns =
1.55. Courtesy of dr
Koechlin Manuel. https://doi.
org/10.3929/ethz-a-006
037351
2.1 Single Ring Resonators
13
the total power flowing through any cross section of the ring waveguide at time t.
The ring is regarded as an oscillator of energy amplitude e(t), normalized so that
p(t) represents the total energy stored in the ring. Energy and power in the ring are
related through:
p(t) = |e(t)|2 = P(t)
2πr
vg
(2.38)
vg is the group velocity. The ring resonator has a resonant frequency of ωR and
amplitude decay time-constant of 1/τ. The decay rate and the power exciting the
ring resonator are related to each other. The decay rate includes the power coupled
to the transmitted wave 1/τ tr , the power lost due to intrinsic effects 1/τ ie , and power
coupled to the output waveguide 1/τ t2 . This leads to:
1
1
1
1
=
+
+
τ
τtr
τie
τt2
(2.39)
The time rate of change in ring energy can then be written as:
d
e=
dt
jω R −
1
e − κ ∗ · E i1
τ
(2.40)
The relation between the coupling parameter κ and the decay rates of the transmitted wave 1/τ tr and the output waveguide 1/τ t2 , is determined by power conservation. The case is considered, when the ring resonator is excited to an energy of
|e0 |2 , no output waveguide is present and no input wave E i1 . The ring energy, with
no intrinsic loss, then decays as follow:
−2t
|e(t)| = |e0 | exp
τtr
2
2
(2.41)
From these set of (2.14)–(2.17), the power transfer characteristic for the drop port
can be calculated with the input wave E i1 being proportional to exp(jωt):
e=
−j
2
τtr
j(ω − ω R ) +
1
τ
E i1
(2.42)
From this equation, we can calculate the transmitted wave at the throughput port:
∗
E t1 = E i1 − κ e =
j(ω − ω R ) +
1
τ
+ jκ ∗
j(ω − ω R ) +
1
τ
2
τtr
E i1
(2.43)
Finally the drop port power transfer characteristic is obtained by using the equation
for power conservation (note, E i2 = 0):
14
2 Ring Resonators: Theory and Modeling
4
|E t2 |2 = |E i1 |2 − |E t1 |2 =
2 2
τt2 τtr
|e| =
|E i1 |2
τt2
(ω − ω R )2 + τ1
(2.44)
This equation can be simplified further if both waveguides couple equally to the
ring, then τ t2 = τ tr .
The Z-Transform
Another approach to simulate ring resonator filters is by using the Z-transformation
to describe the spectral and temporal response of ring resonator filters, described
in detail in Madsen and Zhao (1999). Z-transform relationships for basic optical
elements were first developed for fiber optic filters in Moslehi et al. (1984). This technique is used in pole-zero diagrams to design ring resonator filters in Kaalund and
Peng (2004). In the following chapter, the Z-transform for the basic add-drop configuration (consisting of one ring resonator and two waveguides) is given which shall
serve as a starting point for the calculation of more complex devices. Z-transforms are
discussed extensively in the aforementioned literature on digital signal processing,
therefore only a brief introduction is given here.
The Z-transform is an analytic extension of the discrete-time Fourier transform
(DTFT) which converts a discrete time signal into a complex-variable frequency
signal:
∞
H (z) =
h(n)z −n
(2.45)
n=−∞
Z is a complex variable and h(n) is the impulse response of a filter or the values
of a discrete signal. Each term z−n represents a delay. Of particular interest is when
the absolute value of |z| = 1. This is called the unit circle in the complex plane where
pole and zero locations of the function H(z), which is evaluated along z = exp(jω),
are plotted. In the case of ring resonator filters, |z| = 1 corresponds to resonant
frequencies. A complete roundtrip of the unit circle corresponds to the FSR of the
filter. Poles and zeros are related to the filter’s frequency spectrum by their position
on the complex plane. A zero positioned on the unit circle results in zero transmission
at the frequency corresponding to the angle of this zero. A pole on the other hand
on the unit circle causes unity transmission at the corresponding frequency. As poles
and zeros move away from the unit circle, their effect on the magnitude spectrum is
reduced.
A linear discrete system with input signals x has the following output signal:
y(n) = b0 x(n) + b1 x(n − 1) + · · · + b M x(n − M) − a1 y(n − 1)
− · · · − a N y(n − N )
The Z-transform for this type of filter is then given by:
(2.46)
2.1 Single Ring Resonators
15
H (z) =
1
M
−m
m=0 bm z
N
+ n=1
an z −n
=
B(z)
A(z)
(2.47)
A(z) and B(z) are Mth and Nth-order polynomials. The zeros zm and poles pn of
H(z) can be derived from the roots of the polynomials as follows:
H (z) =
z N −M
M
m=1
N
n=1
(z − z m )
(z − pn )
=
B(z)
A(z)
(2.48)
where is the gain of the filter. In passive filters, the transfer function can never be
greater than 1, so has a maximum value determined by max{|H(z)|z=exp(jω) } = 1
for these types of filters.
A ring resonator has a response which can be expressed in the form:
∞
H (z) =
n=0
a n z −n =
1
1 − az −1
(2.49)
The basic configuration of an add-drop ring resonator filter (Fig. 2.4) is the
simplest filter with a single pole response.
The sum of all optical paths for the drop port is given by:
E t2 (z) = −κ1 κ2 αz −1 1 + t1 t2 αz −1 + · · · E i1 (z)
(2.50)
Using the Taylor series expansion, the equation can be simplified to give the drop
port transfer function:
√
−κ1 κ2 αz −1
E t2 (z)
=
H21 (z) =
E i1 (z)
1 − t1 t2 αz −1
(2.51)
There is a single pole at t 1 t 2 α. As the matrix is symmetric, the transfer function
H 21 (z) is equal to H 12 (z).
The sum of all optical paths for the throughput port resulting in its transfer function
H 11 (z) is given by:
E t1 (z) = t1 − κ12 t2 αz −1 1 + t1 t2 αz −1 + · · · E i1 (z)
κ12 t2 αz −1
E i1 (z)
= t1 −
1 − t1 t2 αz −1
t1 − t2 αz −1
E i1 (z)
=
1 − t1 t2 αz −1
t1 − t2 αz −1
E t1 (z)
⇒ H11 (z) =
=
E i1 (z)
1 − t1 t2 αz −1
(2.52)
16
2 Ring Resonators: Theory and Modeling
Similarly, the transfer function H 22 (z) can be derived to be:
t2 − t1 αz −1
E t2 (z)
=
E i2 (z)
1 − t1 t2 αz −1
H22 (z) =
(2.53)
The obtained results for each transfer function can be expressed in two different
matrix forms. The first form relates the input ports to the output ports and is called
the scattering matrix (see also 2.1) which is given by:
E t1 (z)
E t2 (z)
E i1 (z)
= SRR (z)
E i2 (z)
√
−1
SRR (z) =
t1 −t2 αz
−κ1 κ2 αz −1
−1
1−t1 t√
1−t1 t2 αz −1
2 αz
−κ1 κ2 αz −1 t2 −t1 αz −1
1−t1 t2 αz −1
1−t1 t2 αz −1
(2.54)
The second form relates the quantities in one plane to the ones in another plane
as can be seen in Fig. 2.6. This type of matrix is called the transfer matrix which is
given by:
E i1 (z)
E t1 (z)
= RR (z)
RR (z) =
1
√
E i2 (z)
E t2 (z)
−κ1 κ2 αz −1
1 − t1 t2 αz −1 −t2 + t1 αz −1
t1 − t2 αz −1 1 + κ1 κ2 αz −1
(2.55)
The scattering matrix form is used to express the implication of power conservation and reciprocity. The transfer matrix form is used for describing multi-stage
filters. It is therefore also referred to as the chain matrix. This type of transfer matrix
is suitable to describe multiple serially coupled ring resonators. The transfer matrix
to be used for describing multiple parallel coupled resonators has the form Grover
et al. (2002):
E t1 (z)
= RR (z)
E i2 (z)
√
−1
1
κ1 κ2 αz −1
1 − t1 t√
2 αz
RR (z) =
t1 − t2 αz −1 −κ1 κ2 αz −1 t1 t2 − αz −1
E i1 (z)
E t2 (z)
(2.56)
Using the different simulation techniques described in this chapter it is possible to
build a simulation model for all relevant lateral and vertically coupled ring resonator
filter configurations.
Incorporating Loss in Ring Resonator Filters
In the previous section, losses were briefly discussed to explain the nature of the α
parameter included in the formulas. In particular, loss in ring resonator filters scales
the spectral curves without changing them significantly if the loss is not too large.
2.1 Single Ring Resonators
17
Different types of losses have been considered and described in literature to account
for various fabrication methods and tolerances. A few examples will be given in the
following paragraph to give a starting point for the calculation and simulation of
losses in ring resonators.
A loss which is most obvious is the radiation loss which occurs in the curved
section of ring resonators (Chin and Ho 1998). The radiation loss will become large
for a large surface roughness. The surface roughness on the other hand can induce
contradirectional coupling which can degrade the performance of a ring resonator
filter and even can cause a splitting of the resonant peak (Little et al. 1997). The
calculation of the radiation and scattering losses in ring resonators is presented in
detail in Rabiei (2005). Here a perturbative method for the calculation of losses due
to an arbitrary variation in the refractive index of the core or due to an arbitrary
variation in the shape of ring resonator is described.
Loss in ring resonator devices can also be used advantageously as was demonstrated using (2.16). An analysis of how loss and gain can be used to tune, trim, or
compensate the wavelength response of ring resonator filters is described in Little
and Chu (2000).
In the following chapter the basic model of a ring resonator is extended to analyze
a racetrack shaped ring resonator.
2.1.2 Racetrack Shaped Resonators
The equations in the previous chapter described the general behavior of a basic ring
resonator filter. However, to simulate certain ring resonator configurations, this set
of equations has to be extended. In a waveguide-coupled ring resonator filter, the
coupling gap size is determined by the amount of coupling required and the coupling
length available. Using lateral coupling, a larger gap is desirable as it increases the
fabrication tolerance. In this case, for a given coupling coefficient, the gap size can
be enlarged if the coupling distance is increased to obtain a racetrack shaped ring
resonator (Fig. 2.7).
The coupling distance can be increased by using a lateral or vertical geometry
(Chin and Ho 1998). In the case of the racetrack shaped ring resonator, the coupling
distance is approximately the length of the straight sections (if no coupling occurs
before the actual coupler region starts), which are tangential to the circular arcs at
output and input ports. At the transitions between the curved and the straight sections,
the mode will change adiabatically between the radial mode in a curved waveguide
and the normal mode in a straight waveguide. As the straight sections are lengthened
the radius of the curved sections must be reduced if the total cavity length is to remain
constant. This can not be always achieved in practical applications.
In the case of racetrack resonators, it is important to consider the variation of phase
difference ϕ which occurs in the coupling region in both couplers between t and κ.
The phase difference is length-dependent and affects the output characteristics, not
18
2 Ring Resonators: Theory and Modeling
Fig. 2.7 Z-transform layout
of an add-drop ring resonator
filter
only in the magnitude but also in the resonant conditions. This phase difference can
be implemented in (2.13) and (2.14) using the method described in Lee et al. (2004).
For the throughput port:
E t1 =
2
e jθ t1 t1∗ e j2ϕt1 − κ1 κ1∗ e− j2ϕκ2 e jϕt2
t1 e jϕt1 − t2∗ α1/2
2
1 − t1∗ t2∗ α1/2
e jθ e jϕt1 e jϕt2
(2.57)
For the drop port:
E t2 =
−κ1∗ κ2 α1/2 e jθ1/2 e− jϕκ1 e− jϕκ2
1 − t1∗ t2∗ αe jθ e jϕt1 e jϕt2
(2.58)
The resonant condition (θ + ϕ t1 + ϕ t2 ) = 2π m has changed slightly compared to
(2.9). The output transmission at resonance is no longer independent of t and κ which
can be seen comparing the relevant terms in (2.50) and (2.51). This leads to a significant performance change and confirms the importance of taking into account the
phase difference when analyzing racetrack shaped ring resonator configurations. The
phase difference is not only of importance in directional couplers, but also in multimode interference (MMI) couplers. An analysis of a racetrack shaped ring resonator
add-drop filter having two MMI couplers is given in Caruso and Montrosset (2003).
The MMI length should be selected in order to satisfy the π /2 relation between the
phases of the transmission and the coupling terms to obtain a symmetric transmission characteristic of the throughput and of the drop port. If the π /2 relation is not
satisfied, a strong asymmetry in the transmission characteristic will be obtained.
A further description of the implementation of directional and MMI couplers in
ring resonators is given in Sect. 4.1.
2.2 Double Ring Resonators
19
2.2 Double Ring Resonators
Double ring resonators offer the possibility of realizing a “box like” filter characteristic which is favorably used in optical networks. This is not the only advantage, but
also from the point of characterization, two rings if coupled in series have the drop port
in the same direction as the input port, which is also convenient for interconnection
of many 2 × 2 devices. Serially and parallel coupled ring resonator configurations
have been described in detail in Chu et al. (1999), Little et al. (1997, 2000), Melloni
(2001), and Emelett and Soref (2005).
In the serially coupled configuration, each ring resonator is coupled to one another,
and a signal that is to be dropped from the input port to the drop port must pass
sequentially through each resonator. Because of this sequential power transfer, all
resonators must be precisely resonant at a common wavelength. The resulting resonant line shape in the series configuration is determined physically by the separations
between the ring resonators. In the parallel-coupled configuration, all resonators are
coupled to both the input and drop port waveguides, but usually not directly to one
another (the resonators can also be coupled to one another resulting in a wavelength
selective reflector as is described in Sects. 2.2.2 and 2.3.1). The resonators are instead
indirectly coupled to each other by the optical path lengths along the input and output
waveguides that interconnect them. These lengths determine the details of the resonant line shapes. An optical signal in the parallel configuration passes through all
ring resonators simultaneously. This softens the requirement that the resonances of
each ring have to be precisely identical. Nonaligned resonant frequencies instead
lead to multiple peaks, or ripple in the lineshape.
The ready to use transfer functions of serially and parallel coupled double ring
resonators will be described in the following sections.
2.2.1 Serially Coupled Double Ring Resonator
The schematic of a serially coupled double ring resonator is depicted in Fig. 2.8.
From this model and using the same procedure as in Sect. 2.1.1 the fields depicted
in Fig. 2.8 can be calculated as follows:
θ1
E 1a = −κ1∗ E i1 + t1∗ α1 e j 2 E 1b
θ1
θ1
E 1b = t2∗ α1 e j 2 E 1a − κ2∗ α2 e j 2 E 2b
θ2
θ2
E 2a = κ2 α1 e j 2 E 1a + t2 α2 e j 2 E 2b
θ2
E 2b = −κ3∗ E i2 + t3∗ α2 e j 2 E 2a
(2.59)
(2.60)
(2.61)
(2.62)
20
2 Ring Resonators: Theory and Modeling
Fig. 2.8 A racetrack shaped
ring resonator filter with
integrated platinum resistors
on top of the curved sections
and the coupler (contact pads
visible)
θ1
E t1 = t1 E i1 + κ1 α1 e j 2 E 1b
θ2
E t2 = t3 E i2 + κ3 α2 e j 2 E 2a
(2.63)
(2.64)
where α1,2 = α R11/2 ,R21/2 represent the half round trip loss coefficients of ring
resonator one and two respectively. From (2.58) to (2.63) the general expressions for
the transfer functions for the throughput and the drop port can be derived. A simplified
form can be obtained by assuming a coupler without losses and symmetric coupling
behavior, setting t = t* and κ = −κ* (note that the phase factor −j has not been
introduced into the assumption and can be added if required) which gives the ready
to use amplitude forms for the throughput port (E i2 = 0):
−t1 κ12 α1 e jθ1 t3 α2 e jθ2 − t2
E t1
=
E i1
1 − t3 t2 α2 e jθ2 − t2 t1 α1 e jθ1 + t3 t1 α1 α2 e jθ1 e jθ2
(2.65)
and for the drop port:
θ1
θ2
E t2
κ3 κ2 κ1 α1 α2 e j 2 e j 2
=
jθ
E i1
1 − t3 t2 α2 e 2 − t2 t1 α1 e jθ1 + t3 t1 α1 α2 e jθ1 e jθ2
(2.66)
For realizing a double ring resonator with maximally flat response, first the
input/output waveguide ring coupling coefficient κ 1 (κ 3 ) has to be determined. To
simplify the model further, it is defined that the input/output waveguide-ring coupling
coefficients κ 1 = κ 3 . The calculation of the coupling coefficients to obtain the appropriate coupling values between the two ring resonators in order to achieve maximally
flat response can be made according to Emelett and Soref (2005) and Little et al.
(1997) by using the geometry and index profile shown in Fig. 2.9, where two coupled
waveguides of width 2wp and 2wq with indexes of np and nq , surrounded by a cladding
2.2 Double Ring Resonators
21
Fig. 2.9 Two ring
resonators coupled in series
of n0 , at the plane of smallest separation 2s0 , defined as the center to center gap are
shown.
The approximate coupling coefficient is then given by:
π R [αq (wq −2s0 )]
ωε0 cos k x p,q wq 2
2
n p − n0
e
κ=
αq
2 Pp Pq k x2p + αq2
× αq cos k x p w p sinh αq w p + k x p sin k x p w p cosh αq w p
(2.67)
Using:
Pp,q
β p,q
1
w p,q +
=
2ωμ0
α p,q
k x p,q =
α p,q =
(2.68)
n 2p,q k 2 − β 2p,q
(2.69)
β 2p,q − n 20 k 2
(2.70)
where Pp,q is the mode power, k x p,q is the transverse propagation constant of the core,
and α p,q is the decay constant in the cladding, β p,q is the propagation constant, ω
is the circular frequency, ε0 is the permittivity of free space, all within waveguide
22
2 Ring Resonators: Theory and Modeling
p or q. The refractive index n0 of the surrounding media is set equal to 1 (air). The
coefficient R is defined as the effective radius of curvature of the ring and is given
by:
R=
r1 r2
r1 + r2
(2.71)
where r 1,2 represents the radius of ring one and two respectively. The radii of the
rings are chosen to satisfy the 2π phase shift condition with the completion of one
round trip in the ring resonator which is given by:
mλm = 2πr1,2 n eff
(2.72)
In order to realize a flat passband, the analysis of the power loss ratio, which is
the ratio of total input power to power present at the detected port, is required. The
power loss ratio in polynomial form is given by:
PLR
where
by:
2
4
2 μ1
μ41
4
2
2
2
=1+ 1
− 2μ2
ω +
(2.73)
ω + μ2 −
2
4
μ41 μ42
t2
Ei
= E
ω is the frequency deviation which is related to the resonant frequency ωm
ω = ω − ωm
(2.74)
The coefficient μ is the fractional power coupled. It is given by:
μ21 =
κ12 vg1
κ 2 vg1 vg2
and μ22 = 2 2
2πr1
4π r1r2
(2.75)
The goal of realizing a maximally flat response is obtained when the power loss
ratio is zero at the defined resonance. This is the case for:
μ22 = 0.250μ41
(2.76)
Assuming identical rings, this leads to the coupling coefficient:
κ22 = 0.250κ14
(2.77)
Using these equations, it is possible to design a double ring resonator filter with
maximally flat response for the drop port.
A serially coupled double ring resonator opens up the possibility of expanding the
FSR to the least common multiple of the FSR of individual ring resonators. This is
done by choosing different radii in the double ring resonator. In the case of different
radii, the light passing through the double ring resonator is launched from the drop
2.2 Double Ring Resonators
23
port when the resonant conditions of both single ring resonators are satisfied. The
FSR of the double ring resonator with two different radii is expressed by:
FSR = N · FSR1 = M · FSR2
(2.78)
which leads to:
FSR = |M − N |
FSR1 · FSR2
|FSR1 − FSR2 |
(2.79)
where N and M are natural and coprime numbers.
The use of two ring resonators with different radii opens the possibility to realize a
larger FSR than would be achieved using only a single ring resonator. The transmission characteristic of the throughput port has mainly a Lorentzian shape. A box-like
filter response using two different radii can only be realized by using two parallel
coupled double ring resonators (R1 = R2 ). The use of such configurations as optical
filters is limited by unwanted additional resonant peaks. Investigations on these types
of filters have been performed in Suzuki et al. (1995) and Sorel et al. (1999). Different
types of waveguide coupled ring resonator configurations to expand the free spectral
range have been analyzed in Hidayat et al. (2003).
2.2.2 Parallel Coupled Double Ring Resonator
The schematic of a parallel coupled double ring resonator is shown in Fig. 2.10.
From this model, the fields in Fig. 2.10 can be calculated as follows:
θ1
E 1a = −κ1∗ E i1 + t1∗ α1 e j 2 E 1b
(2.80)
θ1
θ2
E 1b = t2∗ α1 e j 2 E 1a − κ2∗ e jθW κ4 α2 e j 2 E 2a − t4 E i2
(2.81)
θ1
θ2
E 2a = −κ3∗ e jθW t1 E i1 + κ1 α1 e j 2 E 1b + t3∗ α2 e j 2 E 2b
(2.82)
θ2
E 2b = −κ4∗ E i2 + t4∗ α2 e j 2 E 2a
Fig. 2.10 Index profile and
geometry of coupled
waveguides
(2.83)
24
2 Ring Resonators: Theory and Modeling
θ1
θ2
E t1 = t3 e jθW t1 E i1 + κ1 α1 e j 2 E 1b + κ3 α2 e j 2 E 2b
(2.84)
θ2
θ1
E t2 = t2 e jθW t4 E i2 + κ4 α2 e j 2 E 2a + κ2 α1 e j 2 E 1a
(2.85)
θW = k W · n Weff · (2.86)
where θ W is the phase shift introduced by the segment of length with effective
refractive index n Weff of the input waveguide joining both ring resonators.
From (2.79) to (2.85) the general expressions for the transfer functions for the
throughput and the drop port can be derived. A simplified form can again be obtained
by assuming couplers and bus waveguides without losses and symmetric coupling
behavior, setting t = t* and κ = −κ* (note that the phase factor −j has not been introduced into the assumption and can be added if required) which gives the amplitude
forms for the throughput port (E i2 = 0):
θ
f (a + bc)
a + bc
E t1
jθW
jθW 21
h+
+ κ3 t4 α22 e jθ2
= t3 t1 e
+ t3 κ1 α1 e
E i1
1−d
1−d
(2.87)
And for the drop port:
θ
θ2 a + bc
f (a + bc)
E t2
j 21
2 jθ1
h+
+ t2 κ4 α2 e jθW 2
(2.88)
= κ1 κ2 α1 e + κ2 t1 α1 e
E i1
1−d
1−d
where:
a=
κ3 t1 e jθW
1 − t3 t4 α22 e jθ2
(2.89)
θ1
κ1 α1 e j 2
b=
1 − t3 t4 α22 e jθ2
(2.90)
θ1
c=
κ1 t2 α1 e j 2
1 − t1 t2 α12 e jθ1
f =
κ2 κ4 α2 e jθW 2
1 − t1 t2 α12 e jθ1
h=
κ1 t2 α1 e j 2
1 − t1 t2 α12 e jθ1
(2.93)
d =b· f
(2.94)
(2.91)
θ2
(2.92)
θ1
2.2 Double Ring Resonators
25
Similar to the serially coupled double ring resonator, it is possible to increase the
overall FSR of this configuration by adjusting the length of the waveguide joining
the two ring resonators.
The parallel configuration can be treated as a grating. Constructive interference of
the reflected waves from each ring resonator is obtained by choosing to be equal
to an odd multiple of a quarter wavelength.
= (2m + 1)
λ0
4n Weff
(2.95)
where λ0 is the center wavelength of the passband.
If the length is chosen such that the FSR of the ring resonators and the FSR of
the “grating” obey the following condition:
FSR = NRing · FSRRing = MGrating · FSRGrating
(2.96)
The Vernier effect (Griffel 2000) causes the transmission peaks of the ring
resonators within the overall obtained FSR to be suppressed, which results in a
larger FSR than would be achieved for a single ring resonator. The distance between
the resonators can be calculated in this case using:
=
Mgrating n eff
πr
NRing n Weff
(2.97)
These set of equations can of course be transferred to multiple coupled parallel
ring resonator configurations as will be shown in Sect. 2.3.
Parallel Coupled Double Ring Resonator with Coupling Between the Two Ring
Resonators
A special double ring resonator configuration is obtained, when coupling between the
two ring resonators is allowed (Fig. 2.11). The reflective properties of such a device
have been analyzed in Chremmos and Uzunoglu (2005) and the following transfer
functions are based on this reference. A similar wavelength reflective filter consisting
of four interacting ring resonators has been presented in Poon et al. (2004d) which
is going to be described in Sect. 2.3.1 (Fig. 2.12).
Using the fields and coupling coefficient in Fig. 2.11, it is possible to derive
the general expressions for describing the transfer characteristics of this type of
configuration.
A simplified expression for the reflectivity at port E i1 (denoted by the symbol ← as
the superscript) is obtained for the lossless case and symmetric coupling coefficients
between the ring resonator and the bus waveguide (κ = κ 1 = κ 3 ):
26
2 Ring Resonators: Theory and Modeling
Fig. 2.11 Parallel coupled double ring resonator
Fig. 2.12 Double ring resonator with inter ring coupling
2
2 2 t 1+t 2
2
cos θ − 2 ( 2t )
4 κ22tκ
← E i1 = 2 2 2 2
t 1+t 2
cos θ − 2 ( 2t ) + κ22tκ
(2.98)
The phase factor for the distance between the rings does not appear and therefore
does not have an influence on the transfer characteristic. This is a special property of
the double coupled configuration and does not apply for multiple serially coupled ring
resonators. Different reflectivity profiles can be realized using appropriate coupling
2.2 Double Ring Resonators
27
coefficients. Weakly coupled ring resonators lead to single reflection peaks in the
reflectivity function where the height of the peak depend on the value of the coupling
coefficients. In order to realize a maximally flat response with a single peak, the
coupling coefficients have to obey the following equation:
κ2
κ2 = √ √ 2 1 + t 2 + 2t
(2.99)
The corresponding FWHM is given by:
κ2
FWHM = 4 sin−1 κ
3
22 t
(2.100)
The expression for the reflectivity at port E i1 incorporating loss parameter α is
given by:
2 2 2
κ2 κ (α +1)
2
← 2αt
E i1 = 2 2
2
t2 (1+α 2 t 2 ) 2
κ2 (1−α 2 t 2 )
cos θ −
+
2αt
2αt
⎡
t 1+α 2 t 2
cos θ − 2 ( 2αt ) +
⎣
·
2
sin2 θ
+ 1−α
1+α 2
2 ⎤
2
2 2
t2 (1−α )(1−α t )
2
2αt
1+α
⎦
(2.101)
So far ready to use transfer functions for single and double ring resonator configuration have been presented. In the following chapter, different calculation methods
are presented to derive the transfer function of different types of multiple coupled
ring resonators.
2.3 Multiple Coupled Resonators
The use of multiple vertical or lateral coupled ring resonator configurations opens up
the possibility to realize custom designed transmission functions and thus is suitable
for a wide variety of device implementations (Schwelb and Frigyes 2001). Vertical
and lateral ring resonator architectures where the rings are either coupled in series
or in parallel have been implemented in the past. A detailed theoretical analysis of a
vertically stacked multiple coupled ring resonator, where the ring resonators are on
top of each other is presented in Sumetsky (2005). The use of multiple coupled ring
resonator configurations together with other photonic devices like grating couplers
or Mach Zehnder interferometers increases the functionality and transmission characteristic even further (Weiershausen and Zengerle 1996). One of the main targets
28
2 Ring Resonators: Theory and Modeling
of realizing optical filters is to tailor the passband shape. In analogy to electronic
filter design, Butterworth (Butterworth 1930) and Chebyshev type of optical filters
are preferred. Butterworth filters are maximally flat and do not have any ripples in
the passband. The shape of the transfer function does not change for higher order
filters except that the roll off becomes steeper as the order of the filter increases.
Chebyshev filters have a steeper roll off than Butterworth type of filters and have
ripples either in the passband or stopband which distinguishes Chebyshev type I and
type II filters. The square magnitude response of a Butterworth filter has the form
(Madsen and Zhao 1999):
|HN (x)|2 =
1+
1
2N
(2.102)
x
x0
where x 0 is the 3 dB cutoff frequency.
The response of Chebyshev type I and II filters have the form (Madsen and Zhao
1999):
Type I
1
1 + y 2 TN2 xxC
−1
x for |x| ≤ 1
cos N
cos −1
TN (x) =
cosh N cosh x for |x| > 1
|HN (x)|2 =
(2.103)
Type II
1
|HN (x)|2 =
1+
y2
TN2
TN2 (
xS
xP
xS
x
(2.104)
)
where T N (x) is the Nth-order Chebyshev polynomial, y determines the passband
ripples, x C is the center frequency of the filter, x P and x S define the changeover
region on the passband and stopband respectively.
2.3.1 Serially Coupled Ring Resonators
One of the first papers to present a calculation method for serially coupled ring
resonator synthesis is (Orta et al. 1995). The method is based on the Z-transformation
using the transfer matrix (see 2.54). The Z-transformation has also been used in
Madsen and Zhao (1996) to simulate and fabricate a serially coupled ring resonator
filter. The transfer matrix method has also been used in Melloni and Martinelli (2002)
and Poon et al. (2004b) for simulating and designing various serially coupled ring
2.3 Multiple Coupled Resonators
29
resonator configurations. Serially coupled ring resonators are also referred to as
coupled-resonator optical waveguides (CROW) (Poon et al. 2004c). A model for
deriving the transfer functions of serially coupled ring resonators based on the time
dependent calculation as described in Sect. 2.1.1 is presented in Little et al. (1998).
Another method of simulating the transfer function of serially coupled ring resonators
is by using a characteristic matrix approach presented in Chen et al. (2004). These
different methods for analyzing serially coupled ring resonators will be used in the
following to derive the transfer functions.
The Z-transformation is used to start with in the beginning. In order to describe a
serially coupled ring resonator, the filter can be broken down into two components, a
symmetrical directional coupler and a pair of uncoupled guides as shown in Fig. 2.13
(Orta et al. 1995).
Another way to describe the transfer function of a directional coupler is to use a
chain matrix, which is given by:
HkC
= je
Fig. 2.13 Photograph of a
serially coupled triple ring
resonator
jβlk
−e− jβlk cot(φk )
csc(φk )
− jβlk
e
cot(φk ) −e−2 jβlk csc(φk )
(2.105)
30
2 Ring Resonators: Theory and Modeling
where φ k is referred to as the coupling angle and lk is the length of the coupler (note:
this is not the coupling length). The chain matrix of the uncoupled guides is given
by:
HkR
=e
jβdk
1 0
0 e−2 jβdk
(2.106)
where d k is the length of the ring waveguides. The chain matrix for the entire system
is then expressed by:
csc(φk ) z −1 e− jψk cot(φk ) csc(φ0 ) cot(φ0 ) H=
cot(φk ) z −1 e− jψk csc(φk ) cot(φ0 ) csc(φ0 )
(2.107)
k=N ,1
where
ze jψk = −e jβ(lk +lk−1 +2dk )
(2.108)
As previously described in Sect. 2.1.1 the elements of the matrix H are N degree
polynomials. The chain matrix can also be compared to the chain matrix derived in
(2.54). Of interest is again the transfer function for the throughput and the drop port,
both related to the signal at the input port. The polynomials are given by:
E t1
= H11 (z) =
E i1
N
ak z −k
(2.109)
bk z −k
(2.110)
k=0
and
E t2
= H21 (z) =
E i1
N
k=0
The transfer functions of the filter are now based on the definition of these polynomials. Assuming, that the filter is lossless, the scattering matrix is unitary for |z|
= 1. On |z| = 1, z* = z−1 , then the relationship between (2.108) and (2.109) can be
written as follows:
1
1
∗
∗
(2.111)
H11 (z)H11 ∗ = 1 + H21 (z)H21 ∗
z
z
Using this equation, it is possible to calculate H 11 (z) for a given H 21 (z). The
coupling angles φ k (k = 0, …, N) and the phase shift ψ k (k = 1, …, N) are calculated
as follows. First, a superscript is introduced which denotes elements belonging to
the structure formed by the first n + 1 coupler. Then the elements of the chain matrix
[N −1]
[N −1]
[N ]
and H21
are related to H11
relative to the first (N − 1) ring resonators, H11
2.3 Multiple Coupled Resonators
31
[N ]
and H21
through:
csc(φ N ) z −1 e− jψ N cot(φ N )
cot(φ N ) z −1 e− jψ N csc(φ N )
[N −1]
H11
[N −1]
H21
=
[N ]
H11
[N ]
H21
(2.112)
This leads to the equations for the coefficients of the polynomials (2.108 and
2.109), which are given by:
ak[N −1] = ak[N ] csc(φ N ) − bk[N ] cot(φ N )
(2.113)
[N ]
[N ]
cot(φ N ) + bk+1
csc(φ N ) e jψ N
bk[N −1] = −ak+1
(2.114)
and
where k = 1, …, (N − 1) and:
−1]
[N −1]
a [N
= b−1
=0
N
(2.115)
Then the coupling angle of the Nth coupler is given by:
cos(φ N ) =
b0[N ]
a0[N ]
=
]
a [N
N
]
b[N
N
(2.116)
Equation 2.115 is satisfied if the ratio is real. Next step is to determine the phase
shift ψ k using (2.115) and (2.113). All other coefficients follow the same procedure.
In order to start this calculation method and derive a transfer filter characteristic,
[N ]
has to be determined. As stated before in Sect. 2.3, a bandpass
the polynomial H21
filter characteristic is preferred. When using the Z-transform, the resonant frequencies
of the ring resonator filter are all placed on the circumference |z| = 1. For a Butterworth
type filter, the “zeros” are located on z = −1. The zeros for a Chebyshev type of
filter are given by:
!
"
2 j arccos sin( FWHM
) cos (2k−1)π
4
2N
z 0k = e
k = 1, . . . , N
(2.117)
This is an intuitive approach to design ring resonator filters, however it is
challenging to extract the poles of the frequency response.
The time dependent relations which have been presented for a single ring resonator
can be extended to multiple serially coupled resonators. The response of the first ring
(counted from the bottom of the ring filter) can be written as (Little et al. 1998):
32
2 Ring Resonators: Theory and Modeling
e1 =
−κ ∗ E i1
j ω R1 +
2
−κ1∗
∗2
−κ N
−1
j ω R2 ...+ j
ω
RN
⎧
⎫
1
⎪
ω
−
ω
−
j
,
n = 1, N ⎪
Rn
⎨
⎬
τn
ωn = ω − ω Rn − j τ1n − j τ1tr , n = 1, N
⎪
⎩ω − ω − j 1 − j 2 , N = 1 ⎪
⎭
Rn
τn
τtr
(2.118)
where ω is the optical frequency of the input wave, ωRn is the resonant frequency
of ring resonator n and ωn is the complex frequency deviation. The energy decay
rate of each ring is given by τ n . The response of resonator N can be expressed by a
product of continued fractions:
e N = E i1
N
Tn
n=1
where
TN =
T1 =
∗
−κn−1
j ωn +
−κ ∗
j ω R1
2
∗
−κn−1
j ωn−1 +
∗2
−κn−2
2
−κ ∗
j ωn−2 ...+ j ω1
R1
(2.119)
The coefficients for maximally flat and Chebyshev filter characteristics are given
in Table 2.1 for two to six serially coupled ring resonators (Little et al. 1997).
Table 2.1 Coefficients for
maximally flat and
Chebyshev filter
characteristics
No.
Maximally flat
Chebyshev
2
κ1∗2 = 0.250κ ∗4
κ1∗2 = 0.250κ ∗2 (1 + 2y)
3
κ1∗2 = κ2∗2 = 0.125κ ∗4
κ1∗2 = κ2∗2 =
2
0.125κ ∗4 1 + 1.5y 3
4
κ1∗2 = κ3∗2 = 0.100κ ∗4
κ2∗2 = 0.040κ ∗4
5
κ1∗2 = κ4∗2 = 0.0955κ ∗4
κ2∗2 = κ3∗2 = 0.040κ ∗4
6
κ1∗2 = κ5∗2 = 0.0915κ ∗4
κ2∗2 = κ4∗2 = 0.0245κ ∗4
κ3∗2 = 0.0179κ ∗4
y determines the passband ripples of the Chebyshev filter
2.3 Multiple Coupled Resonators
33
Another method of calculating the transfer functions of serially coupled ring
resonator filters is by using a so called characteristic matrix approach, which has
been presented in Chen et al. (2004). The method is based on defining the optical
paths which an optical signal travels form the input port to the drop port. There are
several paths and the shortest path is called the common path or the zeroth-order path
which is defined to be unity. Looking at a serially coupled triple ring resonator, the
light using the first order paths for example has three choices, one additional ring
resonator path and the common path. The mth order transfer function is related to
the m + 1th order transfer function by:
⎤ ⎡
⎤ ⎡
⎤
T11 T12 T13
H1,m
H1,m+1
= ⎣ H2,m+1 ⎦ = ⎣ T21 T22 T23 ⎦ · ⎣ H2,m ⎦ = T · Hm
H3,m+1
T31 T32 T33
H3,m
⎡
Hm+1
(2.120)
t ij are the transfer functions of the additional path in ring resonator i, with previous
path ends in ring resonator j. T is called the characteristic matrix. Using the coefficients for the ring resonators as described previously for symmetric coupling (t = t*
and κ = −κ*), T is given by:
⎤
−κ 2
t1 t2 α1 e jθ1 1 t 2 2 0
2
⎥
⎢
−κ 2 ⎥
jθ
=⎢
⎣ t2 t3 α2 e 2 1 1 t32 3 ⎦
t3 t4 α3 e jθ3 1 1 1
⎡
TDropPort
(2.121)
The general expression for the characteristic matrix for a filter consisting of n ring
resonators is given by:
⎤
−κ 2
t1 t2 α1 e jθ1 1 t 2 2 0 . . . 0
2
⎥
⎢
⎢ t t α e jθ2 1 1 −κ32 0 . . . 0 ⎥
2
⎥
⎢ 23 2
t3
⎥
⎢
=⎢
⎥
.
.
.
1
.
.
.
1
.
.
.
0
⎢
⎥
⎥
⎢
−κn2
⎦
⎣ . . . 1 . . . . . . 1 tn2
tn tn+1 αn e jθn 1 . . . . . . 1 1
⎡
TDropPort
(2.122)
The general expression for the transfer function for the drop port is then given by:
HDropPort
j θk
,
,
k
k κk
k αk e
= UMatrix − TDropPort k = 1, . . . , n
where U Matrix is the unit matrix.
(2.123)
34
2 Ring Resonators: Theory and Modeling
Filter synthesis using (2.121) and (2.122) can be done by solving a matrix eigenvalues equation. The poles of a filter function correspond to unity minus the eigenvalues of T DropPort . The eigenvalues and power coupling ratios for a maximally flat
transfer function are given in Table 2.2 assuming lossless devices.
Using the aforementioned techniques, it is possible to find the transfer functions
for arbitrary serially coupled ring resonators. Each method has its pros and cons and
therefore it is left to the designer to choose the right method which seems convenient
to solve the problem. When designing ring resonator filters, it is appropriate to
evaluate the technological feasibility of certain parameters like coupling coefficients
and loss in order to easily transfer the design to fabrication.
A special serially coupled ring resonator design (Fig. 2.14) has been proposed
and analyzed in Poon et al. (2004a). The following calculation method is based on
this literature.
Depending on the number of rings used the filter can either be reflecting or nonreflecting. The filter acts as a reflector for an odd number of rings (N ≥ 3), whereas
a nonreflecting filter is obtained for an even number of rings (N ≥ 4). The transfer
functions are derived by using a transfer matrix method, starting in defining a vector
x n , which represents the field component in ring resonator n − 1:
Table 2.2 Eingevalues and power coupling ratios for a maximally flat transfer function
No.
Eigenvalues (= 1 − Poles)
Power coupling ratios
2
0.63 + 0.32i; 0.63 − 0.32i
0.5; 0.2; 0.5
3
0.73 + 0.42; 0.71; 0.73 − 0.42i
0.5; 0.14; 0.14; 0.5
4
0.78 + 0.45i; 0.77 + 0.17i;
0.77 − 0.17i; 0.78 − 0.45i
0.5; 0.13; 0.09; 0.13; 0.5
5
0.81 + 0.46i; 0.8 + 0.26i; 0.81; 0.8 −
0.26i; 0.81 − 0.46i
0.5; 0.13; 0.08; 0.08; 0.13; 0.5
10
0.86 + 0.48i; 0.85 + 0.42i; 0.86 + 0.33i;
0.88 + 0.21i; 0.9 + 0.07i; 0.9 − 0.07i;
0.88 − 0.21i; 0.86 − 0.33i; 0.85 − 0.42i;
0.86 − 0.48i
0.5; 0.12; 0.07; 0.07; 0.07; 0.07; 0.07; 0.07;
0.07; 0.12; 0.5
Chen et al. (2004)
Fig. 2.14 Components of a
serially coupled ring
resonator filter
2.3 Multiple Coupled Resonators
35
←
←
xn = E t E i Ei Et
T
(2.124)
n
The arrows used as superscripts are as described earlier for the double ring the
direction of the propagating field, clockwise or anticlockwise without mixing of
waves between the two directions. The coupling between the ring resonators can be
represented by the following 4 × 4 matrix (n ≥ 0):
⎤
0 0
0 0⎥
⎥
=⎣
−t 1 ⎦ · x n = M P · x n
0 0 κ κ
∗
0 0 − κ1 tκ
⎡
xn+1
−t
κ
⎢−1
⎢ κ
1
κ
t∗
κ
(2.125)
Assuming only the phase matched waves are being coupled (L Coupler λ).
The vector xn is related to x n by the following propagation matrix:
⎡
⎢
xn = ⎢
⎣
0
0
0
0
0
jβr (2π−θ )
e
0
e− jβr θ
π (N − 2)
θ = 2π −
N
0
e jβr (2π−θ )
0
0
⎤
e− jβr θ
0 ⎥
⎥ · xn = M Q · xn
0 ⎦
0
(2.126)
Combining (2.124) and (2.125):
xn+1 = M P · xn = M P · M Q · xn = MT · xn
(2.127)
For an N type ring resonator configuration with N > 2, 2.126) yields:
x N = MTN −1 · M P · x0 = M A · x0
(2.128)
Only the components of vector xin hold the transfer functions, therefore the
transfer functions of the ring resonator configuration are derived using the relation for the coupling to the external waveguide and the phase relations in the first
resonator:
xin = M Pin · xin
θ
Et0 = Etin e− jβr 2
←
←
←
←
θ
E i0 = E tin e jβr 2
Ei0 = Ei N e jβr (2π−θ ) E i0 = E i N e− jβr (2π−θ )
←
←
θ
θ
E t N = E iin e− jβr 2
Et N = Eiin e jβr 2
(2.129)
Using (2.127) and (2.128), x N and x0 can be expressed by elements of x in .
Equation 2.127 can then be rewritten as:
36
2 Ring Resonators: Theory and Modeling
m M Pin xin = MTN −1 M P wM Pin xin
⇒ xin = M B xin
(2.130)
←
where m and w represent matrices which express the terms E in , Ein and Ei0 , Ei0 ,
using components of vector x in respectively. The matrix M B can then be expressed
by:
m −1 MTN −1 M P wM Pin
M B = M P−1
in
(2.131)
If only one input is considered as in the previous ring resonator examples, xin can
be expressed by:
←
xin = 0 E 1 E
rin
i in
T
(2.132)
←
The reflection and transmission function Eiin and E rin can then be derived using
elements of matrix M B and solving the following matrix equation:
M B 4,2
1−M B 4,4
1
1
M B 2,4
− 1−M
B 2,2
Eiin
←
E rin
=
M B 4,3
1−M B 4,4
M B 2,3
1−M B 2,2
(2.133)
The following equations are also valid for the solutions:
←
M B 3,2 Eiin + M B 3,3 + M B 3,4 E tin = 1
←
M B 1,2 Eiin + M B 1,3 + M B 1,4 E tin = 0
(2.134)
In using the above equations, it is possible to calculate the reflectance and the
transmittance spectra of this type of serially interring coupled ring resonator.
2.3.2 Parallel Coupled Ring Resonators
Parallel coupled ring resonators have been addressed in literature and the transfer
functions have been derived by several methods. One of the advantages of parallel
coupled ring resonators over serially coupled ring resonators is that their transfer
functions are less sensitive to fabrication tolerances, as each ring resonator can
compensate errors in any of the others. Two configurations are discussed, one where
the ring resonators are coupled to two input/output waveguides and the other, where
all share one input/output waveguide.
2.3 Multiple Coupled Resonators
37
Coupled to Two Input/Output Waveguides
As can be seen from Fig. 2.15, parallel coupled ring resonators coupled to two
waveguides share the same input, throughput, drop and add port.
The synthesis of the transfer functions of parallel coupled ring resonators using a
recursive algorithm is presented in Little et al. (2000). A complex matrix formalism
employing racetrack ring resonator filters is derived in Griffel (2000). A technique
using simple closed-form formulas to determine the Q factor of each involved ring
resonator which leads to the coupling coefficients is demonstrated in Melloni (2001).
These different methods for analyzing the transfer functions will be used in the
following.
The model which has been presented in Fig. 2.10 can be easily extended for
multiple parallel coupled ring resonators. The distance between the uncoupled ring
resonators is chosen so that the transfer functions of each ring resonator add in
phase. The transfer function derived by the recursive algorithm used in Little et al.
(2000) is given by:
Tn =
E tin E tOn
Et
= Rn −
−1 j2θWn−1
Ei
Rn − Tn−1
e
Fig. 2.15 Ring resonator configuration with interring coupling
38
2 Ring Resonators: Theory and Modeling
μin μon
2
2
j ω + 21 μi,o
+ 21 μi,o
n
n
i,o 2
μn
= Rn −
2
2
j ω + 21 μi,o
+ 21 μi,o
n
n
Rn = −
E ti,o
n
(2.135)
where the indices i, o correspond to the through responses of each ring resonator n in
the waveguides joining the ring resonators and ω is the frequency deviation away
from resonance. The term μ is related to the coupling coefficient κ (2.74):
μi,o
n
=
κni,o
vgn
2πrn
(2.136)
The recursion is started with T 1 = R1 . Loss can also be incorporated into this
algorithm by substituting j ω with j ω + 1/τ.
In this type of synthesis, the transfer function is directly related to the coupling
coefficient to obtain any desired filter shape. In the methods described earlier, the
transfer functions are rational polynomials related to frequency, wavelength or z
where the coefficients of the polynomials are adjusted for any specific filter function.
In using the recursive algorithm, it is possible to suppress unwanted sidelobes by
apodization, which is realized by adjusting the coupling coefficients properly.
A straight forward method of designing parallel coupled ring resonator filters is
presented in Melloni (2001). The filter shape can be calculated by using the given
specifications for bandwith, FSR, out of band rejection and selectivity. The formulas
for a parallel N coupled ring resonator filter are as follows:
FSR
gn FWHM
√
2n − 1
π
gn = 2 sin
2N
Qn =
(2.137)
The coupling coefficients are given by:
π2
κn =
2Q 2n
4Q 2n
1+ 2 −1
π
(2.138)
A specific filter characteristic can be derived by using this method and the relations
described in Sect. 2.1.1.
For deriving the transfer functions for parallel coupled racetrack shaped ring
resonators, the matrix formalism described in Griffel (2000) is used. The parallel
coupled filter can be broken down into two components, similar to the method shown
for the serially coupled ring resonator filter, into a ring resonator coupled to two
waveguides and into a pair of uncoupled guides as shown in Fig. 2.16 (Fig. 2.17).
2.3 Multiple Coupled Resonators
39
Fig. 2.16 Photograph of a
parallel coupled triple ring
resonator
Fig. 2.17 Schematic of a parallel coupled ring resonator filter
The transfer matrix for the ring resonator coupled to two waveguides is given by:
⎛
⎛← ⎞
a1n a2n −bn2
0
Ei
a2n
⎜
⎜ ⎟
1
⎜
0
E
⎜ i⎟
a1n
⎜← ⎟ =⎜
⎜
⎝ Et ⎠
0
− ab1nn
⎝
b
n
0
Et n
a2n
0
bn
a1n
a1n a2n −bn2
a1n
0
⎞ ⎛ ⎞
←
− ab2nn
⎟ ⎜ Ei ⎟
0 ⎟
Ei ⎟
⎟·⎜
← ⎟
⎟ ⎜
0 ⎠ ⎝ Et ⎠
1
Et
a
2n
(2.139)
n+1
The transfer matrix for the pair of uncoupled waveguides is given by:
⎛← ⎞
⎞ ⎛← ⎞
⎛ jβW L W n
Ei
0
0
0
Ei
e
⎜ ⎟
− jβW L W n
⎟ ⎜
⎜ 0
⎟
0
0
e
⎜
⎜ Ei ⎟
⎟ · ⎜ Ei ⎟
⎜← ⎟ =⎜
← ⎟
jβW L W n
⎠
⎝
0
0
0
e
⎝ Et ⎠
⎝ Et ⎠
− jβW L W n
0
0
0
e
Et
Et
n
n+1
The coefficients a1n , a2n and bn are given by:
κ1n κ2n e− j(2βW L Cn +β R πrn )
1 − t1n t2n e−2 j(βW L Cn +β R πrn )
t2n e− jβW L Cn − t1n e− j(3βW L Cn +2β R πrn )
=
1 − t1n t2n e−2 j(βW L Cn +β R πrn )
bn =
a1n
(2.140)
40
2 Ring Resonators: Theory and Modeling
a2n =
t1n e− jβW L Cn − t2n e− j(3βW L Cn +2β R πrn )
1 − t1n t2n e−2 j(βW L Cn +β R πrn )
(2.141)
The arrows used as the superscripts indicate whether the field is propagating to the
left or the right direction. Multiplying the transfer matrices in an alternating rhythm,
the transfer functions for a parallel N coupled ring resonator filter can be derived.
Note that in the calculation the propagation constant for the uncoupled waveguides
and for the ring resonators is assumed to be the same for each one, respectively. The
←
drop port E t1 and the throughput Ei N responses from the resulting Matrix H, where
h represent the elements of the matrix, are then given by (assuming only one input,
Ei1 = 1):
←
E t1 =
h 3,2
h 2,2
1
Ei N =
h 2,2
←
where Et N = E i1 = 0
(2.142)
As in the recursive algorithm mentioned earlier in this chapter, the coupling coefficients can also be varied to control the bandwidth of the filter and thus reducing the
sidelobes by apodization.
Several configurations to obtain a box-like filter response using an array of parallel
coupled ring resonators are presented in Ma et al. (2005). A special configuration
consisting of a parallel coupled double ring resonator (with two waveguides), serially
coupled with a single ring resonator has been analyzed in Okamoto et al. (2003).
Coupled to One Input/Output Waveguide
The basic ring resonator filter configuration consisting of a ring and a waveguide is
used to realize a multiple parallel coupled filter. Another term for parallel coupled ring
resonators with only one input/output waveguides is side-coupled, integrated, space
sequence of resonators (SCISSORS) (Heebner et al. 2002). The transfer functions of
these types of filters can be derived using the methods and formulas described earlier
in this chapter. In this chapter the focus lies on the optical properties of this kind of
device which have been analyzed in detail in Heebner et al. (2002) and Pereira et al.
(2002). The following expressions are based on this literature.
In order to describe linear propagation effects, a pulse is considered, which travels
through a single ring resonator, obtaining a frequency dependent phase shift that
results in a delay or distorts the pulse shape (see also Sect. 2.1.1. The time dependent
relations). The effective propagation constant for a resonator spacing of is then
given by:
β0 (ω) =
n eff ω (ω)
+
c0
(2.143)
where (ω) is the phase shift which a field acquires when traversing a ring resonator.
It is derived from the transfer function of a single ring resonator (Fig. 2.2) where the
2.3 Multiple Coupled Resonators
41
throughput field is related to the input field (2.9).
E t1 (ω) = e j(ω) E i1 (ω)
t sin θ (ω)
(ω) = π + θ (ω) + 2 arctan
1 − t cos θ (ω)
(2.144)
The transfer function of a single ring resonator can be expanded into two terms
using the Taylor series, representing the transmitted (expanded about the normalized
detuning θ 0 ) and the exponential phase shift (expanded about the transmitted phase
shift of the carrier 0 ). The transfer function is given by:
3
H (ω) = e
j
=e
j0
∞
1+
n=1
jn
n!
n 4
1 dm m
× (θ − θ0 )
m! dθ m θ0
m=1
∞
(2.145)
Using this equation, the field at some point zl+1 expressed by the field at another
point zl which is only a small distance δz away is given by (the transmitted phase
shift induced by each ring resonator is assumed to be distributed over the separation
, leading to an effective propagation constant which is independent of propagation
distance):
0
n eff ω0
δz ·
El+1 (ω) = exp j
+
c0
3
n 4
∞
∞
j n n eff
1 δz d m m
1+
ωδz +
El (ω)
(θ − θ0 )
n! c0
m! dθ m θ0
n=1
m=1
(2.146)
The Fourier transform of (2.145) leads to a difference equation for the transfer
function expanded to two Tailor series (transmitted and exponential phase shift):
Al+1 (t) = Al (t)
∞
+
n=1
n
∞
j ∂ m
j n n eff ∂
1 δz dm δz +
Al (t)
j
n!
c0 ∂t m=1 m! dωm θ0 FSR ∂t
(2.147)
For weak coupling, (2.146) can be rewritten using:
Al+1 (t) − Al (t) δz→0 dA
−−−→
δz
dz
(2.148)
leading to:
∞
j ∂ m
dA
1 1 dm n eff ∂
A
= −
+j
dz
c0 ∂t
m! ωm θ0 FSR ∂t
m=1
(2.149)
42
2 Ring Resonators: Theory and Modeling
This equation yields the group-velocity reduction and group-velocity dispersion
including higher order dispersion. The group-velocity reduction, which is proportional to the inverse of the first frequency derivative of the propagation constant, is
given by the term:
dβeff
1 d
n eff
+
=
dω
c0
dω
4r
θ0 =0,t≈1 n eff
1+
F
−−−−−→
c0
βeff =
(2.150)
where F is the finesse and r the radius of the ring resonator (see 2.30). The groupvelocity dispersion, which is proportional to the second frequency derivative of the
effective propagation constant, is given by:
2
dβeff
1 d2 =
dω2
dω2
√
π
√
θ0 =± F 3
3 3F 2
−−−−−→ ∓ 2
4π FSR2
βeff =
(2.151)
The dispersion maxima are obtained at a detuning of θ0 = ± Fπ√3 .
Higher order dispersion is derived in a similar way as described before. The
expression for the third-order dispersion is given by the term:
1 d3 dω3
F3
4
θ0 =0,t≈1
−−−−−→ − 3
π FSR3
βeff =
(2.152)
All orders of dispersion have to be taken into account if the pulse bandwidth
corresponds approximately to the resonance bandwidth given by the FWHM.
Ring resonators are versatile devices and do not only exhibit linear properties, but
can also be used to realize nonlinear effects. This can be accomplished by using a
material system like InGaAsP or GaAs for example. The effective nonlinear propagation constant is given by (assuming that the nonlinearity of the bus waveguide
does not contribute significantly and can be neglected):
1 d
1 d dθ d|E i2 |2
=
d|E i1 |2
dθ d|E i2 |2 d|E i1 |2
8r 2
θ0 =0,t≈1
F
−−−−−→ β nl
π
nl
=
βeff
The linear propagation (2.148) can then be modified to:
(2.153)
2.3 Multiple Coupled Resonators
43
∞
n eff ∂
dA
1 1 dm = −
+j
dz
c0 ∂t
m! ωm θ0
m=1
j ∂ m
A
× β nl 2πr B|A|2 +
FSR ∂t
(2.154)
where B is the intensity enhancement or buildup factor (see 2.32–2.36).
This configuration of side-coupled ring resonators exhibits strong dispersive and
nonlinear properties and also supports solitons. As fabrication technologies mature,
integration of these kinds of devices becomes feasible.
The following chapter highlights the realization and characterization of ring
resonator devices in different material systems.
2.4 Microring Resonator Based Electro-optic Effect
When a microring resonator is realized in a substrate showing electro-optic effect, it
is possible to tune its resonance by applying a suitable electric field E. In this case
the guided mode effective index undergoes to a variation:
δn eff =
∂n eff 1 3
∂n eff
δn = −
n reo E
∂n
∂n 2
(2.155)
where r eo is electro-optic coefficient the By recalling that the sensitivity of the
microring resonator is defined as δλ = λδneff /ng , in electro-optic materials it results
that:
δλ = −
∂n eff λ 1 3
n reo E
∂n n g 2
(2.156)
that represents the wavelength variation induced by a change in the refractive index.
Equivalently, the electro-optic turnability T is often used by normalizing the sensitivity to the applied electric field E. Finally, δλ can be expressed in function of the
Q value and it is straightforward to verify that high Q-factor resonators with require
lower applied electric field thanks to the sharper resonances. It is worth mentioning
that E can be written in term of the Voltage applied across the electrodes and its
intensity depends on the geometry of the microring resonator.
2.5 Microring Resonator Modulator
Microring resonator modulators have attracted significant scientific and technological interest in recent years (Sacher and Poon 2008) thanks to their low power
44
2 Ring Resonators: Theory and Modeling
consumption and compact size. Their geometrical configuration can be quite simple,
consisting of a ring coupled to a straight optical waveguide. In this case a continuouswave (CW) incoming optical wave is modulated by varying a certain physical parameter of the microring resonator in a controlled way. This can be achieved by varying
the refractive index of the microring, the losses or the coupling efficiency between
the microring and the bus waveguide respectively. Among the others, modulation by
refractive index variation has been demonstrated to be quite promising because it acts
directly on the optical length of the ring. The modulation of the effective index in the
ring can be achieved exploiting different mechanisms such as, for instance, temperature variations and the electro-optic effect. The first one presents relatively large
time constants being therefore unsuitable for fast signals processing. The electrooptic effect instead has demonstrated to be finely tunable and as fast as needed.
Amplitude modulators based on microrings are quite common and have already
been demonstrated in polymers„ lithium niobate, silicon and compound semiconductor materials respectively, with typical modulation rates in the range of tens of
gigahertz. Microring phase modulators have also been realized although with less
success. A discussion of some modulators devices is presented in Chap. 5. As a final
comment, it is worth mentioning to remember that in a ring modulator, the resonator
is working at an operating wavelength lying on the slope of the resonance peak. As
a consequence, the modulating the of optical length of the ring shifts the resonance
peak, changing the transmission/reflection of the cavity. In general, a greater efficient
modulation is expected at higher finesse and Q values. The best control in the ring
modulator is normally obtained in the so-called linear regime, i.e. when the slope
of the resonance is well approximated to a straight line. However, this configuration
limits the modulation depth and introduces IL. Fast modulators rings have a typical
Q values in the range of 5000–25,000: for higher Q the modulation speed is strongly
limited due to the longer trapping time of light in the ring.
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2 Ring Resonators: Theory and Modeling
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Chapter 3
Materials, Fabrication
and Characterization Methods
Recently, advancing fabrication technologies enabled the realization of ring
resonators in many material systems with excellent optical properties. In this chapter
ring resonators made of different materials using corresponding manufacturing
processes will be presented based on the current state-of-the-art in literature. Device
performance details will be given in Chap. 5.
There are principally two configurations for the coupling between the ring or
disk resonator and the bus waveguides, namely, a vertical coupling configuration,
where the bus waveguides are either on top or beneath the ring or disk resonator and
the lateral coupling configuration, where the bus waveguides and the ring or disk
resonator are in the same plane.
The vertical coupling method allows the precise control of the coupling distance
and thus the coupling coefficient by using epitaxial growth. In this configuration it
is also possible to fabricate the ring and the bus waveguides out of separate materials which opens up the possibility of creating active ring or disk structures when
using an appropriate material. Realizing vertically coupled ring or disk resonators
increases the fabrication complexity because processes like wafer bonding, regrowth
or re-deposition are required. The lateral coupling method is useful for realizing ring
resonators with larger radius (>100 μm) utilizing a weak guiding waveguide layout
where however the confinement of the waveguide mode is still high enough to fabricate ring resonators with negligible bending loss. Ring resonators with small radii
have also been fabricated utilizing the lateral coupling scheme as will be shown in
Chap. 5. Choosing a suitable waveguide design reduces the tight requirements of
fabricating a very small coupling gap which is usually much less than 1 μm in the
case of very strong guiding waveguides. The lateral coupling approach allows the use
of multimode interference couplers with higher processing tolerances with respect
to the power coupling coefficient which eliminates the fabrication of small (<1 μm)
and deep coupling gaps. The incorporation of gain sections inside the ring resonator
using a suitable material can be accomplished by selective area metal organic vapor
phase epitaxy (SAMOVPE).
© Springer Nature Switzerland AG 2020
D. G. Rabus and C. Sada, Integrated Ring Resonators, Springer Series
in Optical Sciences 127, https://doi.org/10.1007/978-3-030-60131-7_3
47
48
3 Materials, Fabrication and Characterization Methods
Both coupling schemes have advantages and disadvantages and it is up to the
device designer to decide which one is more suitable.
As underlined in Chap. 2, the following key parameters need to be defined in
order to achieve a performant integrated ring resonator:
•
•
•
•
•
Free Spectral Range (FSR);
Spectral Width of Resonance (FWHM);
Finesse F;
Quality (Q-) factor;
Intensity enhancement I.
Depending on the application, these parameters must be adjusted to fit the desired
requirements and, consequently, the choice of the material must be adequately triggered. In general, the characteristic equations of microring resonators described
in Chap. 2 have shown that smaller cavity are expected to provide better performances. In this case, however, bending losses set a lower limit for the practically
possible radius. As a matter of fact, they depend significantly on the refractive index
contrast of the microring resonator material and, therefore, are actually one of the
main issues hindering the realization of low-loss devices. For this reasons, small
rings with acceptable low bending losses have been proposed and realized only in
high-contrast materials. Best configurations have been found in waveguides totally
embedded in a low-index material to provide an adequate light confinement in the
integrated microring resonators. The refractive index contrast is not the only one
parameter to look for.
In Telecom applications such as in Wavelength De Multiplexers (WDM), for
instance, the definition number of channels is the one of driving force. If 32 channels
in the C-band (λ = 1520–1560 nm) are processed, a finesse F ≈ 32 would be needed.
With a 50 GHz channels separation (i.e. a dense WDM, or ~0.4 nm in the C-band),
a FSR of 13 nm is consequently required, with a corresponding ring radius r =
12 μm and a minimal attenuation α R ≈ 13 cm−1 . These requirements imply that the
microring resonator must be realized on materials compatible with the micro-scale
structuring in nanoscale precision. High values of Finesse are of extreme interest
also for other applications such as second harmonic generation and nonlinear optics
in general, where high optical intensities are demanded. A microring with a finesse
of 30, in fact, could guarantee a factor 10 of enhancement in the light at resonance.
In that case, a material able to resist to high light power density without changing its
properties is mandatory (Koechlin et al. 2009).
For high-speed switching applications, instead, the maximum switching frequency
(ν max) of the device should be considered. Since a large finesse or Q-factor reduces
the maximum switching speed, for WDM applications an optimized finesse is therefore required, yielding a trade-off between the sensitivity and the switching speed
of the resonator. In the same configuration stated before, i.e. a microring resonator
of radius r 0 = 12-μm and made of and embedded waveguide with refractive index
ng = 2.3, the finesse should be smaller than 50 if a modulation speed of 100 GHz is
requested (Koechlin et al. 2009).
3 Materials, Fabrication and Characterization Methods
49
A more detail discussion of the devices’ characteristic will be dedicated in Chaps. 4
and 5. However, these examples show that the design of the microring resonator is
the result of compromises and, in general, the best material is the one that minimize
them.
Material Choice for Optical Microring Resonators
The choice of the material to achieve given performances starts from the best
compromise among the following parameters:
•
•
•
•
•
adequate refractive index contrast n;
high tunability;
high optical transparency in the required spectral range;
mechanical, thermal and photochemical stability on time;
compatibility with micro-structuring and patterning techniques to define the
desired geometry.
Materials able to fulfil the requirements, at least partially, can be found among
inorganic insulator oxides, semiconductors and polymers respectively.
In order to achieve high refractive index contrasts, thin films, either bonded or
grown, on another material with lower refractive index have been widely investigated.
This parameter can be therefore finely tuned from the design point of view but can
have a deep impact on the durability and mechanical resistance of the device. This
is particularly true when polymers are exploited as low refractive index embedding
material. On the other hand, polymers have proven to be easily patternable and
compatible with photolithography design and therefore among the materials used in
hybrid configurations.
Tunability of a microring resonator is the most demanded feature, being connected
to resonances shifts and light modulation. Among the others, the electro-optic effect
is the tuning mechanisms that gained greatest attention. As a matter of fact, it allows
fast responses (switching speeds >100 GHz) and can be fruitfully combined with
other nonlinear optical properties. For this reason, inorganic and organic electrooptic materials have been exploited in electro-optic based devices. The most common
non-centrosymmetric materials with high electro-optic coefficients are ferroelectric
oxides such as BaTiO3 , KNbO3 , LiNbO3 . Apart oxides, hypothiodiphosphate crystal
(Sn2 P2 S6 , SPS) as well as the organic N-dimethylamino-N-methyl-stilbazolium tosylate (DAST) and the well known semiconductors such as GaAs, GaN and AlN have
been considered. Since the nineties, LiNbO3 has been playing a great role in the
telecom applications as host material for commercially available high performant
optical modulators and, consequently, has gained more attention than other oxides.
The waveguide integration technology in this material has become very mature and
already optimized for high volumes batch processing.
In Table 3.1 the most common electro-optic materials are listed together with
some of their properties for comparison.
As it clearly emerges, although SPS presents an electro-optic effect 5 times
greater than LiNbO3 , for instance, the figure of merit is only 20% higher. This is
to say that the electro-optic coefficient is an useful indicator but cannot be used as
50
3 Materials, Fabrication and Characterization Methods
Table 3.1 Materials for electro-optic microresonators (Koechlin 2009) and references therein cited
Material
LiNbO3
Wavelength
[nm]
Dielectric
constant j
Refractive
index ni
Electro-optic
coefficient r ij
[pm/V]
Figure of merit
ri j n i2 / j [pm/V]
633
3T = 28
n 3 = 2.2
T = 31
r33
5.4
633
3T
3T
3T
1T
1S
T
= 28
n 3 = 2.3
1.9
= 44
n 3 = 2.2
= 130
n 3 = 2.4
= 230
n 1 = 3.0
= 5.2
n 1 = 2.4
= 13
n = 3.5
T = 10
r13
T = 64
r33
T = 105
r33
T = 174
r11
T = 48
r11
r T = 1.2
KNbO3
633
BaTiO3
633
Sn2 P2 S6
633
6.9
3.5
6.8
DAST
720
GaAs
1020
GaN
633
T = 11
n = 2.35
T = 1.9
r33
1.0
633
T
n = 2.0
T
r13
= 1.0
0.4
AlN
= 10
102
1.1
threshold to qualify the material performances. Semiconductors have 1/5 of the figure
of merit of the oxides competitors but take advantage of an extremely advanced technology provided by microelectronics. Depending on the applications and the relative
operational wavelengths, in principle the best material can be identified as the one
optimizing the previously quoted parameters. The interest on micro-resonators has
undergone a great step forward thanks to the strong improvement of the processing
technologies needed for reproducible and affordable devices. However, the material’s choice cannot exempt from budget considerations in the perspectives of getting
batch processing and commercially available solutions. As a consequence, despite
of interesting performances, some alternatives have proved to be unrealistic to enter
into the market and will be not treated in this book.
Despite the promising properties of microring resonators proposed in a variety of
materials like semiconductors (Xu et al. 2005, 2006; Niehusmann et al. 2004; Zhou
and Poon 2006), silica (Little et al. 2004) and polymers (Leinse et al. 2005; Tazawa
et al. 2006) in the last 20 years, improvements have been seeking for faster responses,
wider tunability and spectra range. In summary, although polymers are surely attractive alternatives thanks to their easy-way of processing and structuring, they suffer
from a relative low refractive index that impact on the minimum resonator size and
consequently in the available spectral range. On the other hand, silica-based ring
resonators (see Sect. 3.3) are unable to provide a fast nonlinear and electro-optical
response and therefore has appeared less performant respect the other competitor
materials. Among the others, semiconductor-based ring resonators have demonstrated to be the most promising: they have strongly benefitted from the advances in
microelectronic technologies to realize efficient High-Q resonators with radii lower
than 10 μm as presented in Sect. 3.4. The possibility of tuning the Silicon-based
resonators by way of electrically-driven carriers injection in the core have increased
their popularity in this field although limited to the infrared spectral range due
to its material optical transparency. It is in this scenario that other materials have
3 Materials, Fabrication and Characterization Methods
51
been started to be investigated to overcome these limiting factors and among them,
lithium niobate is surely the most promising as complementary to semiconductors.
Its wide transparent spectral range as well as high electro-optic coefficient enables
to conjugate fast response in a wavelength region not accessible for semiconductors.
In the following sections the most promising materials to realize high quality
microring resonators will be presented. Their performances but also their limits and
constraints will be highlighted for further comparisons. Moreover, in the following
chapters, dry and wet etching, wafer bonding techniques and other lithography applications for realizing laterally and vertically coupled ring resonator devices will be
briefly explained.
3.1 Wafer Bonding
Wafer bonding is referred to a process in which two similar or dissimilar semiconductor wafers are bonded with various crystallographic orientations and lattice
constants to form a single substrate which then features specific properties. The
bonding process is activated by temperature, force, chemicals or plasma. An overview
on wafer bonding can be found in Alexe and Gösele (2004). Wafer bonding techniques can be divided into two groups, one using an intermediate layer (e.g., adhesion bonding, eutectic bonding) and another without using an intermediate layer
(e.g., fusion bonding, anodic bonding) to realize the bond. Wafer bonding allows
using the advantages of different materials, while avoiding their disadvantages,
allowing combinations of materials otherwise unachievable with other techniques.
Wafer bonding is commonly applied to form silicon-on-insulator (SOI) substrates.
Bonding of wafers of different materials has attracted great interest lately, e.g., GaAs
on Si (Georgakilas et al. 2002), or SiC on Si (Kim and Carpenter 2003).
Different methods exist for bonding various materials and it is again up to the
realized device which process is more suitable. In the following sections common
wafer bonding methods are described.
3.1.1 Bonding with Intermediate Layer
Adhesion Bonding
Adhesive bonding uses photoresist, spin on glasses or polymers to deposit a
planarizing material between two wafers. Such materials can be annealed at low
temperature to provide a low-stress wafer stack. It is a relatively simple and inexpensive process. The use of polymers has the advantage of bonding samples which
have been structured already which is the case for vertically coupled ring resonators,
where the bus waveguides have been fabricated before the bonding takes place.
52
3 Materials, Fabrication and Characterization Methods
Eutectic Bonding
Eutectic bonding is a special kind of metal bonding, where the low melting temperature of the eutectic alloy is exploited to achieve low temperature bonding. Eutectic
is a mixture of two or more elements and has a lower melting point than any of its
constituents. Eutectic comes from the Greek word “eutektos” which means “easily
melted.” Eutectic bonds are used when a hermetic or vacuum seal is required. Eutectic
alloys which are used for example are gold–silicon, gold–tin, or lead–silicon. The
metal is usually deposited by plating, while the silicon source can be the wafer
or chemical vapor deposition (CVD). Solid–liquid mixing occurs at temperatures
slightly above the eutectic point and a high contact force (40 kN). A gold–silicon
eutectic bond for example is realized by coating a silicon wafer with ~500 nm gold.
The Au–Si eutectic point is about 370 °C. Au atoms diffuse into Si and the eutectic
alloy is formed. The bonding temperature is higher than the eutectic point which is
due to solid–liquid inter-diffusion at the interface.
3.1.2 Bonding Without Intermediate Layer
The requirements of the surface quality (cleanliness and roughness) and flatness of
the used wafers are very tight when it comes to direct wafer bonding. There are
basically three types of primary interactions which are responsible for forming a first
bond, Van der Waals, electrostatic Columbic, and capillary forces.
Van der Waals forces are, however, quite small and decrease very rapidly as the
distance between two molecules increases. Covalent bonds are established, when the
wafers come into very close contact.
Electrostatic Coulomb forces between two surfaces are usually stronger than the
interaction between two contacted samples if one of the surfaces has been electrically
charged by adsorbing or desorbing electrons or ions.
Capillary forces come into play when water is used in the bonding process. Water
helps to activate the bonding process at room temperature. Due to the surface tension,
the water between the two surfaces pulls the samples together and smoothens out
any surface roughness present, thus increasing the contact area. During the following
heating process, the water reacts with the surrounding oxide or diffuses away from the
surface leading to the formation of covalent bonds. True crystal-to-crystal bonding is
achieved by using hydro-phobic bonding which requires a removal of the naturally
formed oxide present at the surface of the samples.
Fusion Bonding
Fusion bonding uses applied temperature and pressure and is used for example to
bond silicon to silicon without depositing an intermediate SiO2 layer using the native
oxide formation on the surface of the Si wafers. Fusion bonding is commonly used in
mass production of bulk micromachined micro-electromechanical systems (MEMS)
packaging. As the same materials are used in this bonding process, no thermal stress
3.1 Wafer Bonding
53
is induced, which results in a very strong bond strength. Initial bonding is performed
in a temperature range between 300 and 800 °C, annealing is done between 800 and
1100 °C which strengthens the bond. This high annealing temperature is also a key
drawback to fusion bonding. Alternatively work is being conducted by using plasma
processing to reduce the annealing temperatures from ~1000 °C to the range between
200 and 300 °C. Regardless of this plasma pretreatment, most of the work performed
on direct bonding of III/V materials uses hydrophobic surfaces, where the oxide has
been removed, to assure a true crystal-to-crystal bond and good electrical contacting
through the bond.
Anodic Bonding
Anodic bonding or electrostatic bonding is performed by applying a high electric field
across the two substrates. Temperatures used in this process are ~400 °C. An example
of this type of bonding is the bonding of glass/Si. Here a voltage of ~1.2 kV is applied.
Silicon is attached to the positive, glass to the negative electrode. The positive ions
in glass are attracted to the interface between Si/glass where a permanent chemical
bond is formed. The used glass has to be of course electrically conductive.
The Si/Si anodic bonding process, is of course also used, when an intermediate
glass layer (0.5–4 μm) is present. Sputtering or evaporation of for example Pyrex™
or spin on glass (SOG) is used in this bonding process. The advantage is the use
of a low voltage which is between 30 and 60 V. The temperature is in the range of
350–450 °C.
3.1.3 Benzocyclobutene Wafer Bonding
As described in the previous sections, several bonding techniques exist. Due to the fact
that benzocyclobutene (BCB) wafer bonding is widely used to fabricate vertically
coupled ring and disk resonators, the BCB wafer bonding process will be briefly
explained in this section. BCB wafer bonding was first presented in Sakamoto et al.
(1998) for realizing electro-optic modulators on GaAs.
A detailed description of a BCB bonding process for realizing vertically coupled
ring resonators is presented in Christiaens et al. (2004), Christiaens (2005) which
will be used in the following.
BCB is distributed by The Dow Chemical Company under the trade name
Cyclotene∗ .1 There are two varieties: the Cyclotene 3000 series resins (dry etch
type) and the Cyclotene 4000 series resins (photosensitive type). Wafer bonding
has so far been only demonstrated with the dry etch variety. The resins are derived
from B-staged bisbenzocyclobutene-based (BCB) monomers. Typical properties of
Cyclotene are: low curing temperature (~250 °C), excellent planarization properties, a dielectric constant between 2.65 and 2.5 (1 MHz–10 GHz) and low moisture
uptake (<0.2%). One of the downsides of BCB is its insulating nature like all common
1® ™*
Trademark of The Dow Chemical Company (“Dow”) or an affiliated company of Dow.
54
3 Materials, Fabrication and Characterization Methods
polymers and the low thermal conductivity, which is not suitable for realizing active
devices. The refractive index of two types of resins is shown in Fig. 3.1 (https://www.
dow.com/cyclotene/solution/refwave.html).
A schematic of a BCB bonding process is presented in Fig. 3.2. Principally the
process flow for realizing vertically coupled devices is started by growing the waveguiding layers on a suitable substrate (e.g., InP). An etch stop layer is grown between
the substrate and the waveguiding layers which is necessary for a later removal of
1.62
λ = 0.63
λ = 1.31
λ = 1.55
Index of Refraction
1.60
1.58
1.561
1.56
1.552
1.544
1.543
1.537
1.535
1.54
3022 (Hard Cure)
4024 (Hard Cure)
1.52
0.2
0.6
1.0
1.4
1.8
Wavelength (μm)
Fig. 3.1 Index of refraction as a function of wavelength for photo Cyclotene (4024–40) and
nonphoto Cyclotene (3022–46) resins after curing at 250 °C for 60 min
Fig. 3.2 BCB wafer bonding process
3.1 Wafer Bonding
55
the substrate after bonding. After the growth of the layers, the bus waveguides are
defined using photolithographic techniques and etched using a suitable dry etching
recipe. The sample is then spin coated with BCB using an adhesion promoter.
The BCB sample is then placed on a hotplate for outgassing which is followed
by the bonding and a curing process in a nitrogen environment. As transfer substrate
GaAs can be used for example which is chemically inert during the selective chemical etching if an InP substrate is being removed. The bonding process can also
be performed in a vacuum chamber. The substrate is removed by a combination of
mechanical polishing and selective chemical wet etching to the etch stop layer. Then
the etch stop layer can be removed by using a selective chemical wet etching which
does not etch the ring or disk layers. Finally the ring or disk resonator is fabricated
using dry etching and the samples are cleaved. The samples can be antireflection
(AR) coated in order to avoid Fabry–Perot resonances in the bus waveguides.
Several BCB bonded vertically coupled ring and disk resonators will be presented
in Sect. 3.4.
3.2 Dry Etching
Dry etching is a technology widely used in semiconductor processing and has been
developed in recent years to obtain reproducible etching results. In reactive ion
etching systems, ions are accelerated towards the material to be etched, and the
etching reaction is enhanced in the direction of travel of the ion. Different dry etching
systems are available on the market with recipes for etching various material systems.
Examples of systems are conventional reactive ion etching (RIE), inductively
coupled-plasma reactive ion etching (ICP-RIE), reactive ion beam etching (RIBE),
or chemically assisted ion beam etching (CAIBE). Gases which are commonly used
(combining several) in dry etching processes are methane (CH4 ), hydrogen (H2 ),
hydrogen bromide (HBr), nitrogen (N2 ), chlorine (Cl2 ), silicon tetrachloride (SiCl4 ),
argon (Ar), and xenon (Xe).
Despite the existence of numerous recipes, it is important to note that same conditions and used gases in etching processes can differ from machine to machine leading
to different etching results. The reasons for this are multiple and can depend on the
mixture and quality of gases and samples being etched regularly in the dry etching
equipment which determine the chemical composition of the sidewalls in the reaction
chamber. The wanted specific chemical deposition of the sidewalls is also referred
to as conditioning or seasoning of the chamber and is usually done before etching of
devices to obtain stable etch parameters. This conditioning affects the plasma in the
etch chamber physically and/or chemically resulting in changes in the current and
power density in the discharge and reaction rate.
Two ways of etching are distinguished, isotropic and anisotropic etching. RIE is
an anisotropic etching technique. The etch rate which defines the rate of removal
of the semiconductor material is the same in all directions in the case of isotropic
etching. The etch rate is direction dependent in the case of anisotropic etching, which
56
3 Materials, Fabrication and Characterization Methods
is important in the fabrication of ring resonators, where deeply etched waveguides
are needed to obtain a strong mode confinement of the field which in turn results in
a small radius of curvature with acceptable loss.
The pattern of a ring resonator layout is transferred to the material used by
choosing the right masking technique. The unmasked regions like the coupling gap
for example are “etched” away. There are three broad categories of masking materials:
metals [nickel (Ni), chrome (Cr), nickel chrome (NiCr), titanium (Ti), aluminum (Al),
wolfram (W), and platinum (Pt)], dielectrics (SiOx , SiNx ) and polymers (Photoresist,
E-beam resist). Metal masks are extremely etch resistant and good choices for deep
etching, however, metal masks are difficult to remove and the metal grains result in
transferred striations. Dielectric masks provide good etch resistance, and can be used
to etch nanostructures. Dielectric masks are regarded as “soft” which results in very
little transferred striations to the underlying material. Polymers are highly etch resistant when fully cured and can be used as masks for deep etching. However, polymers
as etch resistance are not sufficient to etch the depths (>1 μm) required for realizing
waveguides used for ring resonator circuits and there is a risk of contaminating the
etch chamber.
3.3 Si-Based Materials
Silicon-based devices in photonic integrated circuits are known for quite some time.
A summary of the properties of silicon can be found in Table 3.2. Pure silicon has
an absorption loss much smaller than 0.1 dB cm−1 at the telecom wavelength of
1.55 μm which makes this material interesting for telecommunication devices. The
processing and fabrication technologies for this material system are mature also to
the fact that the electronics industry is a driving force for these enabling technologies.
Another advantage in using silicon is the possibility of combining photonic devices
with electronic circuits, enabling pre- and postprocessing of optical/electrical signals.
An overview of manufactured and characterized integrated ring resonators in silicon
is provided in Wim Bogaerts and coworkers (Bogaerts et al. 2012).
3.3.1 Ring Resonators Based on Si–SiO2
One of the first and smallest ring resonators in the Si–SiO2 material system which
is also known as SOI has been presented in Little et al. (1998) with radii of 3, 4,
and 5 μm. The devices have quality factors up to 250, and an FSR of 20, 24, and
30 nm for a wavelength of 1550 nm, respectively. The intensity difference between
the on-resonance and the off-resonance state is measured to be more than 15 dB. The
layout of a typical SOI waveguide is shown in Fig. 3.3. The width of the waveguide
should be less than 600 nm in order to achieve single mode operation.
3.3 Si-Based Materials
Table 3.2 Properties of
silicon at 300 K
57
Symbol
Lattice constant
5.431 Å
Density
2.329 g cm−3
Dielectric constant
11.7
Auger recombination
coefficient
Cn
1.1 × 10−30 cm6 s−1
Auger recombination
coefficient
Cp
3 × 10−31 cm6 s−1
Debye temperature
640 K
Effective electron
masses
m1
0.98 mo
Effective electron
masses
mt
0.19 mo
Effective hole masses
mh
0.49 mo
Effective hole masses
m1p
0.16 mo
Electron affinity
4.05 eV
Optical phonon energy
0.063 eV
Infrared refractive index n(λ)
3.42
3.38 (1 + 3.9 × 10−5 T)
77 K < T < 400 K
Absorption coefficient
αn
10−18 · no · λ2
λ ≥ 5 μm
https://www.ioffe.rssi.ru/SVA/NSM/Semicond/Si/basic.html
Fig. 3.3 Typical SOI
waveguide layout
The refractive index of SiO2 plotted against the photon energy is shown in
Fig. 3.4.2
The fabrication process is made up of a deposition of a 1 μm thick buffer layer
of SiO2 , followed by a deposition of a waveguiding core layer of amorphous Si
2 https://www.ioffe.ru/SVA/NSM/nk/Oxides/Gif/sio2.gif.
58
3 Materials, Fabrication and Characterization Methods
Fig. 3.4 Refractive index of SiO2 versus photon energy
at 560 °C with a thickness of 0.2 μm. The amorphous Si was annealed at 900 °C
for 2 h to convert it to polycrystalline silicon (polySi) out of which the ring and
bus waveguides (width: 0.5 μm, height: 0.2 μm) were patterned using an HBr–Cl
plasma etch process. In order to increase the fiber-chip coupling efficiency, the bus
waveguides are flared to an 8 μm width. The achieved index contrast is either 3.5:1.5
or 3.5:1.0, depending on whether the material external to the Si waveguide is SiO2
or air, respectively. An SEM photograph of a fabricated device is shown in Fig. 3.5.
Racetrack shaped ring resonators based on a similar fabrication process have been
presented in Vörckel et al. (2003) where the radius is 3 μm and the length of the
straight coupling region is 1 μm, obtaining an FSR of about 24 nm and a Q-factor
of 1800. The device exhibits asymmetrical coupling to achieve minimum intensity
at the throughput port on resonance [see Sect. 2.1.1 (2.16)].
Fig. 3.5 SEM of a filter
incorporating a 3 μm radius
ring, with 0.5 μm wide by
0.2 μm-thick
waveguides Little et al.
(1998)
3.3 Si-Based Materials
59
The thickness of the silicon layer and the buried oxide layer of the SOI substrate are
0.4 μm, respectively. The racetrack shaped ring resonators are defined by electron
beam lithography. The waveguides are etched down to the buried oxide layer by
an HBr inductive coupled plasma reactive ion etching process. The width of the
waveguides is 0.4 μm. The bus waveguides are tapered to a 10 μm width to increase
the fiber–chip coupling efficiency. Two types of coupling distance variations have
been used. In the first one, the fixed coupling distance is 0.2 μm and the other coupling
separation is varied between 0.1 and 0.2 μm. The second configuration used a fixed
coupling distance of 0.25 μm and varying the other coupling separation between
0.125 and 0.25 μm. The throughput port minimum on resonance has been increased
from −7.2 to −12.8 dB. Due to the unreproducibility of the waveguide loss and the
coupling coefficients, an exact adjustment of the critical coupling cannot be possible.
Ring resonators with similar dimensions and figures of merit have been realized
in Dumon et al. (2004) by deep UV lithography with an illumination wavelength
of 248 nm. An SEM photograph of a fabricated racetrack shaped ring resonator is
shown in Fig. 3.6.
Racetrack shaped ring resonators based on the design in Fig. 3.3 but having an
SiO2 cladding with radii down to 20 μm are presented in Kiyat et al. (2005).
A vertically coupled disk resonator fabrication process based on a separation
by implantation of oxygen (SIMOX) has been presented in Koonath et al. (2003);
Koonath et al. (2004, 2005). The SIMOX process involves the implantation of oxygen
ions into a silicon substrate, followed by a high temperature (~1300 °C) annealing of
the substrate in order to cure the implantation damage and to effect SiO2 formation.
The thickness and the depth of the buried oxide layer are determined by the implantation dose and energy. The implantation dose should be in the range of 1 × 1017 –9
× 1017 ions per cm2 , with implantation energies in the range of 40–200 keV to keep
the defect densities below 105 cm−2 . The implantation of oxygen ions is performed
on an SOI substrate which is patterned with thermally grown oxide. The thickness
of the oxide mask is chosen such that the oxygen ions that penetrate into the area
underneath the mask are decelerated. After the high temperature annealing, angled
Fig. 3.6 Racetrack resonator
in SOI. The isolated wire
width is 500 nm, the gap
width is 230 nm. Note that
when the wires get closer
together, the wire width
decreases to 450 nm due to
optical proximity effects
during lithography Dumon
et al. (2004)
60
3 Materials, Fabrication and Characterization Methods
Fig. 3.7 SEM picture of the
fabricated microdisk
resonators on the top silicon
layer with bus waveguides
underneath Koonath et al.
(2003)
side-walls of the buried rib waveguide are obtained due to the lateral spread out of
the implanted oxygen ions. After annealing, rib waveguides can be defined on the
top layer using a conventional lithography and etching process.
Disks with radii of 20, 20.5, and 21 μm have been fabricated. The free spectral
rang of these devices is ~5 nm. In order to fabricate the devices, an SOI wafer with
0.6 μm of silicon on top of a buried oxide layer of 0.4 μm thickness was oxidized
and patterned using a reactive ion etching process to form oxide stripes of thickness
0.06 μm, with widths varying from 2 to 12 μm. The patterned wafer was then
implanted with oxygen ions with a dose of 5 × 1017 ions cm−2 , at energy of 150 keV.
The implanted wafers were then annealed at 1320 °C for 7.5 h in an ambient of
argon, with 1% oxygen, to cure the implantation damage. To form the disks, a silicon
nitride layer of thickness 0.1 μm was deposited on top, and patterned using standard
lithography and reactive ion etching. The substrate was then oxidized to remove the
silicon on the top layer, everywhere except underneath the disks, realizing vertical
coupling to the buried bus waveguides. An SEM photograph of a vertically coupled
disk is shown in Fig. 3.7.
3.3.2 Ring Resonators Based on Ta2 O5 –SiO2
The Ta2 O5 –SiO2 material system has also been used very successfully to realize ring
resonator devices. The advantage of using this material system is the ability to control
the refractive index by adjusting the ratio of Ta2 O5 to SiO2 . Vertically coupled ring
resonators with a radius of 10 μm have been presented in Little et al. (1999). Here
alternating layers of SiO2 and Ta2 O5 –SiO2 are deposited by radiofrequency (RF)
sputtering. The waveguides for the ring and the bus are made using a composition
of 30 mol.% of Ta2 O5 and 70 mol.% of SiO2 leading to a refractive index of 1.7825
at a wavelength of 1550 nm. The bottom cladding layer is made up of 10 μm SiO2 .
Then a 0.5 μm layer of Ta2 O5 –SiO2 material is deposited on top. In order to fabricate
the bus waveguides, a 150-nm-thick Cr mask was evaporated on to the sample and
3.3 Si-Based Materials
61
Fig. 3.8 Dimensions and
layer sequence of a vertically
coupled Ta2 O5 –SiO2 ring
resonator
patterned by photolithography and dry etched to a depth of 0.5 μm. While the Cr on
top of the bus waveguides remained intact, 0.5 μm of SiO2 was sputtered onto the
sample to fill in the amount of bus material etched away. In the Cr liftoff process, the
sample was first soaked in buffered hydrofluoric acid (BHF) for 10 s to remove the
SiO2 deposited on the vertical walls of the Cr. This resulted in a liftoff, of both the Cr
and the SiO2 on top of it. For the vertical separation of the bus and ring waveguides,
a layer of SiO2 is sputtered onto the sample. The thickness of this layer defines the
coupling coefficient between the ring and the bus waveguide. The ring resonator
which is on top of the bus waveguide is made by deposition of a Ta2 O5 layer with
following Cr mask patterning process. The dimensions and the layer sequence of the
device are sketched in Fig. 3.8.
A similar process realizing an eight channel add–drop filter is described in Chu
et al. (1999a). Here the ring and bus waveguide cores are composed of Ta2 O5 –
SiO2 [17:83] mol% which gives a refractive index of 1.6532. SiO2 is used for the
cladding and the buffer layers. The bus waveguides has been slightly offset from the
ring resonator waveguide. The dimensions and the waveguide layout are shown in
Fig. 3.9.
The same waveguide and ring resonator layout has been used in Chu et al. (1999b)
to realize a double ring resonator configuration. Here the composition of Ta2 O5 –SiO2
has been chosen to give a refractive index of 1.539. The ring and bus waveguide width
Fig. 3.9 Waveguide
parameters of the eight
channel add-drop filter
62
3 Materials, Fabrication and Characterization Methods
are both 2 μm. The SiO2 pedestal height for the ring waveguide is 0.5 μm. The bus
waveguide are buried 0.5 μm below the surface with an offset of 0.8 μm.
A vertical coupled ring resonator configuration using the Ta2 O5 –SiO2 compound
has been presented in Hatakeyama et al. (2004) and Kokubun et al. (2005). The
ring resonators are coupled to the bus waveguides using multilevel crossings which
means that there is a lower and an upper bus waveguide. Single, double and quadruple
coupled ring resonators have been demonstrated. The advantage of using a multilevel
structure is to eliminate the scattering loss at bus waveguide crossings. The fabrication
process is similar to the previously described methods, involving an RF sputtering
and photolithography technique. The patterns of the waveguides are transferred using
a Cr mask and a reactive ion etching (RIE) process with C2 F6 gas. The waveguide
core layers are made of Ta2 O5 –SiO2 compound glass (Ta2 O5 30 mol.%, n = 1.785
at the wavelength of 1550 nm), and the cladding and separation layers are SiO2 (n
= 1.451 at the wavelength of 1550 nm).
The fabrication of the vertically coupled ring resonator with multilevel bus waveguide crossing is started by patterning and RIE etching of the lower bus waveguide.
Then the bus waveguide is covered by depositing SiO2 . The SiO2 layer which has been
deposited onto the lower bus waveguide is eliminated by a liftoff process through
chemical etching of the Cr mask using a solution of Cerium (IV) diammondium
nitrate 13.3 wt%, perchloric acid 70% and water. In order to realize a perfect
planarized surface for the coupling to the ring resonator, SOG is used. SOG is spin
coated and baked at 400 °C for 40 min under N2 gas, realizing a height of only
0.2 μm. SOG is made up of ethyl–silicate-polymer 9% (Si 5.9%), ethanol 73%, and
methyl acetate 18%. The width and thickness of a ring waveguide is 1.2 and 0.7 μm,
respectively. The thickness of the separation layer between the ring resonator and
bus waveguides is 0.6 μm. The ring radius is 5 μm, obtaining a record 37 nm FSR.
Other configurations with different dimensions have also been realized.
3.3.3 Ring Resonators Based on SiN, SiON, and Si3 N4
Serially coupled triple ring resonators in SiN have been demonstrated in Barwicz
et al. (2004). The ring and bus waveguides are made of a single layer of SiN. The
high index contrast which is achieved by using this material combination induces
strong polarization dependence. Therefore the device is optimized for transversal
electric (TE) polarization operation. A photograph of a triple ring resonator is shown
in Fig. 3.10.
The fabrication of the device is started by thermally oxidizing a silicon wafer to
obtain a bottom SiO2 layer. Then, a SiN layer is deposited by low-pressure chemical vapor deposition (LPCVD) in a vertical thermal reactor using a gas mixture of
SiH2 Cl2 and NH3 . Next, 200 nm of polymethyl-methacrylate (PMMA) and 40 nm
of Aquasave were spun on. PMMA is a positive E-beam resist while Aquasave is a
watersoluble conductive polymer from Mitsubishi Rayon used to prevent charging
during direct-write scanning-electron-beam lithography (SEBL). PMMA is exposed
3.3 Si-Based Materials
63
Fig. 3.10 Third-order
add–drop filter based on
series-coupled microring
resonators. The rings’ outer
radius is 7.3 μm. The
ring-to-bus gap is 60 nm and
the ring-to-ring gap is
268 nm Barwicz et al. (2004)
at 30 keV using a Raith 150 SEBL system. The Aquasave is removed, and the PMMA
is developed. Next, 50 nm of Ni is evaporated on the structure, and a following liftoff
is performed by removing the nonexposed PMMA. The waveguides are defined by
conventional reactive ion etching (RIE) using Ni as a hardmask. A gas mixture of
CHF3 –O2 in a 16:3 flow-ratio was used during the dry etching process to obtain
vertical and smooth sidewalls. The accuracy of the etch depth is monitored using
several etch steps and is measured with a profilometer. Finally, the Ni is removed
using a nitric-acid-based commercial wet Ni etchant.
The design and the dimensions of the used waveguide are shown in Fig. 3.11. The
device is designed to have an FSR of 24 nm.
A similar design is presented in Wang et al. (2005) with a radius of 25 μm resulting
in an FSR of about 8 nm.
Ring resonators based on SiON are analyzed in Melloni et al. (2003). The ring
radius is 300 μm. The SiON waveguides are made by deposition using standard
Fig. 3.11 Waveguide
dimensions. The refractive
index is given for λ =
1550 nm
64
3 Materials, Fabrication and Characterization Methods
Fig. 3.12 Cross-section and layer sequence of SiON waveguide
Fig. 3.13 Refractive index of Si3 N4 versus photon energy
plasma-enhanced chemical vapor deposition (PECVD) techniques and dry etching.
The cross-section and the dimensions of the used waveguides are sketched in
Fig. 3.12.
Lateral and vertically coupled ring and disk resonators in Si3 N4 –SiO2 and SiON
are presented in Klunder et al. (2001, 2003), respectively. The refractive index of
Si3 N4 plotted against the photon energy is shown in Fig. 3.13.3
The dimensions and the layout of the lateral coupled configuration are shown
in Fig. 3.14. Laterally coupled devices with a radius of 25 μm with and without a
cladding of PMMA have been fabricated. The radius of the realized disk resonator
is 15 μm.
The fabrication of the device is performed using standard lithography and reactive
ion etching. Buffered hydrofluoric acid (BHF) etching is done after RIE to reduce
3 https://www.ioffe.ru/SVA/NSM/nk/Nitrides/Gif/si3n4.gif.
3.3 Si-Based Materials
65
Fig. 3.14 Cross-section of a laterally coupled ring resonator
Fig. 3.15 Cross-section of a vertically coupled ring resonator
the surface roughness and to obtain smoother sidewalls. The layer sequence of a
vertically coupled ring resonator is shown in Fig. 3.15.
Here an additional SiO2 layer is grown by PECVD which defines the coupling
strength between the ring and the bus waveguides.
A high-index contrast silica on silicon technology with neff = 0.02 was developed at the IBM Zurich Research Lab4 based on PECVD deposited silicon oxynitride (SiON) films for realizing integrated ring resonators (Horst et al. 1998). The
minimum bending radius is 1.5 mm. The waveguide layout is shown in Fig. 3.16.
3.3.4 Ring Resonators Based on SiO2 –GeO2
Ring resonators using GeO2 doped silica waveguides and vertical coupling have
been demonstrated in Suzuki et al. (1992). The GeO2 doped silica waveguides are
fabricated by a combination of flame hydrolysis deposition (FHD), electron cyclotron
4 www.ibm.zurich.com.
66
3 Materials, Fabrication and Characterization Methods
Fig. 3.16 Waveguide layout
developed at IBM Zurich
Research Lab
resonance CVD (ECR-CVD) with an applied RF bias (bias-CVD), and RIE. The
waveguides for the ring resonator are realized in a first step unlike the configurations
previously discussed, where the ring resonator is on top of the bus waveguides. The
ring waveguides are made of GeO2 doped silica with a 2% refractive index difference.
The dimension of the ring waveguide etched into an under cladding layer of thickness
30 μm is 3.5 μm × 4 μm. The coupling distance is adjusted to a height of 2.5 μm
between the ring and the bus waveguides by deposition. The dimension of the bus
waveguides with a 0.75% refractive index difference is 5 μm × 6.5 μm. Finally the
bus waveguides are covered by a cladding layer deposited again using FHD. The
radius of the ring is 1.5 mm.
The advantage of using this kind of material is the low propagation loss which
is smaller than 0.1 dB cm−1 at a wavelength of 1550 nm. Several integrated devices
based on this material are presented in Suzuki et al. (1994) using different refractive
index differences for the employed waveguides. The idea which has been followed
is the use of two types of waveguides, weak and strong guiding. Weak guiding
waveguides are used for in and out coupling to reduce the fiber to chip coupling loss.
3.4 III–V Materials
In this chapter the most commonly used III–V material systems GaInAsP on InP and
AlGaAs on GaAs are treated. Ring resonators both vertically and laterally coupled
have been demonstrated in these material systems.
3.4.1 The Quaternary Semiconductor Compound GaInAsP
III/V semiconductors on the basis of InP with a direct bandgap are used for a variety
of components in the all-optical network. The composition of the quaternary (III–V)
3.4 III–V Materials
67
Fig. 3.17 Bandgap of III–V
semiconductor compounds
in eV and wavelength
semiconductor compound GaInAsP lattice matched to InP, can be changed, so that
the bandgap can be adjusted in the range between 0.97 and 1.65 μm. The choice
of the appropriate bandgap, which is smaller than the signal wavelength, enables
the fabrication of passive, transparent waveguides with low loss (<1 dB cm−1 ). This
material system is also used for the realization of lasers and optical amplifiers in
the spectral window around 1.55 and 1.3 μm. A summary on optoelectronic and
photonic integrated circuits on InP can be found in Kaiser and Heidrich (2002).
Electronic components can also be fabricated with this material system, by incorporating Si, Be, Zn, and realizing p- or n-doped areas. The properties of the semiconductor compound (Gax In1−x Asy P1−y ) can be described by Vegard’s law. Using
this law and the known semiconductor compounds GaAs, GaP, InAs, and InP it is
possible to determine the coefficients x and y (Fiedler and Schlachetzki 1987).
L C Gax In1−x As y P1−y = x y L C (GaAs) + x(1 − y)L C (GaP)
+ y(1 − x)L C (InAs) + (1 − x)(1 − y)L C (InP),
where L C is the lattice constant. The composition of the semiconductor compound is
displayed over the bandgap energy or the bandgap wavelength at room temperature in
most diagrams and not x and y. The bandgap of common semiconductors is displayed
in Fig. 3.17.
Physical properties of InP and of lattice matched Gax In1−x Asy P1−y at room
temperature (300 K) are presented in Table 3.3 (Fiedler and Schlachetzki 1987;
Della Corte et al. 2000).
The refractive index of InP plotted against the photon energy is shown in Fig. 3.18.5
5 https://www.ioffe.ru/SVA/NSM/nk/A3B5/Gif/inp.gif.
68
3 Materials, Fabrication and Characterization Methods
Table 3.3 Physical properties of InP and of lattice matched Gax In1−x Asy P1−y at room temperature
(300 K)
Lattice constant
Symbol
Unit
InP
LC
nm
0.58688
Gax In1−x Asy P1−y
y = 2.202x/ (1 +
0.0659y)
Lattice match to InP
1.35
1.35 − 0.72y + 0.12y2
me /m0
0.077
0.07 − 0.0308y
Heavy hole mass/m0
mhh /m0
0.6
0.6 − 0.218y + 0.07y2
Light hole mass/m0
m1h /m0
0.12
0.12 − 0.078y +
0.002y2
Bandgap energy
Wg
Electron mass/m0
eV
Refractive index (λ = neff
1.55 μm)
3.169
Dielectric constant
(static)
Es
12.35
12.35 + 1.62y −
0.055y2
Dielectric constant
(high frequency)
E∞
9.52
9.52 + 2.06y − 0.205y2
Density
W g / T
ρ
g cm–3
10–4 eV
K–1
4.81–2.67
4.81 + 0.74y − 2.67 +
0.102y + 0.073y2
Temperature
dependence of the
refractive index at
300 K
dn
dT
K–1
2.01 × 10- - 5
Temperature
dependence of the
refractive index (λ =
1.523 μm)
dn
dT
K–1
–2.17 × 10–10 × T 2 +
3 5 × 10–7 × T + 1.15
× 10–4
Length increase due
to temperature
1
l
K–1
0.475 × 10–5
·
dl
dT
3.4.2 The Semiconductor Compound AlGaAs
The AlGaAs material system is used in the same context as the GaInAsP material
system and is a major optical material used for lasers and passive waveguide based
devices. This material system is used as a barrier material in GaAs-based heterostructure devices. It is favorably used to fabricate field effect transistors like for example
high electron mobility transistors (HEMTs). Some common physical properties of
GaAs and AlGaAs are listed in Table 3.4.
The refractive index of GaAs plotted against the photon energy is shown in
Fig. 3.19.6
6 https://www.ioffe.ru/SVA/NSM/nk/A3B5/Gif/gaas.gif.
3.4 III–V Materials
69
Fig. 3.18 Refractive index of InP versus photon energy
3.4.3 Lateral Coupling in GaInAsP/InP
One of the first passive ring resonator filters in this material system are presented
in Vanderhaegen et al. (1999). Racetrack shaped ring resonators with a radius of
125 μm and coupler lengths of 80 μm are demonstrated. The layout and the layer
sequence of the waveguide are shown in Fig. 3.20. The waveguide layers are grown
by metal organic vapor phase epitaxy (MOVPE). A 100 nm thick SiN layer is used as
the etching mask which is grown by PECVD. The waveguide patterns are transferred
to the SiN layer by photolithography and a CHF3 based RIE process. The waveguides
are etched using a CH4 /H2 and O2 process.
A bi-level etching technique that permits the use of standard photolithography
for lateral coupling to deeply etched racetrack shaped ring resonator structures is
presented in Griffel et al. (2000), where a ring laser is fabricated and characterized.
Here, deep etching is used to reduce the bending loss at the curved sections, but is
avoided in the coupling region where the straight sections of the racetrack shaped
ring resonator and the input/output waveguides form a gap whose distance defines the
power coupling coefficient (Fig. 3.21). This is a way of eliminating the drawback of
lateral coupling and realizing defined coupling parameters. A radius of curvature of
150 μm is combined with four different coupler lengths of 50, 100, 150, and 200 μm,
positioned at the center of the straight section of the racetrack, which is 50 μm longer.
The width of the used ridge waveguides is 2.5 μm and the gap between resonator and
coupling waveguides is 2 μm. The active waveguide consists of three compressively
strained GaInAsP quantum wells imbedded in a 70 nm waveguide structure of two
compositions with bandgap energy E g = 1.13 and 1.00 eV. The layer sequence of
the used waveguide is shown in Fig. 3.21.
70
3 Materials, Fabrication and Characterization Methods
Table 3.4 Physical properties of GaAs and of Alx Ga1−x As at room temperature (300 K)
Lattice constant
Symbol
Unit
GaAs
Alx Ga1-x As
Lc
nm
0.565325
0.56533 +
0.00078x
x < 0.45: 1.424 +
1.247x
Bandgap energy
Wg
eV
1.424
x > 0.45: 1.9 +
0.125x + 0.143x 2
0.063 +
0.083x (x < 0.45)
Electron mass/m0
me /m0
0.063
Heavy hole mass/m0
mhh /m0
0.51
0.51 + 0.25x
Light hole mass/m0
mlh /m0
0.082
0.082 + 0.068x
Refractive index (λ =
1.55 μm)
neff
3.3
3.3 − 0.53x +
0.09x 2
Dielectric constant
(static)
Es
12.9
12.90 − 2.84x
Dielectric constant
(high frequency)
E∞
10.89
10.89 − 2.73x
Density temperature T
dependence of the
energy gap E g (0 < T <
103 in K)
ρ
g cm−3 eV
5.32 1.519 − 5.405 ×
10−4 × T 2 /(T + 204)
5.32 − 1.56x
Temperature
dependence of the
refractive index (λ =
1.523 μm)
dn
dT
K−1
−1.86 × 10−10 × T 2 +
3.49 × 10−7 × T +
1.47 × 10−4
https://www.ioffe.rssi.ru/SVA/NSM/Semicond/GaAs/index.html
https://www.ioffe.rssi.ru/SVA/NSM/Semicond/AlGaAs/index.html
Della Corte et al. (2000)
A similar method is used in Rabus and Hamacher (2001) where a 3 dB MMI
coupler of length 150 μm is used for coupling in and out of single and serially
double coupled racetrack shaped ring resonators. Here the rings were deeply etched
along the outer wall of their curved sections (Fig. 3.22) leading to a stronger optical
confinement.
Passive single and double racetrack shaped ring resonator with a radius of 100
and 200 μm, respectively, are presented. The layer sequence of the used waveguide
is shown in Fig. 3.23. The GaInAsP waveguide material used for the realization of
the devices has a bandgap wavelength of λg = 1.06 μm at room temperature which
can also be written as Q(1.06) referring to quaternary material.
The fabrication of the waveguides starts with depositing the silicon nitride (SiNx )
mask, realized by PECVD. It serves as the etching mask for the waveguides. The
thickness of the SiNx is ≈200 nm and is deposited at a temperature of 370 °C.
The structuring of the SiNx layer is performed using standard photolithography. The
3.4 III–V Materials
Fig. 3.19 Refractive index of GaAs versus photon energy
Fig. 3.20 Waveguide structure and composition
Fig. 3.21 Layer sequence of the waveguides in the coupling region
71
72
3 Materials, Fabrication and Characterization Methods
Fig. 3.22 Scanning electron microscope (SEM) photograph of the input region of an MMI coupler
with deep etching along the outer walls of the curved sections
Fig. 3.23 Layer sequence of
the waveguide
photoresist used is AZ5214. An exposure dose of 12 mW cm−2 is used. The exposing
time is 24 s and the developing time is between 40 and 50 s for a positive exposure.
The developer used is MIF724. The developed photoresist serves as the etching mask
for the following RIE process. The etching is done using the gases CHF3 (22 sccm)
and O2 (2.2 sccm) at a pressure of 12 μbar and 50 W. The photoresist is removed after
this RIE step and the structured SiNx layer serves as the mask for the next RIE step.
The gases now used for etching the waveguide are CH4 and H2 (6, 40 ml min−1 ). In
order to reduce the formation of polymers during dry etching and to minimize the
sidewall roughness, a small fraction of O2 (0.3 ml min−1 ) is added. The power used
is 150 W at a pressure of 0.02 mbar. The etching is controlled by an ellipsometer and
a mass spectrometer. The etching is stopped when the InP etch stop layer is detected.
The next dry etching step is the realization of the deeply etched section on the outer
wall of the waveguides in the curvatures. The SiNx layer from the previous step
serves as the etching mask which is structured again with standard lithography to
open an etching window for this process. The photoresist which is used to structure
the SiNx layer therefore covers only a part of the waveguide, ideally only half of it.
This self aligning process assures that the width of the waveguide is not changed
3.4 III–V Materials
73
Fig. 3.24 SEM photograph
of a waveguide in the
curvature
by this processing step. The etching is again performed using RIE, but this time
without the portion of oxygen which could partly remove the photoresist mask and
cause etching errors. The photoresist is removed after dry etching by the use of an
oxygen plasma (15 min, power = 500 W, T ≤ 200 °C). An SEM photograph of a
waveguide in the curvature is shown in Fig. 3.24. The samples are AR coated to
avoid Fabry–Perot resonances in the bus waveguides.
In Rommel et al. (2002) a Cl2 /Ar/H2 chemistry is used to etch InP-based racetrack
ring resonators using inductively coupled plasma reactive ion etching. An SEM
photograph of a fabricated racetrack shaped ring resonator notch filter is shown in
Fig. 3.25.
The composition of Cl2 /Ar/H2 has a strong influence on the degree of undercut
in the profile. A nearly perfect anisotropic profile is achieved for ratios between
2/3/1 and 2/3/2. Waveguide losses of 2 dB cm−1 are obtained. The straight length
of the coupling region is 90 μm. The ridge width is 0.9 μm, and the coupling
gap has a width of 275 nm. A radius of 15 μm is used in the curved regions. The
etching depth is 4 μm. Three distinct etching profiles are obtained by adding H2 . For
the Cl2 dominated region (Cl2 /Ar/H2 ratios between 2/3/0 and 2/3/1.5), high etch
rates: 1.8 μm/min and large undercuts of InP and GaInAsP layers are reported.
The second region (Cl2 /Ar/H2 ratios between 2/3/1.5 and 2/3/2.5) has balanced
chemistry yielding low but uniform etch rates between 0.5 and 0.6 μm min−1 and
highly anisotropic InP/GaInAsP profiles. A H2 dominated region is reported for
Cl2 /Ar/H2 ratios above 2/3/2.5. In this region, InP layers exhibit large undercuts,
whereas GaInAsP layers showed little lateral etching. The authors suggest that the
selectivity of GaInAsP layers relative to InP may be increased by increasing the As
concentration.
One of the smallest racetrack shaped ring resonators in InP with a radius in the
curved sections of 2.25 μm is presented in Grover et al. (2003) where an FSR of
19 nm near 1550 nm, with an extinction of more than 25 dB is reported. The length
74
3 Materials, Fabrication and Characterization Methods
Fig. 3.25 The ridge is etched to a depth of 5 μm, and has a width of 0.9 μm and gap of
275 nm Rommel et al. (2002)
of the straight sections is 10 μm and the coupling gap is only 200 nm. The bus
waveguide is tapered to a width of 3 μm away from the coupling region to improve
the fiber to chip coupling. The layer sequence of the device is shown in Fig. 3.26.
The refractive index of the used Ga0.31 In0.69 As0.71 P0.29 compound is 3.39. The
fabrication details are taken from Grover (2003). The process is started by depositing
a wafer with 900 nm of silicon dioxide by PECVD. A Leica VB6 e-beam lithography
machine is used to pattern a bilayer film of polymethyl-methacrylate (PMMA). The
patterning is started by spinning on 100 K MW 5% PMMA in Anisole at 4000 rounds
per minute (RPM) for 60 s, which gives a 113 nm thick film. A bake follows for 15 min
at 170 °C. Next 495 K MW PMMA A4 in Anisole is spin-coated at 2000 RPM for
60 s, which leads to a 204 nm thick film. This is followed by a bake for 15 min at
170 °C. Finally the pattern is written using a dosage of 736 μC/cm2 for waveguides
and ring resonators, and 610 μC cm−2 for device labels. The PMMA-based resist
Fig. 3.26 Layer structure of laterally coupled ring resonator in InP
3.4 III–V Materials
75
is developed with 2-methyl-2-pentanone (methyl isobutyl ketone or MIBK) diluted
with 2-propanol as 1:3 for 2 min 30 s. In a final step the wafer is rinsed with 2-propanol
and nitrogen is used to blow-dry.
The reason for choosing two layers of PMMA is to have the lower resolution
PMMA on the bottom and the higher resolution PMMA on top, so that there is
an overhang of the higher resolution PMMA where the pattern is written. This also
enables a better liftoff in the following process. Next, a 50 nm thick layer of chromium
is deposited and patterned by liftoff in warm 1-methyl-2-pyrrolidone (C5 H9 NO) also
referred to as NMP. The pattern is transferred to the underlying silicon dioxide by
dry etching in trifluoromethane oxygen plasma. Then the InP and quaternary layers
are etched by a methane hydrogen plasma to a depth of 3.2 μm using a Cr–SiO2
mask. The methane based dry etching process evaluating several mask (Ni, NiCr, Ti,
SiO2 , and Ti–SiO2 ) is presented in Grover et al. (2001a). Then in a final step, the
mask is stripped with buffered hydrofluoric acid.
InP based devices are usually thinned to a thickness between 100 and 200 μm
by a bromine methanol based lapping process. This ensures a better cleavage of
the samples and reduces the contact resistance if active devices with top side p and
backside n contact are realized.
Buried heterostructure ring resonators are presented in Choi et al. (2004a). Ring
resonators with a radius of 200 μm are fabricated by first growing a 0.4 μm thick
GaInAsP (λg = 1.25 μm) waveguide layer on a (001) oriented InP substrate by metal
organic chemical vapor deposition (MOCVD). The waveguide layer is then covered
by a SiNx layer which serves as the mask for the following CH4 based dry etching
process. The bus waveguides are aligned parallel to the [110] direction in the crystal
lattice. The width of the buried waveguides is between 0.8 and 0.9 μm. The polymers
generated on the sidewalls during the dry etching process are removed by an oxygen
plasma treatment and the SiNx mask is removed by a buffered oxide etchant. The
waveguides are covered by a 1.5 μm thick InP layer. Finally the sample is thinned,
cleaved, and AR coated. The waveguide loss of the straight bus sections is measured
to be between 0.2 and 0.3 cm−1 . The dimensions and layout of the buried waveguide
are shown in Fig. 3.27.
SEM photographs of a waveguide section and a cross-section of a buried
waveguide are shown in Fig. 3.28 (Choi et al. 2004a).
Fig. 3.27 Dimensions and
layout of the buried
waveguide
76
3 Materials, Fabrication and Characterization Methods
Fig. 3.28 a SEM image of a
dry-etched ring resonator
mesa. b SEM cross-sectional
view of a buried
waveguide Choi et al.
(2004a)
3.4.4 Vertical Coupling in GaInAsP/InP
One of the first vertically coupled disk resonators with a diameter of 44 μm, both
in the GaAs and InP materials systems, fabricated by wafer bonding is presented in
Tishinin et al. (1999). The device design in both material systems incorporates an
etch-stop layer (0.2 μm thick layer of InGaAs/InP and Al0.95 Ga0.05 As/GaAs) and
two waveguiding layers (waveguide layers 0.5 μm thick and disk layers 0.3 μm
thick) with low index material layer (thickness 0.5 μm) in between. In the GaAs
sample, Alx O is used for lateral confinement of the light in the disk structure. The
bus waveguides and disk are fabricated by standard optical lithography and chlorine
based ECR-RIE. First, the waveguides are etched down through both the top cladding
layer and the waveguiding layer and etching is stopped within the separation layer.
The bus waveguides are multimode and have a width of 2 μm. After etching the bus
waveguides, this processed side is wafer bonded to another substrate and the original
substrate is removed after it has been lapped down to a thickness of 100–150 μm by
3.4 III–V Materials
77
selective chemical wet etching. GaAs samples are bonded to GaAs and InP samples
to InP substrates. A bonding temperature for GaAs wafers of 750 °C and of 400 °C
for InP-based materials is used. It is important to mention that the transfer substrate
need not be the same material. After the removal of the original substrate, the disk
is fabricated by back side alignment optical lithography and ECR-RIE.
A vertically coupled GaInAsP thin film disk resonator with a diameter of 10 μm
resulting in an FSR of 20 nm using polymer wafer bonding with benzo-cyclobutene
(BCB) is presented in Ma et al. (2000). The wafer structure with a 0.4 μm thick
GaInAsP (λg = 1.2 μm) guiding layer is grown on an InP substrate by molecular
beam epitaxy (MBE). A 400 nm thick SiO2 layer is used as a hard mask and is
deposited by PECVD. The wafer is patterned using electron beam lithography with
a 180 nm thick 2% polymethylmethacrylate (PMMA) resist. The structured PMMA
resist is transferred to the underlying SiO2 layer using RIE. Inductively coupled
plasma (ICP) RIE with a gas mixture of Cl:Ar (2:3) is used to transfer the pattern
onto the epitaxy wafer through the SiO2 hard mask at a temperature of 250 °C. The
waveguides are etched to a depth of about 1.3 μm. The SiO2 hard mask is removed
after RIE using buffered HF. The BCB bonding process is started by spin coating
BCB onto both the patterned wafer and the transfer wafer (here GaAs is used). Then
the wafers are brought into contact with their BCB side facing each other using an
appropriate weight. The wafer stack is put into a nitrogen filled furnace at 250 °C
for 1 h. BCB becomes fully cured and the two wafers are glued together. The overall
thickness of BCB is 3 μm. The InP substrate is removed after bonding using selective
wet etching (HCl:H3PO4 = 2:3). The input and output waveguides are 2 μm wide
and are tapered down (taper length = 500 μm) to 0.4 μm in the disk region. The bus
waveguides and the disk are separated by a gap of approximately 180 nm.
Vertically coupled single mode ring resonators also using BCB wafer bonding
with a radius of 5 and 10 μm are presented in Grover et al. (2001b) and Grover
(2003). The layer sequence of the used device is shown in Fig. 3.29.
The patterns are transferred by photolithography to a 400 nm thick SiO2 layer
using a 10× i-line stepper and a CHF3 /O2 plasma RIE process. The waveguides and
ring resonator in GaInAsP–InP are etched using SiO2 as the mask in a reactive ion
etching system with a CH4 /H2 /Ar plasma.
Fig. 3.29 Layer structure used for BCB bonded vertically coupled ring resonators
78
3 Materials, Fabrication and Characterization Methods
The fabrication process starts with etching of alignment keys to a depth of 2 μm
down to the GaInAs layer. The use of Alignment keys eliminates the use of infrared
(IR) backside alignment for processing the other side. Then the waveguide layer is
etched to a depth of 0.9 μm. Benzocyclobutene (BCB; n = 1.5) is used for bonding
to a GaAs transfer substrate. A thickness of 1–2 μm is chosen for the BCB layer.
The growth substrate is thinned to a height of about 100 μm by chemo-mechanical
polishing. The remaining growth substrate is selectively etched and removed using
H3 PO4 :HCl (1:1) which stops at the GaInAs etch stop layer. This etch stop layer
is then selectively etched using H2 O2 :H2 SO4 :H2 O (1:1:10) which stops at the InP
layer opening the second GaInAsP–InP layers for fabricating the ring resonator. The
top layer is etched to a depth of 0.9 μm, leaving a gap of 200 nm to decrease losses
caused by leakage to the substrate. Finally the whole device is encapsulated with
BCB.
This fabrication process uses the advantages of both materials combining GaInAsP
and GaAs. As appropriate, either layers of GaInAsP or GaAs are removed leading
to a vertically coupled device.
A thermal wafer bonding process is used in Djordjev et al. (2002b) to realize
vertically coupled disk resonators with radii of 4, 6, 8, 10, 12 μm. The layer sequence
and design are shown in Fig. 3.30.
A novel feature which is incorporated in the design of the disk resonator is a
circular post below the resonator. It improves the mechanical stability of the structure, improves current/field uniformity in active devices and suppresses higher order
modes improving the transmission characteristics. A disk supports whispering gallery
modes, which propagate by means of total internal reflection from the disk/air interface (see Chap. 7). The first order mode has the smallest volume and occupies the
outmost region of the disk in the radial direction. All of the higher order modes have
larger volume and are therefore closer to the center of the disk which results in a
leakage into the post. The post and the waveguides are separated by 1.2 μm which
is large enough to prevent coupling between them.
The fabrication process is described using (Djordjev 2002). The layers are grown
by low pressure MOCVD on a (001) InP substrate at 655 °C. A 100 nm thick SiNx
is used as a hard mask for the bus waveguide and disk etching process which is
Fig. 3.30 Design of vertically coupled disk resonator
3.4 III–V Materials
79
deposited at 275 °C with a power of 30 W using a pressure of 450 m Torr7 and
the gases SiH4 /NH3 /N2 at a ratio of 40/20/60. This silicon nitride layer is structured using Shipley S1813 photoresist and a low pressure (10 mTorr) ECR-RIE CF4
(30 sccm) plasma at 20 °C, 500 W for 300 s. Before spin coating the photoresist,
Silicon Resources AP405 is used to increase the adhesion of the photoresist on the
silicon nitride. The photoresist is developed using Microposit MF321 developer.
The bus waveguides are etched using a CH4 / H2 / Ar RIE process. The process used
is described in detail in Choi et al. (2002). The width of the waveguides is between
0.7 and 0.9 μm. The waveguide width is tapered adiabatically to 2.5 μm to the edge
of the chip to enhance fiber chip coupling. After the etching of the bus waveguides,
the sample, which is usually 1 cm2 , is bonded to a transfer substrate of the same
size. The cleanliness of the surface of the samples is vital for the following bonding
process and many cleaning steps are performed (deionized (DI) water, trichloroethylene (TCE), acetone, methanol). After a final DI water rinse, both samples are brought
into contact under water and are “wet bonded.” This prevents oxidation and contamination of the surfaces. The samples are then loaded into a chamber which is evacuated
and heated to 100 °C for 10 min. Then H2 is led into the chamber and the samples
are heated to a bonding temperature of 505 °C for 30 min. In a final bonding step,
the samples are cooled down to room temperature in 15 min. The fabrication of the
disk starts by removing the InP substrate which is done using mechanical polishing
and a selective chemical wet etch (HCL:H2 O—3:1). The etching is automatically
stopped, when the InGaAs layer is reached. The etch stop layer is then removed
using H2 SO4 :H2 O2 :H2 O (1:1:3) which opens the waveguide layers of the disk. In
order to align the bus and the disk waveguides, the sample is etched down to the
waveguide pattern on the edge in a small area making the alignment marks visible
which have been patterned together with the bus waveguides. The disk is etched after
the opening of the alignment marks using the same processing steps as for etching
the bus waveguides.
One of the first ring resonators coupled to buried heterostructure (BH) bus waveguides in GaInAsP are presented in Choi et al. (2004b). A two step regrowth process
is used in fabricating the devices. The radius of the ring resonators is 10 μm. The
buried bus waveguides are made by growing a 0.4 μm thick layer of GaInAsP with a
bandgap wavelength of 1.1 μm on to an InP substrate followed by an SiNx masking
and etching step. The width of the bus waveguides is 1 μm. The area between the bus
waveguides is filled with epitaxially grown InP. The silicon nitride masking layer is
removed and the second growth step is initiated leading to the ring resonator. The
material for the waveguide layer which has a thickness of 0.4 μm is GaInAsP with
a bandgap wavelength of 1.4 μm. The ring waveguide and the bus waveguides are
separated by a 0.8 μm thick InP buffer layer. The InP cladding layer for the ring
waveguides has a thickness of 1 μm. An SEM photograph of a cross section of the
ring resonator device showing the buried bus waveguides and the layer for fabricating
the ring resonator is shown in Fig. 3.31. The fabricated ring resonator is shown in
Fig. 3.32. The bus waveguides are AR coated to avoid Fabry–Perot resonances.
7 760
Torr = 1 atm = 101,325 kPa = 1013,25 h Pa = 101,325 bar.
80
3 Materials, Fabrication and Characterization Methods
Fig. 3.31 Cross-section of a
planar vertically stacked
waveguide produced on BH
mesas Choi et al. (2004b)
Fig. 3.32 Ring resonator
coupled to buried
heterostructure bus
waveguides Choi et al.
(2004b)
3.4.5 Lateral Coupling in AlGaAs/GaAs
One of the first ring and disk resonators based on this material system are presented
in Rafizadeh et al. (1997). Ring and disk resonators with diameters of 10.5 and
20.5 μm have been fabricated and characterized. The layer sequence of the used
device is shown in Fig. 3.33.
The layers are grown by MBE. The coupling gap used is only 100 nm wide.
A waveguide loss of 3.2 cm−1 is measured for TM polarized light at a wavelength of 1.55 μm. The devices are created by writing patterns upon a PMMA
3.4 III–V Materials
81
Fig. 3.33 Layer structure of
AlGaAs/GaAs based ring
and disk resonator
Fig. 3.34 Layer sequence
and dimensions of
AlGaAs/GaAs waveguide
resist layer by electron-beam lithography (JEOL JBX 5DII). The AlGaAs/GaAs is
etched using chemically assisted ion-beam etching (CAIBE). The electron-beam
lithography exposure conditions are a 300 pA probe current, a 50 eV acceleration
potential, an 80 μm × 80 μm field, and an 11 mm working distance. The PMMA
mask is transferred to an underlying SiO2 layer by RIE which provides a robust
mask capable of withstanding the CAIBE process. The CAIBE parameters used, are
a beam voltage of 500 V, a beam current density of 0.14 mA cm−2 , a chlorine flow
rate of 15 standard cubic centimeters per minute (SCCM) at STP,8 an argon flow
rate of 2 SCCM, and an elevated substrate temperature of 100 °C. The SiO2 mask
is removed after the CAIBE process. The etch rate achieved is 0.1 μm min−1 . The
sidewall roughness (vertical striations) observed under the SEM is 10–20 nm.
A similar layer sequence with waveguide parameters in the same range is presented
in Absil (2000) where racetrack shaped ring resonators with radii between 1.2 and
10 μm have been realized. The layer sequence and dimensions of the used waveguide
is shown in Fig. 3.34.
A coupling gap between 0.1 and 0.3 μm is envisaged. The fabrication of the
laterally coupled ring resonator devices starts by depositing a 420 nm thick SiO2
layer with a nominal deposition rate of 13.6 nm min−1 by PECVD at 300 °C which
serves as the mask for the CAIBE process. Before deposition of the SiO2 layer, the
sample is rinsed in acetone, methanol and isopropanol followed by a 20 min soak in
8 Standard
temperature and pressure. The volume measurement is made at or adjusted to a
temperature of 0 °C and a pressure of 1 atmosphere, or 101.325 kPa.
82
3 Materials, Fabrication and Characterization Methods
OPD 4262 (a photoresist developer) to increase oxide adhesion on the surface of the
wafer. After deposition of the oxide mask layer, the sample is solvent cleaned and
dried in a vacuum oven at 120 °C for 1 h. This step is used to increase the adhesion
of the electron beam PMMA resist on the oxide. The PMMA resist is spin coated
onto the sample leading to a thickness of 500 nm. The resist is cured on a hotplate
at 195 °C for 150 s. A Leica Cambridge EBMF 10.5 is used at 50 keV to transfer
the ring resonator patterns to the resist. The sample is developed using a solution of
MIBK:IPA (1:3) at 25 °C for 150 s and rinsing with isopropanol. The patterns are
transferred from the PMMA to the underlying oxide mask layer by RIE using CHF3
and O2 (18:2) with a pressure of 40 mT and an RF power of 175 W. The etch rate of
the oxide is 32.5 nm min−1 . The waveguides are etched using a CAIBE process in
an ultrahigh vacuum system with 200 eV argon ions and chlorine gas. The etch rate
for GaAs is 0.08 μm min−1 . The etching process is performed in three etching runs
in order for the sample to cool down. After etching, the oxide mask is removed in an
HF dip. Then the sample is spin coated with a 4 μm thick layer of cyclotene or BCB
which serves as a protection and planarization layer. The polymer is cured at 200 °C
for 2 h. The chip is thinned down in a final step to a thickness of 100 μm which is
similar to the InP based devices, also using a bromine/methanol chemo-mechanical
process. In order to avoid Fabry–Perot resonances in the bus waveguides, the facets
are AR coated using a 250 nm Al2 O3 layer which has a refractive index of n = 1.62.
3.4.6 Vertical Coupling in AlGaAs/GaAs
One of the first BCB bonded vertically coupled ring resonators in this material system
is presented in Absil et al. (2001), Grover et al. (2001c). Here a single ring resonator
channel dropping filter and a 1 × 4 multiplexer/demultiplexer (MUX/DEMUX)
crossbar array with double ring resonator filters is demonstrated. The radius of the
fabricated ring resonators is 2.5, 5, and 10 μm. The waveguide width is 0.7 μm.
The waveguides are tapered to 2.5 μm towards the facet of the chip to improve the
fiber to chip coupling efficiency. The layer sequence of the used device is shown in
Fig. 3.35. The layers are grown by MBE. A 10× i-line stepper is used for transferring
the patterns by photolithography. ICP etching is used for fabricating the bus and ring
waveguides. BCB with a thickness between 1 and 2 μm is used to bond the sample to
a GaAs transfer substrate and cured at 200 °C. After removing the original substrate,
alignment of the ring resonator layer and etching the same, the sample is encapsulated
with BCB. This ensures a refractive index symmetry profile, which is also necessary
when identical ring resonator structures are realized on both layers for multiring
resonators. In order to reduce the effect of layer misalignment a thin layer (~0.2 μm)
of AlGaAs is being unetched.
3.4 III–V Materials
83
Fig. 3.35 Layer sequence of
vertically coupled
GaAs–AlGaAs ring
resonators
3.4.7 Implementation of Gain in Ring Resonators
Introducing gain inside the ring resonator adds additional functionality and device
features. One of the first ring resonators with integrated semiconductor optical amplifiers (SOA) in the GaInAsP material system is demonstrated in Rabus et al. (2002).
Single, double and triple parallel and serially coupled ring resonators are presented
in Rabus (2002). A photograph of a ring resonator with integrated SOA is shown in
Fig. 3.36.
The SOA integration is based on a selective area MOVPE process which has also
been used in Hamacher et al. (2000) to integrate lasers, photodiodes, waveguides,
and spot size converters. The cross section of the used ridge waveguide (RW) semiconductor optical amplifier (SOA) structure is shown in Fig. 3.37. The dimensions
are given in Fig. 3.38.
The layer sequence is given in Table 3.5. The layer sequence and composition of
the used SOA is as follows (from bottom to top).
The calculated mode field profile of the RW structure is given in Fig. 3.39. The
quantum wells (QWs) and the barrier layers have been considered as one layer with
Fig. 3.36 Photograph of a
ring resonator with
integrated SOA
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3 Materials, Fabrication and Characterization Methods
Fig. 3.37 SEM of
cross-section of ridge
waveguide SOA, covered
with metal contact layer
Fig. 3.38 Device structure
of the SOA ridge waveguide
Table 3.5 Layer stack of the used SOA
No.
Material
λg (nm)
Thickness
Dopand (cm−3 )
Function
1
InP–Sn-sub
360 μm
2
InP-buffer
500 nm
Si: 3 × 1018
Buffer
3
n-GalnAsP
1150
250 nm
Si: 3 × 10
n-contact
4
n-GalnAsP
1290
10 nm
Undoped
Barrier
5
Q 1% compressive strained
6 nm
Undoped
6 × QW
6
Q-1.29
1290
10 nm
Undoped
6 × barrier
7
GalnAsP
1150
180 nm
Undoped
LD-WG
8
InP
1500 nm
Zn: 5 × 1017
p-top
50 nm
Zn: 1 ×
200 nm
Zn: 1 × 1019
9
GalnAsP
10
InGaAs
1300
Substrate
1018
p-top
p-contact
3.4 III–V Materials
85
Fig. 3.39 Mode profile of
the SOA (TE polarization)
an effective refractive index of neff = 3.4. Due to the multiquantum well structure,
the SOA was designed for favoring TE polarization. The effective index of the SOA
is determined to be neff = 3.238. The center of the guided mode in the RW structure is
located lower compared with the passive waveguide structure. Thus, it is necessary
for the integration process to adjust the height of the active–passive transition to
assure minimal coupling losses.
The butt coupling losses at the passive–active waveguide interface have been
calculated by the finite difference method (Fig. 3.40). The calculated vertical and
lateral offset between the active and passive waveguide results in a minimum
theoretical coupling loss of <1 dB.
The starting point for the calculation of the horizontal shift has been chosen so that
the passive structure is located symmetrical in the center of the active section. The
calculation of the vertical shift starts with the passive–active section, butt coupled
Fig. 3.40 Calculated butt-joint losses 6 μm
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3 Materials, Fabrication and Characterization Methods
Fig. 3.41 Lateral
dimensions of the
active–passive waveguide
interface
at the position where the rib starts for the passive structure and in the middle of
the active layers for the SOA section. The practical realization of the active–passive
transition is done in using a special taper structure at the interface. The lateral design
is shown in Fig. 3.41.
The use of the tapered structure enables the propagating wave coming from the
passive waveguide to laterally broaden, interfere, and propagate into the active waveguide with a different refractive index and scale down to the dimension of the active
waveguide.
Another technological challenge is the fabrication of a low resistance contact of
the active section. As directly contacting the SOA on the ridge with a metal needle
would destroy the SOA in the worst case, so called “support mesa” are designed
at a distance of a few micrometer away from the SOA ridge on either side. The pcontact of the SOA is then located on these mesa for securely placing a measurement
needle and for later wire bonding. The support mesas have the same active material
layer stack as the SOA. The technological challenge lies in creating a low metal–
semiconductor p-contact on the SOA. The isolation of the metal layer on top of the
support mesa is performed with a SiNx layer, which is removed only on top of the
SOA waveguide. A sketch of the cross section of the SOA with support mesa is
shown in Fig. 3.42. The n–contact is realized by metal coating the backside of the
wafer.
The fabrication starts with the epitaxial growth of the SOA layers by using
MOVPE. The first CVD processing step is the deposition of an SiNx layer which is
≈230 nm thick at a temperature of 370 °C for the fabrication of the etching mask.
The lateral active mesa structures are defined in a resist pattern by using standard
photolithography (positive process, photoresist AZ5214, exposing time ≈24 s, developer MFI724, developing time ≈50 s). The resist pattern serves as an etching mask
for the following reactive ion etching step (CHF3 —22SCCM and O2 —2.2 SCCM,
Fig. 3.42 Cross-section of
the SOA section with
support mesa
3.4 III–V Materials
87
pressure = 0.012 mbar, power = 50 W). The photoresist is removed with an O2
plasma (10 min, power = 500 W, T < 250 °C) after this process. The p-top mesa are
etched in the following step by using RIE (CH4 —8 ml min−1 and H2 —20 ml min−1 ,
pressure = 0.006 mbar, power = 200 W). In order to remove the polymer which
is formed during reactive ion etching, an O2 plasma (20 min, power = 550 W, T <
250 °C) and a solution of KOH (20%) are used. The p-top is etched down to a distance
of about 1.1–1.2 μm followed by a wet etching step by using a solution of 20 H2 O:5
HBr:H2 O2 . This wet etching process is the “undercut” etching. In this step, part of
the sidewall is removed. A layer of InP protects the active sections underneath. The
etching of the undercut is indispensable for the second epitaxial growth step of the
passive waveguide. The undercut reduces the formation of high “rabbit ears” during
selective area MOVPE at the vicinity of the mask and enables adequate control of
the layer thickness in order to achieve the necessary vertical alignment within the
active–passive transition. For further improvement of the SAMOVPE growth step,
the “undercut” is covered by a layer of SiNx which is realized by depositing the entire
wafer with SiNx and removing the material on the bottom of the wafer by reactive ion
etching, leaving the sidewalls covered. The next step is the final etching of the p-top
and the active layers using RIE (CH4 —8 ml min−1 and H2 —20 ml min−1 , pressure
= 0.006 mbar, power = 200 W). The control of the etch depth is very important
in order to adjust the re-growth of the passive material. The following step is the
regrowth of the passive material using selective area MOVPE (SAMOVPE). The
correct height of the passive material is defined by the thickness of an InP buffer
layer. The regrowth process is followed by the removal of the entire SiNx at the
“undercut” using hydrofluoric acid (HF—5%). After this step, the entire wafer is
covered again with a SiNx layer (≈190 nm) at a temperature of 370 °C. An SEM
photograph of the active–passive transition is shown in Fig. 3.43.
The SiNx is removed at the top of the active mesa using a photolithographic step,
followed by a dry etching step (CHF3 —22 SCCM and O2 —2.2 SCCM, pressure =
0.012 mbar, power = 50 W). The photoresist is removed after the dry etching step
using KOH (20%). The following diffusion process (T = 575 °C, 18 s) is carried
Fig. 3.43 Active–passive
transition
88
3 Materials, Fabrication and Characterization Methods
out using zinc arsenide as the dopand. In the next step, the waveguide is etched
together with the laser ridge in a so called self-aligning process, where the active–
passive interface is generated using RIE (CH4 —6 ml min−1 , H2 —40 ml min−1 ,
O2 —0.3 ml min−1 , pressure = 0.02 mbar, power = 150 W). Due to the larger height
of the laser ridge, the remaining material is etched by selective wet chemical etching
using a solution of HCl and H3 PO4 (1:4). The wet etching is automatically stopped,
when the quaternary layers are reached. The deep etching of the passive waveguide,
which is necessary in order to achieve sufficient optical confinement in small bent
waveguides (radii < 200 μm), is the next processing step. The etching mask material
is again a SiNx layer structured in a photolithographic and dry etching step. The SiNx
layer also serves as a protection layer for the laser ridge. The deep etching of the
passive waveguide is done by reactive ion etching using CH4 (8 ml min−1 ) and H2
(20 ml min−1 ) with a pressure of 0.006 mbar and a power of 200 W. The SiNx which
was deposited for the protection of the SOA ridge has to be removed only at the very
top of it, to be able to place a metal layer for realizing an electric contact. Therefore,
the entire wafer is covered with photoresist and is exposed for a few seconds (≈14 s)
at the areas of the SOA ridge which results in opening the tip of the laser ridge. The
photograph of the top view of an SOA ridge with structured photoresist is shown in
Fig. 3.44.
In this process the exposing time of the photoresist is the key figure. If the time
is too high, the photoresist will become very thin between the SOA ridge and the
support mesa and might uncover the insulating SiNx layer which will be etched in
the next fabrication step and so cause unwanted short cuts. On the other hand, if the
exposing time is too short, only part of the photoresist on top of the SOA ridge is
removed and the SiNx layer can not entirely be etched away in the following process.
The SEM photograph of the cross-section of a developed SOA ridge is shown in
Fig. 3.45.
The SiNx layer at the top of the SOA ridge is completely free of photoresist. The
area in between the SOA ridge and the support mesa and also the entire wafer are
Fig. 3.44 Top view of an
SOA ridge with structured
photoresist
3.4 III–V Materials
89
Fig. 3.45 SEM photograph
of the cross section of a
developed SOA ridge
covered by photoresist with a thickness of about 800 nm which is a sufficient amount
for protecting the SiNx layer from being etched in the next step. The SiNx is removed
from the p-top in a dry etching process (CHF3 —24SCCM, H2 —1SCCM, pressure
= 0.012 mbar, power = 50 W). Now, the metal contacts are fabricated starting with
a photolithographic step for the definition of the contacts. The p-top of the SOA, the
area in between the ridge and the support mesa and the top of the support mesa is
deposited with titanium, platinum, and gold and the remaining metal is removed in
a “liftoff” process using NMP (n-methyl-2-pyrrolidon, C5 H9 NO).
A vertically stacked asymmetric twin waveguide structure is used in Menon et al.
(2004) to integrate an SOA into an MMI coupled single ring resonator notch filter.
The asymmetric twin waveguide structure is grown on a (100) n+ InP substrate using
gas source MBE. The layer sequence is shown in Fig. 3.46. The width and height of
the single mode passive waveguide is 4 μm and 1.9 μm, respectively. The SOA is
formed by etching a 500 μm long stripe, and is coupled optically to the lower passive
guide via two-section adiabatic lateral tapers. The width of the taper varies linearly
from 3.5 to 2 μm over a 25 μm length followed by a second linear section that varies
from 2 to 0.5 μm over a 150 μm length, resulting in a coupling loss of <0.5 dB per
taper. The length and width of the MMI is 685 μm and 12 μm, respectively. The
input and output waveguides are angled at 7 °C to the cleaved edge of the chip in
Fig. 3.46 Layer sequence of asymmetric twin waveguide structure
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3 Materials, Fabrication and Characterization Methods
Fig. 3.47 Layer sequence of active and passive waveguide used in TIR ring resonator
order to avoid Fabry–Perot resonances in the bus waveguide. The wafer is planarized
using silicon nitride (SiNx ) followed by a short etch back to open the SOA ridges
and the taper. Electron beam evaporation was used to deposit Ti–Ni–Au p-contacts
on the active ridge including the tapers. The p-contacts are annealed at 415 °C for
30 s. The wafer is thinned to 130 μm, and a Ge–Au–Ni–Au n-contact is deposited
on the back of the substrate, and annealed at 360 °C for 90 s.
Total internal reflection (TIR) mirror based GaInAsP ring resonator notch filters
integrated with SOAs are presented in Kim et al. (2005a). The ring resonators are
made out of four TIR mirrors, an MMI coupler with a length of 113 μm and the
SOA (see also Fig. 5.36). The layer sequence of the active and passive waveguide is
shown in Fig. 3.47.
The passive waveguide A which leads to the facet and the TIR mirrors is tapered
down (taper length 15 μm) from a width of 1.5 μm to a width of 3 μm. The edge
depth is 1.8 μm for this type of waveguide as well as for the active waveguide. The
passive waveguide B is connected to waveguide A and differs only from type A by
a deeper etch depth which is 4.5 μm. The fabrication of the device is started by
growing the active layers on a n+ InP substrate. The multiquantum wells consist of
seven quantum wells, each 6.5 nm thick, separated by barrier layers with a thickness
of 8 nm. The active layers are etched away in unwanted areas in the next step, which
is followed by a regrowth step with passive material. Standard RIE and metallization
techniques are used for realizing the device.
Vertically coupled disks with radii of 10 μm employing gain are demonstrated
in Djordjev et al. (2002a). The fabrication of the vertically coupled disk is based on
the passive disk explained earlier (see Fig. 3.30). The layer sequence of the active
disk is listed in Table 3.6. In order to limit the interaction of the optical field with the
metal bond pads, a 3 μm thick layer of polyimide is applied between the surface of
the substrate and the metal layer by using a standard liftoff process which leaves the
active regions polyimide free for creating the metal contact.
Finally the sample is thinned down to a thickness of 100 μm, the n-metal contact
is deposited and contact annealing is performed. Then the samples are cleaved into
3.4 III–V Materials
91
Table 3.6 Layer sequence of active disk (Djordjev 2002)
Bandgap λ
Layer No.
Material
Thickness (nm)
Doping
17
InP
300
n+ , 106
16
InP
700
n, 5 × 1017
15
GaInAsP
400
n, 3 × 1017
14
InP
800
n, 3 × 1017
13
GaInAsP
1.25
170
12
GaInAsP
1.55; 1% strain
4×8
11
GaInAsP
1.25
3 × 10
10
GaInAsP
1.25
170
9
Inp
100
8
InP
100
p, 3 × 1017
7
InP
100
p, 5 × 1017
6
InP
600
p, 1 × 1018
5
InGaAs
200
p+ , 1 × 1019
4
InP
100
3
InGaAs
200
2
InP
100
1
InP
1.1
n, 3 × 1018
n+
bars and deposition of AR coating on both facets is applied. A SEM photograph of
the cross section of a vertically coupled disk is shown in Fig. 3.48.
These active disk resonators are the first of its kind employing gain to change the
resonant filter characteristic.
A detailed theoretical analysis of vertical coupled ring resonators employing active
and passive layers is presented in Tee et al. (2006). A design layout based on the
calculations is developed.
3.5 Polymers
Polymer photonic integrated circuits have always been playing an important role in
literature (Ma et al. 2002). Polymers have recently attracted again a lot of attention
due to the lower cost of the material (if standard polymers are used), easier processibility and integration than semiconductor materials. Polymers can be doped with
appropriate materials for engineering desired properties. Different polymer material
systems exist on the market today for realizing not only purely passive devices, but
also electro-optic and thermooptic devices. In the following chapter polymer based
ring resonators made by using different fabrication technologies will be presented.
92
3 Materials, Fabrication and Characterization Methods
Fig. 3.48 Cross-sectional scanning electron microscope photograph of an active microdisk
device Djordjev et al. (2002a)
3.5.1 Conventional Fabrication Techniques
In order to fabricate polymer waveguide based components, mainly two processing
methods are used, which are well known from the semiconductor field, namely
photoresist based patterning and direct lithographic patterning (laser direct writing,
photobleaching, electron beam direct writing). Both methods are briefly sketched in
Fig. 3.49.
A polymer waveguide generally consist of a core and a cladding polymer where
the refractive index of the core is higher than the cladding to enable the propagation of
optical waves. Of course the cladding can also be left out and air can be used instead,
which depends on the application. Figure 3.50 shows a typical photograph of the
facet of a polymer waveguide, realized by RIE and spin coating in poly (perfluorocyclobutylaryl ether) (PFCB). As can be seen from the photograph the core waveguide
has a nearly rectangular shape. RIE processes are aimed for obtaining smooth and
vertical sidewalls to reduce scattering losses.
One of the first integrated polymer ring resonator add drop filters with a radius of
4.5 cm is presented in Haavisto and Pajer (1980). The ring resonator is fabricated by
photopolymerization of doped polymethylmethacrylate (PMMA) films spun onto a
silicon wafer. The patterns are written by a focused 325 nm He–Cd laser. The width
of the achieved waveguides is 10 μm. The coupling gap is 17.5 μm, measured from
the waveguide center to center. A prism coupling arrangement is used for measuring
the device.
3.5 Polymers
93
Fig. 3.49 Photoresist (left) and direct lithographic (right) patterning for realizing polymer
waveguides
Fig. 3.50 Polymer
waveguide realized by RIE
and spin coating
A ring resonator notch filter with a radius of 15.9 mm using polymers synthesized
from deuterated9 methacrylate and deuterated fluoromethacrylate are described in
Hida et al. (1992). The ring resonator is fabricated on a silicon substrate by spin
coating, photolithography and dry etching. The height and width of the waveguide
core is 6.4 and 7.0 μm, respectively. The relative refractive index difference between
the core and the cladding is set to 0.5% by controlling the copolymerization ratio of
the two monomers. A coupling gap of 3 μm is realized between the bus waveguide
and the ring.
Polymer ring resonator filters and modulators with vertically coupled input and
output waveguides are demonstrated in Rabiei et al. (2002). Two different kinds of
9 Introduction
of deuterium into the chemical compound.
94
3 Materials, Fabrication and Characterization Methods
Fig. 3.51 Layer sequence
and dimensions of
waveguides (refractive
indices are given for a
wavelength of 1550 nm)
Fig. 3.52 Photograph of a
passive polymer ring
resonator add-drop
filter Rabiei et al. (2002)
ring resonator filters are fabricated, one with an index difference between core and
cladding of 0.1 and a radius greater than 220 μm, and a second one with an index
difference of 0.3 between core and cladding and radius greater than 25 μm. The layer
sequence and the dimension of the waveguides used in the passive ring resonator filter
are shown in Fig. 3.51. A photograph of a passive ring resonator filter is shown in
Fig. 3.52.
The fabrication of the device with an index difference of 0.3 between core and
cladding starts by spin coating a 2.8 μm Teflon film (11% solution of Teflon AF 1600
(Dupont) in 3M FC-40 solvent) on a silicon substrate. The Teflon layer is etched for
2 min in oxygen by RIE to improve the adhesion of the Teflon to the next layer. A
1.5 μm SU-8 (negative photoresist) layer is spin coated onto the etched Teflon layer
and patterned by lithography to form the ring resonator. The ring resonator waveguides are planarized by spin coating a 4.5 μm thick Teflon layer. The Teflon layer
is again etched by RIE in oxygen to increase the adhesion of the following polymer
layer. The bus waveguides are realized by lithographic patterning, RIE etching of
the Teflon cladding layer, spin coating a UFC 170A (URAY Co., Korea) layer, UV
curing, and baking. Remaining UFC 170A which is not part of the waveguide is
removed using RIE. For the fabrication of the ring resonator filter with an index
difference of 0.1 between core and cladding layers the cladding material is UFC
170 A and the vertically coupled bus waveguides are made out of NOA61 (Norland
3.5 Polymers
95
Fig. 3.53 Layer sequence
and dimensions of
waveguides used in the
modulator
Products). The fabrication of the polymer ring resonator modulator is in principal the
same as for the passive device. The layer sequence of the ring resonator modulator
is shown in Fig. 3.53.
The CLD1/APC polymer is aligned using corona polling for 30 min at a polling
temperature of 145 °C and an applied voltage of 10 kV. An upper gold electrode is
deposited and patterned on top of the device to cover the ring resonator modulator.
A photograph of a fabricated ring resonator modulator is shown in Fig. 3.54.
A free standing polymer ring resonator notch filter is presented in Paloczi et al.
(2003a), Huang et al. (2004). The polymer waveguides are embedded in a lower
cladding of UV-15 (n = 1.5, λ = 1.55 μm) and an upper cladding of OG-125 (n
= 1.46, λ = 1.55 μm). The waveguide cores which are made of SU-8 (n = 1.57, λ
= 1.55 μm) are 2 μm wide and 1.6 μm thick. The SU-8 waveguides are patterned
by direct electron beam lithography and following development process. The upper
cladding is spin coated and UV cured. The free standing feature is achieved by a
thin gold layer deposited on to the silicon substrate onto which the UV-15 layer is
spin coated. Due to the weak adhesion of the UV-15 layer, it is possible to peal of
the polymer layer (thickness ~10 μm) with the integrated ring resonators. Optical
quality facets are realized by simple cutting with a scalpel.
One of the smallest ring resonator add drop filters with a radius of 10 μm is
demonstrated in Chen et al. (2004) in the polymer BCB (Cyclotene 3022-46 from
the Dow Chemical Company). An SEM photograph of a fabricated ring resonator is
shown in Fig. 3.55.
Racetrack shaped ring resonators with bending radius of 10 and 4 μm straight
coupling sections are also presented. The layer sequence of the device is shown in
Fig. 3.56.
BCB is cured at a temperature of 250 °C. SiO2 is used as an etch mask to transfer
the patterns of the waveguides from photoresist to the used BCB. SiO2 is etched using
a trifluoromethane and oxygen plasma, BCB is etched using a sulfur hexafluoride
96
3 Materials, Fabrication and Characterization Methods
Fig. 3.54 Fabricated polymer ring resonator modulator Rabiei et al. (2002)
Fig. 3.55 BCB microracetrack resonator. The filter section has 0.9 μm wide waveguides, which
are tapered to 2.5 um at the input–output sections Chen et al. (2004)
3.5 Polymers
97
Fig. 3.56 Layer sequence of BCB ring resonator
Fig. 3.57 Left: Microscopic front view of a cleaved sample showing the Si substrate, the SiO
barrier, and the cross-section of a port waveguide. The structures are by about 10% thinner than
the films before development since the oxygen at the surface reduces the polymerization during
the exposure. Right: Microscopic top view of a laterally coupled ring resonator of Ormocore. The
external radius of the ring is 50 μm with a cross-section of 3.8 μm width and 4.5 μm height; the port
waveguides are 2.7 μm wide and 3.6 μm high. The gaps at the couplers are 0.3 μm wide Rezzonico
et al. (2006)
and oxygen plasma. The etch mask is removed by buffered hydrofluoric acid. The
width of the waveguides is 0.9 μm at the coupling gap and is tapered to 2.5 μm at
the facets.
Laterally coupled organic–inorganic hybrid polymer ring resonator add drop
filters with a radius of 50 μm are presented in Rezzonico et al. (2006). A photograph of a fabricated ring resonator and a cross-section of a waveguide are shown in
Fig. 3.57.
The waveguides are made out of Ormocore, from the family of Ormocer®10 a
commercially available inorganic–organic hybrid polymer (negative photoresist, n =
1.536, 0.6 dB cm–1 at a wavelength of 1.55 μm, T g > 270 °C). A two step lithography
process is used to realize the laterally coupled ring resonator add drop filter. The
layer sequence is similar to the one shown in Fig. 3.56 for the BCB ring resonator,
10 Trademark
München.
of the Fraunhofer–Gesellschaft zur Forderung der angewandten Forschung e.V.
98
3 Materials, Fabrication and Characterization Methods
substituting Ormocore for BCB. The SiO2 layer used has a thickness of 4 μm. In a first
step, the port waveguides are defined using an exposure in oxygen poor atmosphere
through a negative chrome mask. The sample is developed in methylpentanone. Then
the sample is spin coated again with Ormocore, patterned and developed for realizing
the ring resonator. The gap between the ring and the bus waveguides is aimed to be
0.5 μm (measured 0.3 μm). The sample is hard baked at 150 °C in inert atmosphere.
The width and height of the bus waveguides is 2.7 and 3.6 μm, respectively. The
width and height of the ring waveguide is 3.8 and 4.5 μm.
3.5.2 Replication and Nanoimprinting
One of the first ring resonators realized using a nanoimprint technique is presented
in Chao and Guo (2002). Here waveguides made out of PMMA, polystyrene (PS)
and polycarbonate (PC) are demonstrated. SEM photographs of directly imprinted
polycarbonate racetrack and disk resonators are shown in Fig. 3.58.
Two fabrication methods are demonstrated, direct imprinting (Fig. 3.59) and
template filling (Fig. 3.60).
The fabrication (Fig. 3.59) of the molding tool is performed in two steps. First, a
silicon substrate is etched using RIE, realizing the first molding tool for imprinting
the device pattern into PMMA which is used as a resist for the following Ti/Ni liftoff
process. The remaining PMMA on the surface of the sample is etched using an
oxygen RIE process, thus only leaving the structured PMMA in place. Ti/Ni which
is deposited on to the sample is used as a hard mask for the following RIE process
to etch the SiO2 layer, realizing the second and final molding tool for imprinting the
waveguides again in PMMA with a molecular weight of 15,000 (imprinting time =
10 min). In order to increase the optical confinement of the mode in the waveguides,
a buffered hydrofluoric acid (BHF) etch is performed, resulting in an undercut of
the SiO2 layer underneath the waveguides forming a pedestal. In order to separate
the molding tool from the polymer waveguides, the molding tool is coated with a
Fig. 3.58 Directly imprinted polycarbonate racetrack and disk resonators Chao and Guo (2002)
3.5 Polymers
99
Fig. 3.59 Process flow for directly imprinting into a polymer
Fig. 3.60 Process flow for polymer template filling
surfactant to provide a low surface energy. SEM photographs of PMMA waveguides
sitting on top of a thermally grown SiO2 pedestal are shown in Fig. 3.61.
In the template filling method (Fig. 3.60), a second layer of SiO2 is grown by
PECVD which is structured using the same processing steps as in the direct imprinting
method for obtaining the molding tool, spin coating PMMA, imprinting and removal
of residual PMMA by dry etching, deposition, and liftoff of Ti/Ni for the hard mask
fabrication, dry etching of the PECVD SiO2 layer and removal of the metal layer. The
molding tool is filled with polymer. Planarization is done with a flat molding tool. The
residual polymer is removed by RIE and the sample is heated to remove unwanted
air bubbles in the polymer. Finally, the sample is again etched with a buffered HF
100
3 Materials, Fabrication and Characterization Methods
Fig. 3.61 Cross-section SEM picture of a rectangular PMMA waveguide sitting on top of a SiO2
pedestal. b PMMA waveguides in the coupling region of a microring device Chao and Guo (2002)
realizing the pedestal for the polymer waveguides. To reduce the surface roughness
induced scattering loss and therefore increase the performance of the polymer ring
resonator devices, the authors propose a thermal reflow technique in Chao and Guo
(2004). Polymer ring resonator devices are heated with controlled time duration (60–
150 s) in a temperature range of 10–20 °C below the glass transition temperature
of the polymer. This lowers the viscosity and enhances the fluidity of the polymer,
resulting in a reflow which reduces the surface roughness significantly under the
action of surface tension. The variance of surface roughness is estimated to decrease
by 35–40 nm in the ring and by 15–20 nm in straight waveguides.
Replication of polymer ring resonators using a soft lithography method is demonstrated in Huang et al. (2003). The fabrication process is illustrated in Fig. 3.62. Ring
resonators made out of SU-8 are presented.
The samples are cleaved after molding and curing to achieve optical quality facets.
A photograph of a ring resonator is shown in Fig. 3.63.
This soft lithography method has also been used in Poon et al. (2004) to fabricate
ring resonator devices without cladding and cladding in polystyrene (PS) and SU-8,
respectively. Here a 3 μm thick layer of OG-125 (n = 1.456, a UV curable epoxy) is
used as the under cladding instead of growing a SiO2 layer with PECVD as previously
done which is UV cured at 80 °C for 2 min. The ring resonators without cladding are
fabricated by deposition of 10 μl of PS solution (4 wt% in toluene) on the sample
and pressing the mold against the chip with a force of 25 N for 20 min. The toluene
evaporates through the PDMS mold, leaving behind a 200 nm residual film which
does not influence the characteristic of the ring resonator. Finally the chip is baked
at 80 °C for 3–5 min. The SU-8 ring resonator is fabricated in a similar way. The
only difference is that SU-8 is UV cured and the sample is baked at 80 °C for 3 min.
Another layer of OG-125 with a thickness of 3 μm is spin coated, UV cured and
baked at 80 °C for 3–5 min to form the upper cladding. All samples are cleaved
3.5 Polymers
101
Fig. 3.62 Replication of polymer ring resonators by soft lithography
Fig. 3.63 Optical
microscope image of
microring optical resonator
fabricated by soft
lithography. The inset shows
the detail of coupling region.
The ring diameter is 200 μm,
the waveguide width is
2 μm, and the gap between
the straight waveguide and
the microring is
250 nm Huang et al. (2003)
for device separation. The ring radius is 200 μm and the height and width of the
waveguide is 1.5 and 1.9 μm, respectively.
Polymer racetrack shaped ring resonator notch filters with radii of 100 μm and
200 μm and a coupling length of 100 μm and 40 μm, respectively, fabricated using
an imprinting technique with a smoothing buffer layer are presented in Kim et al.
(2005b). The width of the coupling gap used is 200 nm. The layer sequence and
dimensions of the used waveguide is shown in Fig. 3.64.
The stamp fabrication starts by patterning a quartz glass wafer coated with
chromium using photoresist. After UV exposure, the chromium is etched and the
so achieved hard mask is used to transfer the pattern to the substrate by RIE. The
smoothing buffer layer is made by depositing an SiN film using LPCVD. The pattern
on the stamp is transferred to the cladding of the sample by general imprinting,
where the stamp is pressed against the polymer layer. The cladding is UV cured and
102
3 Materials, Fabrication and Characterization Methods
Fig. 3.64 Layer sequence
and dimensions of
waveguide
the stamp is removed, leaving behind the trench for the core waveguide. The core
polymer is spin coated onto the sample and cured. Finally the sample is cleaved and
the devices are separated.
Imprinting technologies are an attractive way of realizing ring resonators, especially due to the fact that the manufactured stamp can be used several times. This
aspect is important, when it comes to producing a large number of devices which is
a requirement for realizing low cost products for the telecommunication and sensor
market. The rise of these fabrication technologies enables a renaissance of polymer
materials and opens up the way for new materials with appropriate manufacturing
properties suitable for replication.
3.5.3 Novel Polymer Devices
In the early 2000s, micro-ring wavelength filters and resonant modulators using
polymer materials at 1300 and 1550 nm have been started to be massively designed
and demonstrated, as already reviewed in the previous sections. Initial results referred
to rings integrated with vertically coupled input and output waveguides (Rabiei et al.
2002) where devices have been realized by optical lithography. Filters with a finesse
of 141 and free spectral range of 5 nm at 1300 nm and finesse of 117 with a free
spectral range (FSR) of 8 nm at 1550 nm have been therefore reported (Rabiei et al.
2002) with a Q value close to 1.3 × 105 at 1300 nm. The interesting feature of these
filters was the temperature tuning at the rate of 14 GHz/°C. In parallel resonant ring
modulators based on electrooptic polymers granted resonance wavelength voltage
tunes at the rate of 0.82 GHz/V and bandwidth larger than 2 GHz. Using the resonant
modulator, and open eye diagram at 1 Gb/s is demonstrated. Inorganic–organic hybrid
polymer polysiloxane-liquid (PSQ-L) have also been used for all-polymer microring
resonators fabrication (Teng et al. 2009). In this case the waveguide circuits have
replicated by a simple ultraviolet-based soft lithography method bringing to 6-dB
extinction ratio at the through port and 18-dB extinction ratio at the drop port is
demonstrated. A Q-factor of 4.2 times 104 has been reported, with scattering loss
of the ring waveguides estimated to be about 1.6 dB/cm. These promising results
have been continuing to push for further research and applications because polymers present the great advantage of being cheap and scalable for mass production,
and compatible with both 2D and 3D geometries. Several different techniques have
been optimized such as the previously cited soft lithography. Among the others soft
3.5 Polymers
103
nano imprint lithography (NIL) process have been exploited for producing devices
with smooth surfaces, combined with fast sol–gel technology providing highly transparent materials (Bar-on et al. 2018). Standard soft NIL is based on casting an elastomeric material such as Polydimethylsiloxane (PDMS) on a prefabricated template
exhibiting the desired geometry of the final device. The PDMS is cured and peeled
off from the master, forming a mold with the negative geometry of the master that can
be used for further replicas by imprinting\molding. This process can be performed
also in a dual step configuration, the first step to eliminate the roughness of the
device surfaces while the second step transforms the device into fast sol–gel respectively (Bar-on et al. 2018). The combination of these two steps allow to achieve low
surface roughness but highly transparent material based devices, in both 2D and 3D
geometries. A sketch of this two steps procedure is reported in Fig. 3.65.
This approach has demonstrated to be highly efficient in realizing micro ring
resonators made by direct laser writing (DLW) to achieve a quality factor improvement from one hundred thousand to more than 3 million, a step forward in getting
higher and higher Q-factor devices for UV-curable integrated micro-ring resonators
(Bar-on et al. 2018) (Fig. 3.66).
An example of the resulting transmission and Q-factors are reported in Fig. 3.67.
The absorption limited Q-factor is determined by the propagation losses approximately close to 10−3 dB cm−1 . This value corresponds to a potential intrinsic quality
factor of Q ~ 6 × 108 .
Fig. 3.65 Dual-step soft nano imprint lithography process. a Master device fabricated using DLW
made of crosslinked SU-8 (Grey). b First soft NIL step—Replication of the master device into
non-crosslinked SU-8 (Yellow). c Reflowed replica from non-crosslinked SU-8 (Yellow). d Second
soft NIL step—Replication of the reflowed resonator into sol–gel (Blue) (Bar-on et al. 2018)
104
3 Materials, Fabrication and Characterization Methods
Fig. 3.66 SEM images of sol–gel micro-resonators generated using a Standard soft NIL. b DSSNIL. The numbers on figure ‘a’ point to defects from the original fabrication process. (1) Roughness
resulted from the finite voxel size. (2) Bump resulted from the start stop point of the DLW process.
As can be seen, both of these defects almost disappear entirely after the reflow process (Bar-on
et al. 2018)
Fig. 3.67 a Transmission spectra of a reflowed resonator. b Q-factor comparison between resonators
generated using standard NIL compared to DSS-NIL (Bar-on et al. 2018)
Starting from these technological improvements on the preparation techniques,
novel polymer devices have been recently launched and gained extreme interest and
some will be briefly commented in the following.
Novel Polymer Microring Resonators for Optical Modulation
The microring phase response can be suitably converted to an intensity modulation by combination with a Mach–Zehnder interferometer (MZI). An example of
this principle has been presented in polymer based structures in Leinse (2005).
When switching between the on and off-resonance conditions, in fact, the difference
between the two branches of the MZI can be switched from π to zero. An example
3.5 Polymers
105
of such a combination between an microring resonator and MZI, as is shown in
Fig. 3.68.
The functionality of polymeric electrooptic microring resonators have been shown
in a device with waveguide and the microring done by reactive ion etching (RIE). It
is worth mentioning that RIE can induce roughness and therefore introduces losses
in both the ring and the waveguides. This problem can be overcome by exploiting an
etch-free lithographic process. In order to achieve a MZI+ring configuration, Leinse
and coworkers optimized the process by sesigning the waveguide with the aid of a
negative photoresist (SU8, n = 1.57 at 1550 nm) in a two-layer lithographic process.
The first layer defined the 0.7 μm-thick slab of the waveguide, of which t he part
under the microring is removed. The second layer is a thin layer of 300 nm in which
2-μm-wide waveguides are defined lithographically. Between the waveguides and
the MR, a 1-μm-thick layer of a methyl-silicone based resin (n = 1.4 at 1550 nm)
was used. The same was exploited for the 4-μm cladding layer over the microring.
The last had a height of 0.8 μm and a radius of 150 μm respectively. It is important
to notice that the microring losses have been reduced by post heating processes so
that the polymers could reach temperature close to the glass transition temperature
and consequently smooth the sidewalls. The MZI was balanced by applying a heater
over one of the branches (Leinse 2005). The measured spectrum of the MZI ring
device is reported in Fig. 3.69 (Leinse 2005).
Fig. 3.68 Top: MZI+ring
schematic three-dimensional
view; Bottom: section
through MR and waveguides
(Leinse 2005)
106
3 Materials, Fabrication and Characterization Methods
Fig. 3.69 Measured spectrum (TE) of the MZI ring device. The vertical line indicates the
wavelength of the CW tunable laser chosen for the modulation measurements (Leinse 2005)
Novel Polymer Microring Resonators for Lasing
A novel polymer based microring resonator configuration for lasing has been
proposed by Chandrahalim (2015): in their work a wavelength configurable on-chip
solid-state ring lasers fabricated by a single-mask standard lithography is made. A
single- and coupled-ring resonator hosts were realized on a fused-silica wafer and
filled with Dye doped polymers. In particular d3,3 -Diethyloxacarbocyanine iodide
(CY3), Rhodamine 6G (R6G), and 3,3 -Diethylthiadicarbocyanine iodide (CY5)doped polymer as the reconfigurable gain media have been used. In Fig. 3.70 a
sketch of the realized device is depicted (Fig. 3.71).
The system demonstrated a lasing threshold ~220 nJ/mm2 per pulse for the singlering resonator laser with R6G. This achievement results in being among the lowest
threshold shown by solid-state dye-doped polymer lasers fabricated with a standard
lithography process on a chip. A single-mode lasing from a coupled-ring resonator
system with the lasing threshold of ~360 nJ/mm2 per pulse was also demonstrated
through the Vernier effect. As far as the renewability of the dye-doped polymer is
concerned, the authors in Chandrahalim (2015) removed and redeposited the dyedoped polymer on the same resonator hosts for multiple cycles. They recorded consistent emissions from the devices for all trials, showing that the proposed technology
can be applied in numerous photonic and biochemical sensing applications that entail
for sustainable, reconfigurable, and low lasing threshold coherent light sources on
a chip. An example of the achieved results is reported in Fig. 3.72 were different
Lasing spectra are represented depending on the dye system under consideration.
Recent advances have been shown also in the application of roll-to-roll nanoimprint lithography (R2RNIL) to produce all-polymer devices, including microring
resonators, waveguides, photonic crystals, diffraction gratings (Shnneidman et al.
2018). In particular loaded quality factors as high as 57,500 have been measured in
ring resonators at the telecom wavelength range and frequency resolution of ~25 pm,
3.5 Polymers
107
Fig. 3.70 3-D and cross-sectional schematic of the fused-silica ring resonator coated with a gain
medium doped high refractive index polymer (Chandrahalim and Fan 2015)
Fig. 3.71 Scanning microscope images of the fabricated ring resonators: a Single ring resonator
with inner and outer radii and depth of 110, 150, and 12 μm respectively. b Coupled ring resonators
with an outer radius of 150 μm and 145 μm, respectively. Both ring resonators are 40 μm wide and
12 μm deep. The coupling distance between the two rings is approximately 1 μm (Chandrahalim
and Fan 2015)
enabling on-chip high resolution sensors and spectrometers. Examples of produced
devices are reported in Fig. 3.73: a master of a 1 mm ring resonator coupled to an sshaped waveguide (3.2 μm wide, 1.5 μm tall) via a 1.2 μm coupling gap is presented
s (Shnneidman et al. 2018).
The related results of the optical transmission measurements are summarized in
Fig. 3.74.
Microring resonators have been also realized by femtosecond laser-induced twophoton photopolymerization in photoresist SU-8 (Zhang et al. 2020). By tuning the
108
3 Materials, Fabrication and Characterization Methods
Fig. 3.72 Lasing spectra of a CY3-doped SU-8, b R6G-doped SU-8, and (C) CY5-doped SU-8
single ring resonator lasers. All spectra are vertically shifted for clarity. d–f Spectrally integrated
laser outputs (542–548 nm for CY3-doped SU-8, 586–601 nm for R6G-doped SU-8, 760–770 nm
for CY5-doped SU-8) after fluorescence background removal as a function of the pump intensity
extracted from (a–c). The lasing thresholds for CY3, R6G, and CY5-doped SU-8 are approximately
1.9, 0.2, and 3.9 μJ/mm2 , respectively. Error bars are obtained with 3 measurements (Chandrahalim
and Fan 2015)
laser parameters, it has been demonstrated that the performance of the polymeric
microring resonator can be tailored with high accuracy, including the magnitudes of
the radius and cross section. These authors have reported that the free spectral range
of the microring resonator is closely related to the values of ring radius, resonance
wavelength, cross section of the microring as well as the polarization of the light.
In particular it has been demonstrated that a ring resonator has a free spectral range
linearly increasing with the ring radius and in particular a radius of 60 μm corresponds
to a free spectral range of 3.9 nm (Zhang et al. 2020). A summary of these results is
reported in Fig. 3.75 together with a micrograph of the obtained microring structure.
Although it is expected that the free spectral range does not change in multiple
microrings, in this case the full-width half-maximum of the resonance is larger. Moreover, the polarization modes of the microring resonator present different resonance
wavelengths due to different effective refractive indices. The transmission spectra of
microring resonators with different radii values in SU8 are reported in Figs. 3.76 and
3.77 respectively.
Among the various structures for integrated waveguide photonic based polymers devices, it is worth mentioning that polymers based microring resonators have
attracted great attention especially in the frame of developing biosensors. Thanks to
their high Q-factor, compactness, and potential high-density array they in fact are
excellent candidate for sensing multiple targets. A recent comprehensive review of
the optical sensing properties of ring resonators has been made in Ciminellin et al.
(2013). In particular the high Q-factor provides an enhanced interaction between the
3.5 Polymers
109
Fig. 3.73 Variety of structures fabricated by the R2RNIL method. SEM images of a master (top),
stamp (middle), and replica (bottom) for a 1D nanobeam photonic crystal cavity (the waveguide
width and height are 700 and 220 nm, respectively, the pitch is 300 nm, and the hole diameter
decreases from 165 nm at the center to 80 nm at both ends); b master (top) and replica (bottom) of a
1D nanobeam photonic crystal cavity with elliptical holes (3.2 μm wide and 500 nm tall waveguide,
pitch was 550 nm, ellipse minor and major axes linearly decrease from the center to both ends from
165 to 140 nm, and from 1.44 to 1.22 μm, respectively); c master (top) and replica (bottom) of a
portion of a photonic crystal slab featuring 100 × 100 array of holes with 100 nm radii, 700 nm
center-to-center distance, and approximately 90 nm hole depth; d master of a 1 mm ring resonator
coupled to an s-shaped waveguide (3.2 μm wide, 1.5 μm tall) via a 1.2 μm coupling gap (inset,
SEM of the coupling region in the replica coated with 10 nm of 80:20 Pt:Pd to prevent charging)
(Shnneidman et al. 2018)
optical evanescent field and the biological analyte that can be put into contact with the
ring structure and therefore be sensed or analyzed as it will be detailed in Chap. 5. In
this cases, polymer microring-based biosensors have been designed with ridge shape
waveguide structure by selective imprinting technique (Wang et al. 2012). Polymer
microrings have been shaped in racetrack with a radius of 350 μm, with a gap and
coupling length between the straight waveguide and the microring waveguide are 1
and 70 μm, respectively.
110
3 Materials, Fabrication and Characterization Methods
Fig. 3.74 Optical transmission measurements. a Cartoon of the full device, consisting of a ring
coupled to an s-waveguide. b Transmission measurement at telecom wavelengths, showing dips in
transmission due to ring resonances. c Images taken with an IR camera when the laser wavelength
is fixed either off resonance (red border), where scattering is seen from the waveguide only, not
from the ring, or on resonance (green border), where scattering is seen both from the waveguide
and the ring. d High resolution scan of one resonance dip. Q from fit: 57,500 ± 200 (Shnneidman
et al. 2018)
Fig. 3.75 Morphologies of microring resonators fabricated in SU8 systems: a a microring with a
radius of observed by an optical microscope. b Dependence of free spectral range on 1/R (Zhang
et al. 2020)
3.6 Temperature Insensitivity
111
Fig. 3.76 Transmission spectra of microring resonators with radii of a 60, b 80, c 100, and d,
respectively. e Dependence of free spectral range on 1/R (Zhang et al. 2020)
3.6 Temperature Insensitivity
Temperature stability of photonic integrated circuits is a key challenge which applies
to all devices, especially resonant based devices like ring resonator filters. In ring
resonator filters, the wavelength to be filtered out for example has to exactly match
the rings resonance wavelength. Temperature shifts the resonance spectra of ring
resonator filters depending on the materials used for fabricating the device. For
stabilizing the resonance wavelength of ring resonator filters, a temperature control
unit with a heater or a Peltier cooler is needed. This requires a permanent power
consumption of a few watts and electronic control circuits. The major goal is therefore to eliminate these additional expenses and sources of defect. For this reason,
temperature insensitive or athermal waveguide based devices have been investigated
(Kokubun et al. 1993; Chu et al. 1999c; Keil et al. 2001). The temperature dependence of photonic integrated circuits (PICs) is mainly caused by the temperature
dependence of the optical path length. In the case of ring resonator add/drop filters,
the center wavelength of the passband is determined only by the optical path length
of the ring resonator. The temperature induced effective index shift in a ring waveguide cannot be compensated by a similar induced effective index change of the bus
waveguides.
112
3 Materials, Fabrication and Characterization Methods
Fig. 3.77 Morphologies and transmission spectra of single-ring and four-ring resonators with a
radius of 80μ and ring cross section of 4.48 μm × 4.23 μm (Zhang et al. 2020)
The basic principle of an athermal waveguide is derived in the following using
(Kokubun et al. 1997). The temperature dependence of the center wavelength of a
device can be expressed by
dλ0
=
dT
1 dS
L dT
·
λ0
,
n eff
(3.1)
where λ0 is the central wavelength, L is the waveguide length of the device, T is the
absolute temperature and neff is the effective index of the waveguide [see also (2.4)].
S is the optical path length and is given by
S = n eff · L .
(3.2)
The temperature dependence of the optical path length of an optical waveguide
on a substrate is given by differentiating (3.2) with T, dividing both sides by L
1 dL
1 dS
dn eff
dn eff
=
+ n eff
=
+ n eff αth ,
L dT
dT
L dT
dT
(3.3)
3.6 Temperature Insensitivity
113
where α th is the coefficient of thermal expansion.
In the case of a waveguide, the coefficient of thermal expansion is the one of
the substrate, since the thickness of the substrate is much larger than the waveguide
layer. Table 3.7 gives the coefficient of thermal expansion for some bulk materials.
In order to achieve an athermal condition, the following equation has to be
satisfied.
dn eff
+ n eff αth = 0
dT
⇒
αth = −
1 dn eff
.
n eff dT
(3.4)
From (3.4), two possibilities exist of designing an athermal waveguide based
device. Either a substrate with a negative value of α th or a waveguide material with
a negative value of dneff /dT can be chosen.
One of the first temperature independent ring resonator filters based on a striploaded athermal waveguide is presented in Kokubun et al. (1997). Here, a transparent
material having a negative value of dneff /dT is chosen for the design of the waveguide.
This gives more freedom in designing the waveguide, as the parameters of used bulk
materials obviously cannot be changed. The structure and dimensions of the athermal
waveguide used are shown in Fig. 3.78. The design makes use of the negative value
of dneff /dT for PMMA which is −105 × 10−6 at λ = 633 nm for bulk material.
Table 3.7 Coefficients of
thermal expansion of some
materials
Fig. 3.78 Dimensions of
athermal waveguide design
Material
Coefficient of thermal expansion α th (×10−6 /°C)
BCB
42
MMA
68
Si
2.6
InP
4.6
GaAs
5.8
Au
14
Al
24
Ag
18
Pt
9
114
3 Materials, Fabrication and Characterization Methods
The radius of the ring is 5 mm resulting in a free spectral range of 0.037 nm. The
finesse is measured to be 2.6. The athermal design leads to a temperature coefficient
for the central wavelength of 7 × 10−4 nm K−1 .
Another ring resonator filter where the temperature dependence of the center
wavelength is compensated by application of a polymer overlay is demonstrated in
Chu et al. (1999c). The design of the waveguide is similar to the one described in
Figs. 3.8 and 3.9. The material which is used as the polymer overlay is a copolymer
made by a combination of PMMA and tri-fluoroethyl-methacrylate (TFMA). The
refractive index at room temperature is 1.44 and the value of dneff /dT is −1.44 ×
10−4 /°C. The material is deposited onto the device using spin coating realizing a
height of more than 3 μm. The center wavelength shift due to rising temperature
increases linearly without compensation by 0.0137 nm °C−1 from room temperature
to 103 °C. Using the polymer overlay, this value is decreased in the temperature range
between 25 and 55 °C resulting in a wavelength shift of −0.0025 nm °C−1 . Above
55 °C this value increases to −0.03 nm °C−1 mainly due to the low glass transition
temperature (T g ) of the polymer which is around 80 °C. Polymers with a higher T g
like polymides are preferred in utilizing this method to realize an athermal behavior.
A similar method employing a birefringent polymer overlay can also be used to
realize polarization independent ring resonator filters (Kokubun et al. 2001).
A different approach for realizing athermal waveguide based devices is presented
in Keil et al. (2001). Here an all-polymer approach is used. Polymer materials are used
for both the waveguide and the substrate. The substrate is chosen to have a positive
coefficient of thermal expansion (CTE) and the polymer used for the waveguides
is chosen to have a negative thermo-optic (TO) coefficient (dneff /dT ). An athermal
(measured between 25 and 65 °C) and polarization independent arrayed waveguide
grating (AWG) is demonstrated. The CTE of the substrate is 80 ppm K−1 . The
temperature dependent drift of the center wavelength of the device is ±0.05 nm over
the entire temperature range between 25 and 65 °C. This approach can readily be
adapted for realizing athermal ring resonator devices.
3.7 Polarization Independence
Handling polarization has been and is an issue when developing photonic integrated
circuits especially for telecommunication systems. A polarization insensitive ring
resonator filter is desirable as different polarization states lead to undesired shifts in
the filter spectrum of the resonator and degrade the optical performance of the filter.
A well-know method for realizing polarization insensitive devices is by using a
so called polarization diversity architecture. The idea behind this method is to split
the optical input signal into two signals having an orthogonal polarization state, like
for example one arm is for TE polarized signals, the other arm is for TM polarized
signals. In order to perform integrated polarization handling of the input signals,
polarization splitters, and rotators are needed. Polarization converters using sharp
bends are demonstrated for example in van Dam et al. (1996). An example of a
3.7 Polarization Independence
115
polarization insensitive heterodyne receiver in InP employing polarization rotator
and splitter elements is presented in Kaiser et al. (1996).
A theoretical analysis of a filter comprising two identical ring resonators, two
identical polarization converters, straight and curved sections which is based on the
polarization-dependent architecture is presented in Klunder et al. (2002). The layout
of the filter is sketched in Fig. 3.79.
The ring resonators are assumed to be ideal polarization splitters which drop the
TE polarized light with wavelengths within the pass band completely and the TM
polarized light and the remaining TE polarized light not in the passband, pass the ring
resonator unaffected. The polarization converters are also assumed to ideally convert
from one polarization state into the other without losses. The calculated polarization
dependence of the filter for the drop port is 0.7 dB, using a polarization converter
with a conversion efficiency of 98%.
A tunable ring resonator filter utilizing a Vernier architecture with polarization
diversity is presented in Van et al. (2004). Here a polarization beam splitter separates
TE and TM polarized light into a waveguide which leads to two third order ring
resonator filters with two different FSRs, 575 and 650 GHz. The two waveguide
arms are joined using a polarization beam combiner after the light passes the ring
resonators. A polarization dependent loss of 0.4 dB and a differential group delay of
better than 5 ps are obtained. A similar architecture is realized in Watts et al. (2005)
using integrated polarization splitters and rotators and third-order ring resonators
with a diameter of 16 μm.
Polarization converters with periodical spectral response based on ring resonators
are theoretically proposed and discussed in detail in Morichetti and Melloni (2006).
Several device layouts of parallel coupled and directly coupled ring resonator
configurations are presented.
Polarization independent ring resonator filters are also analytically analyzed in
Chin et al. (2004). Two approaches are being considered. In the first approach, laterally strong confined single mode waveguides with a large etch depth are analyzed
Fig. 3.79 Layout of a polarization independent filter
116
3 Materials, Fabrication and Characterization Methods
regarding the effective refractive index for TE and TM polarization depending on
the width of the waveguide. The effective indices become equal at the critical width
where the mode is circular. Another issue despite achieving a critical polarization
independent waveguide width is the critical bending radius below which no etchdepth can meet the differential loss criterion, as losses for the fundamental modes
also become to high for achieving an acceptable filter performance. In this case, this
radius should not be smaller than 30 μm. The next approach is to realize polarization independent coupling. MMI couplers (see also Sect. 4.1.2) are proposed, which
can be designed for polarization insensitive operation. Finally in adding polarization
independent waveguides and couplers, polarization insensitive ring resonators can
be fabricated.
The idea of polarization independent waveguides and couplers is used in Headley
et al. (2004) for fabricating a racetrack shaped ring resonator notch filter in SOI. A
layout and layer sequence of the waveguide used is shown in Fig. 3.80.
A coupling length of 500 μm and a bending radius of 400 μm are used in realizing
polarization insensitivity within a shift of the resonance peaks of 2 pm between TE
and TM polarized input over a spectral range of four times the FSR of 192 pm. The
devices are covered with a passivating surface oxide after etching of the waveguides
and the coupler, which helps to protect the waveguides during end facet preparation.
The wafers are diced and the end facets are polished and AR coated in order to
minimize Fresnel reflections and to reduce Fabry–Perot resonances inside the device.
One of the first polarization independent filters using a birefringent fluorinated
polyimide overlay (birefringence = 0.11) is presented in Kokubun et al. (2001).
Here a vertical coupling scheme is used together with single mode rib waveguides
for achieving polarization independent operation. The geometry and layer sequence
of the used waveguides is shown in Fig. 3.81.
Fig. 3.80 Layer sequence
and dimension of used
waveguides
Fig. 3.81 Layer sequence
and waveguide dimensions
the refractive indices are
given for a wavelength of
1.55 μm
3.7 Polarization Independence
117
All glass layers are deposited by RF sputtering and patterned by RIE. The polyimide cladding layer is spin coated onto the sample. The RIE parameters are: RF
power (30 W), gas pressure (0.67 Pa), flow rate of CF4 and O2 (10:3 SCCM). An
advantage in using a polymer overlay is that remaining polarization dependence can
be eliminated by UV trimming of the polyimide film, due to the fact that the thickness
of the film can be reduced by more than 20% by UV irradiation while keeping the
refractive index and the birefringence constant (see also Sect. 5.2).
Several methods exist for realizing polarization insensitive devices and as can be
seen, the chosen method again depends on the material system and the device layout
for appropriate polarization compensation.
Now that ring resonator theory and device fabrication have been addressed, the
focus in the following chapter lies on determining the performance of the devices,
therefore possible characterization methods will be explained in Sect. 3.8.
3.8 Characterization Methods
The standard characterization of waveguide based devices usually involves fibers for
in and out coupling of the device, a light source and a detector. Due to the advance in
current fabrication methods, analyzing the performance of ring resonator filters with
regard to where the loss occurs is necessary for improving the manufacturing process
and thus improving the characteristic of the filter. Besides the standard optical fiber
characterization setup, microscope examination, SEM and atomic force microscopy
(AFM) measurements, several methods exist to analyze the performance of waveguide based devices such as cut-back (destructive), Fabry–Perot (requires single mode
lasers) (Park et al. 1995), prism coupling method (requires a minimum length of the
waveguide of several cm), optimum end-fire coupling (OEC) method (Haruna et al.
1992) and many others. The description of some of the mentioned characterization
methods will be done in the following paragraphs.
The main goal of each method is to determine the losses of the device. In order
to compare the loss parameters, a definition for the standard parameters is given in
the following paragraph.
The insertion loss α insertion of the device is the minimum transmission for a specific
wavelength range for all polarization states. It represents the worst possible loss
through the device. The insertion loss uniformity of a device is the difference between
the insertion loss of the best-case and worst-case channels. The insertion loss α insertion
is defined for an input intensity I in and output intensity I out as
αinsertion = −10 · log
Iout
.
Iin
(3.5)
The total insertion losses α insertion includes the intrinsic losses α propagation and the
fiber–chip coupling losses α coupling
αinsertion = αpropagation + αcoupling (dB cm−1 ).
(3.6)
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3 Materials, Fabrication and Characterization Methods
The intrinsic losses can be described by the following equation:
αpropagation
Iout
1
10 · log
=−
+ αcoupling (dB cm−1 ),
L
Iin
(3.7)
where L is the total length of the measured waveguide.
3.8.1 Conventional Characterization
One of the standard setups for the measurement of ring resonator devices is shown
in Fig. 3.82. Here an external cavity laser (ECL) is used as the light source which
is connected via a polarization controller (PLC) and a tapered or lensed fiber to the
input waveguide.
The transmitted signal is detected using for example the lock-in technique
employing a photo diode and a lock-in amplifier. The ECL signal is coupled to
the input waveguide by using for example a tapered fiber, which can be adjusted by
a three axis piezo drive. Tapered fibers are usually used to couple into strong guiding
waveguides and reduce the fiber to chip coupling loss considerably compared to a
standard butt fiber due to the reduction of the mode field diameter which suits the
high index contrast waveguides better than the large field diameter of the butt fiber.
The near field of the output waveguide can then be focused on a photodiode (PD) by
using a microscope lens which has a sufficient aperture to guarantee correct power
measurement. The device under test (DUT) is placed on a Peltier—cooler/heater so
that all measurements are performed at a definite temperature. Instead of using a
microscope lens on the output side, a tapered fiber can again be used to couple light
from the drop or throughput port which is fed to an optical power meter or an optical
spectrum analyzer.
This setup can now be used to extract various device parameters including the filter
characteristic. The coupling losses can for example be calculated from measuring the
Fig. 3.82 Example of a standard optical measurement setup
3.8 Characterization Methods
119
loss of different waveguide lengths of the same device. This internationally recognized reference test method is known as the cut-back technique. The measured insertion loss is plotted against different lengths of the measured devices. The slope
of the obtained curve is determined by the propagation losses of the waveguide.
The coupling losses are obtained from the point, where the extrapolated measurement curve crosses the Y-axis at a device length of zero (unit length). The cut-back
method is a destructive method to obtain the propagation and coupling losses of
straight waveguides.
A nondestructive method which is commonly used is the Fabry–Perot method.
This method has first been introduced in 1978 by Kaminow and Stulz. The chip is
regarded as a Fabry–Perot resonator for waveguide losses <1 dB cm−1 , where the
facets of the chip serve as the mirrors of the resonator. The optical wave is reflected
back and forth within the waveguide. The resulting “filter” spectrum depends on the
intrinsic losses and the reflection factor of the facets. The optical length is changed
by varying the temperature of the whole chip or the wavelength exploiting the group
velocity dispersion. The following calculations closely follow (Regener and Sohler
1985; Feuchter and Thirstrup 1994). The transmission spectrum of a Fabry–Perot
resonator is given by
IT
=
I0 η
1−
T 2 e−αinsertion L
,
2 + 4R
sin2 φ
R
(3.8)
2
The equation for describing the Fabry–Perot resonator is very similar to the one
describing a single ring resonator notch filter. Here It is the transmitted intensity, I0 is
the intensity of the input laser signal, η is the coupling efficiency to the fundamental
waveguide mode, φ = 2βL is the internal phase difference, R is the end-face reflectivity, L the length of the resonator and α insertion the insertion losses of the waveguide.
The contrast K of the Fabry–Perot resonances, which is independent of I0 and η, is
given by
K =
Imax − Imin
.
Imax + Imin
(3.9)
The transmitted maximum and minimum intensities can be described by
Imin =
(1 − R)2 · e−αinsertion L
(1 + R · e−αinsertion L )2
(3.10)
Imax =
(1 − R)2 · e−αinsertion L
.
(1 − R · e−αinsertion L )2
(3.11)
From (3.10) and (3.11) K can be rewritten as
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3 Materials, Fabrication and Characterization Methods
K =
2R
.
2
1+ R
(3.12)
This leads to
= 1 1 −
R
R
1 − K2 .
(3.13)
The value of K is taken from the measurement of the Fabry–Perot resonances.
The maximum value of K is obtained for lossless waveguides. Increasing losses on
the other hand reduces the contrast.
If the end-face reflectivity is known, the insertion loss of the device is given by
αinsertion =
4.34
+ ln R
− ln R
L
(dB cm−1 ).
(3.14)
Equation (3.14) can also be written using I min and I max directly
√
−1 1+ u
1
ln
cm
√ + ln R
L
1− u
Imin
u=
.
Imax
αinsertion =
(3.15)
When the reflection factor of the chip is unknown, it can be calculated from
the insertion loss measurements plotted for different device lengths using (3.14) or
(3.15). The measurement is approximated by a straight line from which the reflection
factor can directly be taken. The slope of the curve is again the value for the intrinsic
losses α propagation of the waveguide, which is given by
√
1+ u
(dB cm−1 ).
4.34 · ln
√ or − 4.34 · ln R
1− u
(3.16)
Another way of calculating the reflectivity of the end faces, which is valid for
weak guiding waveguide structures, is by using:
R=
n eff − 1
n eff + 1
2
.
(3.17)
When the reflection factor is known, the intrinsic losses of the chip are
easily determined without the necessity to cut the waveguide several times for
characterization.
3.8 Characterization Methods
121
3.8.2 Optical Low Coherence Reflectometry
In optical low-coherence reflectometry (OLCR), the output of a low-coherence source
is coupled into an optical fiber and split in a 3-dB coupler as sketched in Fig. 3.83.
It is basically a white light Michelson’s interferometer.
Half of the input signal travels to the DUT, while the other half is launched
into free space towards a mirror on a scanning translation stage. When the optical
path length from the coupler to the mirror equals the optical path length from the
coupler to a reflection in the DUT, the signals from the two arms add coherently
to produce an interference pattern which is measured in the detector arm of the
coupler. When the optical path length difference becomes larger than the coherence
length of the source, this interference signal fades and is lost eventually. Therefore
the spatial resolution critically depends on the coherence length of the light source.
Reflections with a spatial resolution better than 10 μm can be localized. Refractive
index discontinuities less than 10−4 (dynamic range of ≈ −80 dB) in the device can
be detected. The amplitude of the interference signal is proportional to the magnitude
of the reflection from the DUT. Movement of the mirror allows the reflectivity of
the DUT to be mapped as a function of distance, which allows the localization of
waveguide discontinuities and imperfections. To achieve precise control of the fiber
chip coupling and to record the transmission data, the output end of the setup can
be coupled to an infrared-sensitive camera and an optical spectrum analyzer (OSA),
respectively. This setup is referred to as the reflection mode. The reflection mode
setup is used to characterize for example an active–passive butt joint, but can also
be used to measure ring resonator devices without AR coated facets. Due to the AR
coating of the facets, which is applied to most devices incorporating ring resonator
filters, a setup called the transmission mode (Fig. 3.84) is used for the characterization
of ring resonator devices.
A detailed analysis of ring resonator filters using OLCR is presented in Gottesman
et al. (2004). An example of a so called reflectogram of a ring resonator notch filter
without AR coating with a codirectional coupler (length = 150 μm, coupling gap =
0.9 μm) and radius r = 100 μm is shown in Fig. 3.85. The first peak is measured at
the input facet of the device. The second peak (out1 ) is measured at the output facet.
There are no significant reflection peaks in between those peaks coming from the ring
resonator, which shows that the input signal has passed the resonator undisturbed.
Fig. 3.83 Basic OLCR
measurement setup in
reflection mode
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3 Materials, Fabrication and Characterization Methods
Fig. 3.84 OLCR measurement setup in transmission mode
−
−
−
−
Fig. 3.85 Reflectogram of ring resonator with r = 100 μm without AR, measured in reflection
mode
The peaks in between peak out1 , peak out2 , and peak out3 result from multiple
roundtrips in the ring resonator. The distance between the peaks out1–2 is 2 mm
which corresponds to the chip length. The distance between two peaks coming from
the ring resonator is equal to half of the cavity length which is measured to be
≈466 μm (physical value 464 μm).
A reflectogram of a ring resonator notch filter measured in transmission mode is
shown in Fig. 3.86.
The first peak is the transmission passing the coupler without entering the ring.
The second peak is the transmission from one roundtrip in the ring. The third peak is
the transmission from two roundtrips and so on. The roundtrip loss is evaluated from
the transmission data beginning from the second peak. In this calculation the loss
in the straight waveguide is not considered and is contained in the coupling factor
and the roundtrip loss. The length between the peaks is equal to half of the optical
length of the ring resonator. The average optical length (in the ring) is taken from the
3.8 Characterization Methods
123
−
−
−
−
−
−
Fig. 3.86 Reflectogram of ring resonator with r = 100 μm without AR, measured in transmission
mode
measurement (e.g., distance between peak 2 and 3) and is equal to 6171.86 μm. The
measured ring has a resonator length of 1776.64 μm. The group index is calculated
from this data to be ngr = 3.47. This is the average group index which the traveling
light wave experiences when it passes the coupling region, the curved sections and
the straight section in the resonator.
The active–passive transition can also be analyzed using the OLCR measurement.
The result for a straight waveguide with a 500 μm long SOA section, measured in
reflection mode is shown in Fig. 3.87.
-
Fig. 3.87 Reflectogram of a straight waveguide with integrated SOA
124
3 Materials, Fabrication and Characterization Methods
The facets are not AR coated which is shown in the high reflection peaks at the
input and output facets. The return loss from the first butt joint is about −32 dB. The
length of the SOA section can also be taken from the OLCR measurement and is
proven to be 500 μm.
The reflectogram of a single ring resonator with SOA (see inset) is shown in
Fig. 3.88.
The ring resonator has a radius of r = 200 μm, a coupler length of 150 μm
(coupling gap = 1 μm) and a gain length of 100 μm. The return loss resulting from
the butt joint is only −50 dB which indicates a lower reflection than from the straight
waveguide with SOA. This is due to the bending loss in the ring resonator, where part
of the reflected intensity from the butt joint is lost, leading to a lower value for the
return loss. There are again no reflection peaks due to imperfections in the resonator
or straight waveguide which indicates a high quality cavity.
The OLCR method shows only a qualitative indication of the reflection coefficient, because OLCR takes into account the unknown absorption during propagation.
A technique to evaluate the coupling efficiencies and reflection coefficients simultaneously at the butt-joint interface is presented in Song et al. (2005). The technique
described here is based on the Hakki–Paoli method (Hakki and Paoli 1975), which
is widely used to extract the gain spectra of semiconductor lasers and the reflectivity
of the AR coating by measuring amplified spontaneous emission (ASE) spectra.
In summary, the OLCR measurement method enables an insight study of the
quality of the ring cavity and has the potential to efficiently extract all necessary ring
parameters to describe the spectral behavior of the ring resonator configuration.
-
Fig. 3.88 Reflectogram of a ring resonator with integrated SOA
3.8 Characterization Methods
125
3.8.3 Evanescent Field Measurement Methods
Near field techniques have become attractive for optical characterization. Probing
the near field enables to overcome the diffraction limit of conventional microscopy.
Spatial resolutions much smaller than the optical wavelength can be obtained,
approaching λ/50.
Near-Field Scanning Optical Microscopy
Near-field scanning optical microscopy (NSOM) or scanning near-field optical
microscopy (SNOM) which is used as an alternative name is another scanning probe
microscopy (SPM) related technique. An optic fiber is stretched and thinned such
that it has a very sharp point. The fiber is coated with metal such that a small aperture
(approximately 25 nm diameter) is formed at the tip of the fiber. This aperture serves
to illuminate a small spot on the sample which is much smaller than the conventional
diffraction limit. The sample is then scanned beneath the tip and the image is formed
in the same fashion that a dot matrix printer prints a picture. The tip is brought very
close to the surface. The tip–surface distance can be measured via the force acting
between the two. The tip is scanned across the surface as in scanning tunneling
microscopy (STM). NSOM (or SNOM), can detect objects below the diffraction limit
(down to the nm regime) and thus represents a powerful new technique in optical
microscopy. The significance of NSOM is that it allows spatial resolution with more
than an order of magnitude improvement over the best conventional optical methods,
including laser scanning confocal microscopy.
Although optical characterization is the most widespread method to analyze materials from biology to the semiconductor industry, it suffers from one inherent problem:
the diffraction limit provides a spatial resolution limit of about half of the wavelength
of light. Thus, features smaller than 250 nm can not be imaged or spectrally characterized with visible light. NSOM combines scanning probe microscopy instrumentation
with optical microscopy and spectroscopy to provide optical characterization with,
in some cases, 15 nm resolution in using visible light.
One of the first experiments using NSOM to measure the internal optical modes
inside ring resonators with a radius of 25 μm is presented in Vander Rhodes et al.
(2000). The ring resonators which are analyzed are described in detail in Chu
et al. (1999a) and have also been described in Sect. 3.3.2. The setup used in the
NSOM experiment consists of a standard optical measurement setup as described in
Sect. 3.8.1 using a lensed fiber for coupling into the ring resonator, an ECL and a
photodiode at the output port and in addition the NSOM probe, which is fed into an
InGaAs detector to collect the light from the sample. A multimode fiber optic is used
at the output facet of the ring resonator chip which enables the simultaneous monitoring of both the through and drop port of the ring resonator when performing the
NSOM scans. The NSOM probe is scanned over the surface of the waveguide with
a tip–surface separation of 10 nm using an interferometrically calibrated translation
stage to scan the tip with an accuracy of ±0.3 nm. Results of NSOM scans of a ring
resonator are shown in Fig. 3.89.
126
3 Materials, Fabrication and Characterization Methods
Fig. 3.89 Multiple NSOM scans of the ring resonator, stitched together for an image of almost
the entire ring on resonance. Entire scan is 58 μm square: a shows the optical modes, clearly
showing the light coming into the resonator in the upper right, with about half of that light leaving
the resonator at the drop port in the upper left. The launch orientation used here is not especially
efficient in coupling to the drop port, which is why very little light is seen at the drop port in the
upper right and b is topography, with a height difference of 1.45 μm from black to white Vander
Rhodes et al. (2000)
Photon Scanning Tunneling Microscope
Photon Scanning Tunneling Microscope (PSTM) is another configuration of a scanning near field system described before. A PSTM is a device where the object is
illuminated by an evanescent wave generated at the face of a prism or slide and the
field is detected via a fiber probe in the near-zone of the sample (as in NSOM).
PSTM measurements are inherently holographic since the sample is illuminated by
an evanescent field and that same field serves as reference.
The PSTM tips are obtained in a similar way as NSOM probes, by pulling an
optical fiber, coating it with about 7 nm of Cr, which results in no aperture at its
very extremity. The PSTM tip scans at constant height. In this mode of operation,
the signal detected by a PSTM is related to the spatial distribution of the intensity of
the optical electric field in the near-field zone. Ring resonators have been analyzed
using photon scanning tunneling microscopy in Quidant et al. (2004). A photograph
of a fabricated ring resonator is shown in Fig. 3.90.
The used ring resonators are made of a 150 nm thick TiO2 layer (residual roughness
of 3 nm) coated on a glass substrate with a residual roughness of 1 nm by ion assisted
deposition. The waveguides are fabricated using RIE. The dimensions of the ring
resonators are 6 μm in diameter, 250 nm wide and 150 nm high.
In this PSTM experiment, an He–Ne laser (633 nm) injected in a lensed single
mode fiber is used to illuminate the ring resonator. The end of the fiber is oriented
in such a way that the beam can be focused at the interface between the dielectric
3.8 Characterization Methods
127
Fig. 3.90 Scanning electron
microscopy picture of a TiO2
ring coupled with a linear
waveguide ridge. Photograph
courtesy of Dr. Romain
Quidant [ICFO—Institut de
Ciències Fotòniques, Parc
Mediterrani de la Tecnologia,
Av. del Canal Olímpic s/n,
08860 Castelldefels,
(Barcelona), Spain]
ridge and the glass substrate. Only TM polarized incident light is being considered.
The Gaussian beam is focused at the right end of the straight bus waveguide in such
a way that the components of the incident wave vector parallel to the surface of the
substrate align along the longitudinal axis of the bus waveguide. The tip is scanned
at a constant height above the sample surface while monitoring the light intensity
level. A photograph of the resulting image is shown in Fig. 3.91.
Several state-of-the-art characterization techniques have been described. Due to
the decreasing dimensions of ring and disk resonator devices and the increase in
integration density, a combination of several characterization methods is inevitable
in the future to guarantee optimum device performance.
3.9 Lithium Niobate and Hybrid Solutions
Lithium Niobate (LN) is a key material in photonic industries because of its peculiar combination of functional properties and its commercial availability. Although
discovered in the sixties, in the nineties it made its successful in optical communications due to the pushing demand of greater bandwidth as well as the ability
to route signals without complicated electronic interfaces (Lawrence 1993; Wooten
et al. 2000; Wang et al. 2018a, b). As a matter of fact, lithium niobate is an insulator
material benefitting from excellent properties such as high optical transparency in
a wide spectral range (0.33–4.6 μm), high refractive index and birefringence (no
≈ 2.28, ne ≈ 2.20 at 0.63 μm), high electro-optic coefficients (r 33 ≈ 30.8 × 10−12
3 Materials, Fabrication and Characterization Methods
Intensity (arb. units)
0
−4
−2
0.2
0
x (µm)
0.4
2
4
0.6
128
−4
−2
0
y (µm)
2
4
Fig. 3.91 PSTM image recorded above the microring. The probe tip scans in plane parallel to the
sample located at 50 nm from the TiO2 structures. Photograph courtesy of Dr. Romain Quidant
m/V at λ = 0.63 μm) and piezoelectric ones, chemical resistance and even biocompatibility. It is commercially available up to 4 inches wafers, commonly in X, Y,
Z cut configurations, i.e. where the optical axis is parallel to the Z direction and it
is normal to the Z-cut surface. The material is grown by the Czochralski technique
at a very high optical quality. Furthermore, lithium niobate has a high second order
optical nonlinearity (d33 ≈ −33 pm/V at λ = 1.064 μm) enabling parametric wavelength conversion and optical signal generation. It is not by chance that Periodically
Poled LN crystals are commercially available for Second harmonic generation units.
Its properties can be tailored by suitable doping, either locally or in the bulk (Bazzan
and Sada 2015), to increase its resistance to the optical damage or its photorefractivity,
to host active ions or to produce optical waveguides as well.
These features allowed to integrate in this material complex integrated optics
circuits including fiber pigtailed light sources, beam splitters, optical modulation
systems, polarizers and polarizer combiners if needed, signal detection such as a
photodiode or laser-fibre detector system, dependently on the application. Although
widely investigated since the last twenty years, LiNbO3 has still continued to attract
great attention in developing optical components for Integrated Optics (IO) systems
and in the last ten years great advances have been made in realizing LN based microring resonators. Several different commercially available waveguiding configurations
have been realized combining local doping on pure LN crystal and bulk doped ones
(such as Mg-doped LN crystals). Others are promised to become mature in a short
time but are still not commercially available. Local doping by thermal diffusion
and proton exchange are those optimized in LN-based IO devices thanks to their
3.9 Lithium Niobate and Hybrid Solutions
129
scalability and batch processing compatibility. Recently, the combination of several
techniques has paved the way of great improvements in the waveguiding properties
especially for what concerns the optical confinement and mode overlap. In particular
ion implantation combined with etching techniques and local doping, have been
used to get complex but extremely performant devices even in LN thin film bonded
with low refractive index materials. These opportunities have been widely exploited
to get micro-ring resonators with high tunability provided by its high electro-optic
response. In this case local doping was used to realize the optical waveguides whilst
ion implantation was exploited to allow to get thin film as it will be described in the
following sections.
Lithium Niobate Waveguides: Ti-Indiffusion
Ti in-diffusion is one of the most widespread technology to prepare optical waveguides in LN crystals. Thin Ti film are deposited on the material surface and then
thermally annealed under controlled atmosphere. It is compatible with standard
photolithographic techniques to obtain channel waveguides and more complicated
optical circuit configurations such as optical switches, Mach–Zehnder interferometers and optical modulators (Janner et al. 2009), couplers with high coupling efficiencies and large bandwidth around 1.55 μm (Bazzan and Sada 2015). The technology
is so mature that LN-based modulators are commercially available and cover a big
slice of the current market. Ti-indiffused waveguides present significant light confinement on both ordinary and extraordinary refractive indices, allowing both TE and
TM propagation modes and preserving to a good extent the electro-optical properties
of the material. For a conventional Ti:LN waveguide, which is usually fabricated by
diffusion of 6–10-μm wide, ~100 nm-thick Ti-strip at 1030–1060 °C for 9 h, the
surface Ti4+ concentration is around 1021 ions/cm3 and no (ne ) is ~0.006 (0.012)
at the 1.55 μm wavelength, respectively. A sketch of the Channel waveguide process
is reported in Fig. 3.92.
Depending on the Ti content, no lies in the range 0.003–0.01 for Y cut and
0.001–0.01 in Z-cut crystals, whilst ne lies in the range 0.002–0.04 for Y cut and
0.002–0.02 for Z-cut. Its drawback relies mainly on the optical damage induced by
waveguiding high power densities, crosstalk in switches and drift in interferometers,
especially in visible range (that starts to be a limiting factor even below 1 μW at
0.633 μm). For this reason, Ti-in diffusion has been widely exploited in the NIR
region (wavelengths longer than 1 μm, with optimization in the telecom spectral
range). Recent works on the topics, however, have been more focused on the study
of co-diffusion with other dopants to remove or, at least, smooth the optical damage.
Since the Eighties, Ti diffusion in MgO-doped lithium niobate has been widely
investigated, and co-doping with at least 4.9 mol.% of MgO turned to be effective
in suppressing the optical damage effect. Other dopants that have similar effect
are Zn2+ , Sc3+ , In3+ and Tm3+ , Hf4+ , Zr4+ , and Sn4+ but have not been successful
from a commercial point of view. The need to further optimize the growth process
led their use limited to research, being to much expensive so far. Despite of these
limitations, Ti:Zr co-diffused waveguides have demonstrated to support both TE and
TM in single-mode at the 1.5 μm wavelength with losses ≤1.3/1.5 dB/cm for the
130
3 Materials, Fabrication and Characterization Methods
Fig. 3.92 a Scheme of the Ti Channel waveguide realization process; b Ti compositional in-depth
profile; example of Near field Optical mode detected from a 6 μm wide and 2 μm thick channel
waveguide
TE/TM mode, respectively (Zhang et al. 2015). The refractive index at 1.553 μm
was measured to be close the Ti:LN doped sample, i.e. the presence of Zr slightly
affects it with a contribute close to 10−4 for both no and ne .
Lithium Niobate Waveguides: Proton Exchange
As an alternative to Ti in-diffusion, the Ion Exchange technique has been widely
used and in particular the Proton Exchange (PE). PE consists in the immersion of
a lithium niobate specimen into a liquid source of hydrogen at high temperature.
Under these conditions, the replacement of Lithium ions (Li+ ) by hydrogen ions, or
protons (H+ ), causes an increase in the extraordinary refractive index (ne close to
0.1) and, normally, a reduction in the nonlinear coefficients. The waveguide, therefore, supports modes only on the extraordinary polarization. For this reason, proton
exchange has been preferred for every application where propagation is in the visible
spectrum. The most common sources of H+ are the benzoic acid and the toluic acid,
heated at temperatures ranging from 150 to 400 °C (Korkishko and Fedorov 1999). PE
is often followed by annealing in a controlled atmosphere, leading to the so-called
Annealed Proton Exchange (APE) to increase the high polarization rejection and
promote a better resistance to the optical damage as well as to recover the nonlinear
coefficients. For nonlinear optical applications, Soft Proton Exchange (SPE) and
Reverse Proton Exchange waveguides are used when the refractive index jump ne
can lay between 0.01 and 0.03 and better optical confinement is requested (Korkishko and Fedorov 1999). Vapor-phase Proton Exchange (VPE) was also investigated
to combine a strong confinement (ne = 0.09) and preserved nonlinearities, but
difficulties in controlling the fabrication conditions limited its industrial application
3.9 Lithium Niobate and Hybrid Solutions
131
(Tsou et al. 2002). As an alternative, High Vacuum Proton Exchange (HiVacPE) has
been recently proposed (Rambu et al. 2018): it consists in vacuuming the exchange
ampoule to decrease the water content of the acidic bath to the greatest extent. In
this case, a refractive index contrast in X-cut crystals as high as 0.04 was demonstrated with low propagation losses close to 0.16 dB/cm and preserved optical nonlinearity. Different devices already realized in the years 1990–2005, such as modulators,
switches, multiplexers and de-multiplexers (Castaldini et al. 2007; Wang et al. 2007),
Y branches and micro-ring resonators as well (Korkishko and Fedorov 1999). High
quality channel waveguides with propagation losses as low as 0.086 dB/cm and a
coupling efficiency to optical fibers of 90 per cent at 1.550 μm: the splitting ratio
of a set of directional couplers could be predicted with an accuracy of ±0.06. The
combination of PE with other technique was explored to get new configurations as
well: PE LiNbO3 crystals were subjected to 70-meV argon-ion irradiation as well as
performed on photorefractive—resistant substrates such as MgO:LiNbO3, and even
combined with Ti indiffusion, in periodically poled structures and even in Zr:LiNbO3
bulk doped substrate (Langrock et al. 2016).
Lithium Niobate Waveguides: Ion Implantation
Ion implantation is another widespread technology exploited to realize optical waveguides in LN crystals. It consists in bombarding a surface with ions at an impact energy
Eo so that they implant within the material after releasing their energy. In this process,
the energy of the bombarding ion beam is transferred to the crystal lattice by way
of two main processes dependent on the ions’ velocity: energy loss due to electronic excitations and nuclear collision losses. Nuclear collisions induce displacement damage, resulting in the formation of point and/or extended defects responsible
for the refractive index change. Moreover, both the electronic and nuclear processes
tend to create colour centres (optical absorption sites). Consequently, an annealing
treatment is commonly necessary for all the ion-implanted waveguides in crystals in
order to recover the optical properties of the material.
When combined with photolithographic patterning of the surface, this procedure
allows for selective implantation in 2D structures: high resolved patterns can be
achieved by focusing the ion beam down to about 100 nm (Focused Ion Beam, FIB),
as already demonstrated also in LiNbO3 . The first works were published on the Ar+
and Ne+ in the seventies (Naden and Weiss 1984), although He+ -implantation in
LiNbO3 at high fluences (1016 ions/cm2 ) has reported the greater success promoting
a ordinary refractive index with a typical barrier-type profile, whilst the extraordinary
refractive index showed more complex changes. Following the implantation of other
ions at low fluences, such as B, C, O, F, Si, and P, ne was found to be sufficient to
realize high quality guided regions (a review on recent results is in Bazzan and Sada
2015), with good confinement and low losses, around 1 dB/cm. Ion implantation
of Si was exploited as well, realizing monomode optical waveguides and indicating
the potential generality of the method. Waveguides in co-doped Nd (0.3 At.%):MgO
(5 mol.%) X-cut LiNbO3 crystals were also obtained using O ions as well with irradiation in the regime of high electronic stopping power (~5–6 keV/nm) and ultra-low
fluence (2 × 1012 cm−2 ), because of the short irradiation time required. Recently, the
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3 Materials, Fabrication and Characterization Methods
use of swift heavy ion (Ar) irradiation to modify refractive indices of optical materials
was reported for fabrication of single and multimode waveguides at 1.064 μm (Chen
et al. 2017). Surface and cladding-like optical waveguides with thicknesses of ~13,
~36 and ~23 μm at Ar implantation energies of ~120, ~240, and ~(120 + 240) MeV,
respectively have been reported. The modal confinement and the optical losses were
measured together with the second harmonic generation (SHG) at 532 nm with an
efficiency close to 6% at room temperature. In the case of H+ implantation, the values
of the electro-optic coefficients (r13 and r33 ) were well preserved in the waveguides,
independently of the implanted-proton fluence in the investigated range (1–10 × 1016
ions/cm2 ). Even the non-linear d33 coefficients had almost the same value of virgin
LiNbO3 . Olivares et al. studied the SHG of 20 and 22 meV F-implanted LiNbO3
waveguides, and high SHG coefficients were obtained (50–80% of a bulk LiNbO3 ).
Recent advances were reported on Zr:doped LiNbO3 crystals (2 and 4 mol.% of
ZrO2 ), where planar and channel waveguides were fabricated in Z-cut wafers by
the double-energy proton beam implantation at 470 keV (at the fluence of 1 × 1016
ions/cm2 ) and 500 keV (at the fluence of 2 × 1016 ions/cm2 ). The propagation losses
of the channel waveguide were measured close to 3.6 dB/cm. The proton implanted
waveguides in Zr:LiNbO3 crystals showed a relatively high optical damage threshold
at the wavelength of 532 nm, which was one order of magnitude higher than that of
the previously reported ion implanted waveguides in undoped LiNbO3 . It was also
found that the optical damage threshold (9.0 × 104 W/cm2 ) of Zr:LiNbO3 channel
waveguides was much higher than that of the corresponding planar waveguide (2.0
× 103 W/cm2 ).
These promising results of ion implantation have not been enough to let this technology replace Ti-indiffusion, mainly because of the bulky and expensive equipment
required when implantation energies higher than 500 keV are needed. However,
it has become attractive for other applications requiring impact energy lower that
about 200 keV such as the needed for LN micro-structuring approaches such as
smart cutting. As it will be detailed in the following sections, in fact, the nuclear
damaged region become amorphous with different mechanical resistance respect
the surrounded unaltered material. The damaged region can be tailored to become
“cleavage plane”, i.e. the starting point where to exfoliate thin LN film. On the
detached LN film high refractive index contrast stacks can be produced as building
blocks of micro-ring resonators devices.
Lithium Niobate Waveguides: Ridge Waveguide
In combination to the previously quoted technologies, high lateral optical confinement respect to the previously reported cases can be achieved by using the so-called
ridge waveguide configuration. This is a key aspect in the design of micro-ring
resonator where high index contrast must be achieved. Different alternative technologies have been used to design ridge waveguides such as reactive ion etching (RIE),
ion beametching with inert and reactive ions (IBE, RIBE), sputtering with focused
ion beam (FIB) as well as wet chemical etching, ion exchange and ion irradiation
(IBEE: ion beam enhanced etching) respectively. The most widespread is surely
chemical etching, either wet or dry, or by plasma activated processes starting from
3.9 Lithium Niobate and Hybrid Solutions
133
a previously fabricated planar waveguide by conventional processes as those previously described. Most often, a mixture of HF and HNO3 is used on the Ti:LiNbO3 and
LiNbO3 patterned surface by way of chromium (Cr) stripes. Low-loss monomode
ridge guides with a height of up to 8–10 μm and a width between 4.5 and 7.0 μm
were demonstrated by etching Ti-planar waveguides, with propagation losses close
to 0.3 dB/cm for transverse-electric and 0.9 dB/cm for transverse-magnetic polarization, respectively, at 1.55 μm wavelength (Hu et al. 2007). Ridge waveguides demonstrated to have reduced bending losses for small curvature radii, thus improving the
level of integration, and also to reduce the modal sizes, enhancing the efficiency
of non-linear devices, or lowering the threshold in integrated lasers (Brüske et al.
2017). Since imperfections at the edges could strongly affect the propagation losses,
the quality of the ridging process is determinant. However, the propagation losses
were significantly decreased to 0.05 dB/cm by exploiting the proper etching protocol
respect to the Ti-in-diffusion step. New advances in the state of the art were recently
proven by the development of high precision machining: by employing a diamond
blade (optical grade dicing) (Courjal et al. 2011) high aspect ratio ridge waveguides
were demonstrated, with depth greater than 10 μm (Courjal et al. 2016; Caspar
et al. 2018), and used to successfully realize electro-optic modulators. An example
of achievable results by commercially available Diamond blade-slicing technique in
lithium niobate is reported in Fig. 3.93 with optically polished array of ridges with
micron-scale.
It is worth mentioning that an optimized process for fabrication of Ti:LiNbO3
ridge waveguides with propagation losses lower than 0.2 dB/cm was demonstrated,
exploiting waveguide sidewall smoothening during high temperature Ti diffusion
(Gerthoffer et al. 2014).
The turning point in the developing of microring and integrated optics devices
has come from patterning of sub-micrometer wide waveguides and coupling gaps
by way of electron-beam- and laser-lithography as well as electron-beam written
mask for standard UV photolithography. These advanced technologies have reached
a mature level and affordable costs to widespread their use not only in research labs
but also at in industries environment. In general electron-beam lithography systems
have higher resolution than laser writers one. However, the last are more exploited
for fast prototyping of integrated optical devices. Electron-beam written masks to
define high precision photoresist stripes with 1–7 μm width and a thickness close to
1.7 μm have been optimized as etch masks by the Group of University of Paderborn).
Inductively coupled plasma (ICP) etching with Ar-ions has been implemented to
pattern suitable design upon demand. Typical examples of structures that can be
achieved are shown in Fig. 3.94: 500–700 nm LN layers are bonded on 0.7–1.5 μm
thick SiO2 layer on a Z-cut LiNbO3 substrate with final rms surface roughness of
about 0.5 nm. This technology represents the core business to develop high resolved
and precise Lithium on Insulator (LNOI) patterned microstructures, the building
block of microring resonator and new concept ridge waveguides.
A step forward in the accuracy and precision have been also achieved by IBEE
thanks to its high selectivity, independence from the crystal symmetry and short
production times. In this case multiple implantation with different energies and
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3 Materials, Fabrication and Characterization Methods
Fig. 3.93 Top: SEM views of the ridge structures obtained by diamond blade slicing. a Trenches
with a depth of 526 μm. Rights: inserts show zoom views of the thinnest ridge of the serie. b Different
depths can be achieved on the same sample. Bottom: Ridge-based EO device. a Electro-optical ridge
buffer layer with electrodes and spot-size-converters. b SEM image of an EO ridge with vertical
buffer layer and electrodes (Courjal et al. 2016)
Fig. 3.94 Schematic diagram of the cross-section of a LNOI sample (left) used to fabricate photonic
wires by Ar-milling (Hu et al. 2009)
fluences can be used to obtain deep structures with smooth bottoms and vertical
walls (Hartung et al. 2008). For lateral patterning, chromium layer with a thickness around 500 nm and a photoresist layer of 1000 nm standard photoresist were
deposited onto the substrate by means of sputtering and spin coating, respectively.
Using a mask aligner and an electron-beam-written mask, waveguide structures with
different widths could be realized by means of photolithography. Chromium was
3.9 Lithium Niobate and Hybrid Solutions
135
easily etched by standard RIE using a chlorine–oxygen plasma so that IBEE process
can be carried out and be affective of unpatterned regions. Commonly Ar+ ions are
irradiated a different multiple energies (i.e. 60, 150, 350, and 600 keV at suitable ion
fluences) to generate an amorphous layer within the noncovered regions starting at
the surface down to a depth of approximately 450 nm. Amorphous lithium niobate
was then removed by wet etching for 10 min in a 3.7% solution of hydrofluoric acid
at an etching temperature of 40 °C. At this process the ratio of the etching rates of
amorphous and crystalline lithium niobate has been reported to be beyond 1000:1
and the chromium mask was not affected by the etching process. The standardization of this procedure allowed the definition of sharp and accurate structures as those
needed in the microring resonators, with a technology that is commercially available
and largely exploited at industrial level.
In order to get a faster process, compact laser lithography systems have been
tested and let be commercially available. In this case a continuous-wave, frequency
stabilized diode laser (the most common is operating at with 375 nm wavelength) has
been shaped and focused by acousto-optic deflectors to provide a two-dimensional
scanning system. The focused laser beam is shaped at the right spot size on the sample
that can be moved and positioned in a controlled way by three XYZ motorized linear
stages a sample (Koechlin et al. 2009). Channel guides with dimensions in the range
of sub-micrometer widths and heights respectively have been optimized with optical
polishing to enable efficient end-fire coupling of light.
Recently, even fs-laser writing technique has been used to define ridge waveguide
lasers in z-cut Nd-doped LiNbO3 substrates as well as Y-branch waveguiding structures (1 × 2 beam splitters) which reach splitting ratios of ~1:1 at 4 μm in LiNbO3 (Li
2017). Laser ablation was also combined to get ridged waveguide in ion implanted
planar waveguides (Yao et al. 2018) for efficient beam splitters configurations.
High confinement ridge waveguides have been then achieved using smart-cut slab
waveguides and lateral ion milling techniques with a lithographically defined mask.
The thickness of the smart-cut waveguide is normally in the range 0.6–0.75 μm,
and the lateral width was reduced down to 1 μm, with mode field area close to
0.3–0.4 μm2 at 1.55 μm wavelength, i.e. about one order of magnitude smaller than
conventional Ti-diffused waveguides. The optical losses were reported to be lower
than 10 dB/cm for both polarizations. This is of great interest for non-linear optical
application, as it allows obtaining high power densities even at low input powers. It
was already reported that channel waveguides embedded in BCB (n = 1.55) and SiO2
(n = 1.45) can be narrower than 1 μm in order to achieve single-mode waveguiding
at λ = 1.55 μm.
Lithium Niobate Thin Film and Waveguides: Smart Cut
In microring resonators the need of high refractive contrast between the ring and
the environment is a key parameter and, consequently, several attempts have been
made to integrate LiNbO3 films onto lower refractive index structures. Different
136
3 Materials, Fabrication and Characterization Methods
techniques started to be investigated and optimized, including deposition of ferroelectric thin films by molecular beam epitaxy (Betts and Pitt 1985), radio frequency
sputtering (Lansiaux et al. 2001), sol–gel (Yoon and Kim 1996) and chemical-vapor
deposition (Sakashita and Segawa 1995; Saulys et al. 2000) respectively. Despite the
promising results and the clear advantage of having integrated built-in stack configurations, no disruptive advances were reported in the last decade in terms of process
reproducibility. The main limiting factors come from difficulties in achieving high
crystalline quality, the cost and long time of deposition, the level of contaminants or
the final surface quality. It is in this scenario that the so called smart-cut technology
has made its debut. It consists of detaching a thin high quality single crystalline
Lithium niobate slice from the surface of a LN wafer. This thin LN film can be used
as standing alone or bonded on the top of another lower refractive index insulator
substrates i.e. “lithium niobate on insulator” (LNOI) structures. They present high
refractive index, which can be as high as n ~ 0.7 thanks to the LiNbO3 /dielectric
interface (Boes et al. 2018). Called ‘smart cut’ as heritage of the industrial silicon-oninsulator (SOI) wafer fabrication, films produced by this technique preserve basically
the same crystalline properties of the starting material and its high refractive index.
In the bonded configuration, the thin LN layer is sandwiched among lower refractive
index materials to achieve the desired high refractive index contrast stack and provide
for the needed optical barrier. Slab waveguides with superior optical and structural
properties can be therefore achieved with respect to other bottom-up approaches,
such as epitaxial growth, chemical vapor deposition, pulsed laser deposition, sol–
gel, and so on. In order to detach the thin LN slice the best approach is Crystal Ion
Slicing (CIS) technique exploiting the ion implantation as proposed at the end of the
90s by the Osgood’s group. Normally light ions have been exploited such as H and
He, the last being preferred due to its inert activity in the material. In the implanted
layer, He forms so called blisters, i.e. gaseous bubbles (Poberaj et al. 2009, 2012).
At this stage LN thin film can be either exfoliated or lifted-off either by wet-etching
or thermal treatment. Depending on the technique, different bonding approaches have
been used. In the pioneering work of Osgood’s group, Z-cut single crystal LN wafer
was implanted with a 3.8 meV He ions with a fluence of 5 × 1016 at/cm2 . At this condition, a buried amorphous layer was generated at 10 μm below the surface, dissolved
by wet etching with diluted hydrofluoridic acid. It is well known that LiNbO3 has
excellent resistance to chemical attack. As a consequence, the buried amorphous
later could be etched in several hours without impacting on the undamaged LiNbO3
surface quality. With this technique a free-standing LN single crystal membrane
could be obtained with a thickness equal to the implantation range. The eventual
residual damage induced by the ion implantation process can be easily removed by
a thermal annealing process so that to recover the pure single crystal LN linear and
nonlinear optical properties of the starting wafer (Levy et al. 1998; Radojevic et al.
1999). The chemical etching procedures have reached a mature optimization, with
etching selectivity as high as 10,000 (Radojevic et al. 1999) Despite of these results,
wet-etching is suitable for films of several micrometer thick, with thickness that can
vary from the center towards the edges, where the exposure to HF was longer (Levy
and Radojevic 2004).
3.9 Lithium Niobate and Hybrid Solutions
137
As an alternative, uniform sub-micrometer thin LiNbO3 films have been obtained
by the so called thermally induced exfoliation. In this case a thermal treatment at
temperature of the order of 200 °C, is performed to promote the growth of microcavities in the damaged layer. When micro-cracks form, the implanted layer is detached
from the substrate that can be achieved in a controlled way by split-off or exfoliation
(Poberaj et al. 2009). In this way a LN membrane could be realized with desired thickness tailored by varying the ion implanted energy. By tuning the implantation conditions improvements have been achieved since the nineties to arrive to produce 500 nm
thick LN single crystal slices that are now commercially available. With hundred of
KeV light implanted ions, in fact, LN smart cut slices with thicknesses below 1 μm
can be obtained. In order to prepare high refractive index contrast stacks, the smart
cut technology has been combined with wafer bonding. The bonding consists of
pressing one against the other two carefully cleaned and polished surfaces promote
chemical bonding by heating. Bonding is surely one of the most critical steps in
fabrication of large-area thin films. Depending on the materials bonded to LN, the
heating temperature can span from 100 up to 250 °C and the treatment can require
up several hours. A sketch of the process step is presented in Fig. 3.95.
A LN single crystal substrate (LN-A) is ion-implanted to achieve a damaged region
below the surface. Another substrate (LN-B) is deposited with a lower refractive index
(in the figure, SiO2 with refractive index close to 1.45 in the visible range). The
two substrates, adequately cleaned and polished, are therefore bonded by thermally
assisted mechanical pressure. By performing a suitable thermal treatment to recover
Fig. 3.95 Smart-cut technology (Bazzan 2015)
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3 Materials, Fabrication and Characterization Methods
eventual residual damage followed by chemical etching, the cut in two pieces is
achieved at the level of implanted region. A part of the wafer A is therefore sacrificed
whilst the rest is used to produce the high refractive index contrast stack.
Moreover, SiO2 , Si, SiC and polymers have been already demonstrated to be efficiently bonded to lithium niobate and the relative process optimized. More sophisticated configurations have been tested such as embedding a metallic interlayer playing
the role of electrode between SiO2 and LN interface. This has represented a significant improvement allowing the exploitation of the electro-optic properties of the
material even in an embedded LN thin film (Rabiei et al. 2013). The geometry of
the stack has been widely investigated in order to prevent residual strain induced by
thermal mismatch. This configuration requires SiO2 layers of the thickness of about
1 μm. Examples of LN smart cut slices of less than 1 μm are presented in (Sulser
et al. 2009; Geiss et al. 2010).
Among the polymers, excellent results have been achieved by implement the
crystal ion slicing technique in LiNbO3 bonded with benzocyclobutene (BCB). The
BCB binding technique has been described in Sect. 3.1.3 and only applications to
LiNbO3 will be provided in this context. The use of polymer adhesive relaxes the
requirements for flatness, roughness, and cleanliness of the bonded surfaces. Moreover, LN substrate can also be coated with a thin metal layer before the bonding
procedure take place, providing electrodes integration suitable for electro-optically
active devices. Often 50 nm Cr is used as adaptive interlayers to optimize the Au overlayer adhesion. First applied to LiNbO3 at ETH Zurich by Guarino et al. (2007), BCB
has excellent properties such as high transparency in the visible and infrared region
and low refractive index (n ~ 1.55). Best results have been achieved by implanting
a fluence of 4.5 × 1016 /cm2 He+ ions at 195 keV to provide an implanted project
range close to 670 nm (Guarino et al. 2007; Poberaj et al. 2009). The implanted
wafer, cleaned with RCA 1 standard solutions, has been bonded to a 2-μm BCB
layer coated LiNbO3 substrate. Afterwards the sample has been gradually heated up
to 220 °C to strengthen the bonding and to enable the sacrificial layer to split off
the thin film from the donor wafer. The transferred film has been then annealed at
a temperature of 300 °C for several hours to recover any residual defects induced
by implantation. Finally, the surface of the thin film could be smoothened by Ar+
ion etching or mechanical polishing depending on the finitude requirements. This
procedure has resulted in a 600-nm thick LiNbO3 film with an area of >1 cm2 , a
surface roughness of 4 nm (rms), and a high index contrast of n = 0.65. Alternatively, mechanical polishing can be applied to reduce the surface roughness below
1 nm rms. The described procedure enables the fabrication of both X- and Z-cut
LiNbO3 thin films, which are needed for different integrated optics devices (Sulser
et al. 2009). A scheme of the fabrication steps is reported in Fig. 3.96.
Sophisticated structured have been demonstrated with polished edge: 200-nm
thick LiNbO3 film with a 600-nm high ridge waveguide for end-fire light coupling
(see Fig. 3.97) (Poberaj et al. 2009). They have been exploited as a platform for the
first realization of electro-optically tunable microring resonators as well as singlecrystalline LiNbO3 photonic crystal slabs as will be presented in ten following
sections.
3.9 Lithium Niobate and Hybrid Solutions
139
Fig. 3.96 Schematic of the
LiNbO3 thin film fabrication
method. Left: an implanted
He+ substrate of LiNbO3
donor wafer is bonded to
another LiNbO3 substrate
already deposited with Cr
and BCB layers respectively.
Right: a slow-ramp thermal
treatment promotes a strong
bonding, LN film split-off,
and annealing
Fig. 3.97 a Photograph of
an ion-sliced LN thin film
(12 mm × 10 mm × 600 nm)
bonded on a Cr-coated LN
substrate. b Polished edge of
a LN thin film with a
structured ridge waveguide
for end-fire light coupling
(Poberaj et al. 2009)
For completeness, it is worth mentioning that lithium niobate suspended structures
can be achieved as well by combining ion implantation–induced amorphization with
the etching by other microfabrication techniques such as Focused Ion Beam (FIB)
milling. This exfoliation technique has been used to get LiNbO3 membranes with
thickness lower than 1 μm. Apart from being a technology to realize optical waveguide. it has been recently demonstrated as valid alternative to achieve microring
resonators as will be briefly presented in the following section. The typical scheme
representing how FIB milling can be used to achieve suspended structures is reported
in Fig. 3.98.
Fig. 3.98 Fabrication of a suspended waveguide (Bazzan and Sada 2015)
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3 Materials, Fabrication and Characterization Methods
3.9.1 Ring Resonators Based on Lithium Niobate
The development of high performant photolithographic and etching techniques optimized in lithium niobate allowed the realization of complex configurations required
in ultra-efficient integrated photonics circuits, in quantum photonics and optical
communications respectively such as those micro-rings and racetrack resonators.
In general, the possibility to shift the microring resonator resonances by applying
an external perturbation is of high interest. This is especially true when searching
for WDM dynamic filtering, intensity modulation switching and resonance tuning
of a to the optical signal in second-harmonic generation. In lithium niobate it can be
achieved by exploiting its high electro-optic effect to get a fine tuning in the resonance conditions. Two main approaches have been used in lithium niobate to prepare
efficient microring resonators:
• a monolithic approach that requires the direct microstructuring of LN to achieve
high optical confinement in the active region. This type of process has been
normally carried out by etching and have been optimized to reduce the propagation
loss;
• hybrid configurations integrating an easy-to-etch material (such as silicon or
silicon nitride) with LN thin films to guide light with a relatively low propagation
loss (0.3 dB/cm).
In the following the most important achievements will be revised, with special
care devoted to those peculiarities that characterize LN crystals respect other material
and justify why LN based microring resonators needs to be developed, such as the
electro-optic tuning of resonance.
Electro-Optic Tuning of the Resonance Conditions in LN
In electro-optically active microring resonators, the application of an applied electricfield δE changes the effective index of the guided core mode. In this case it is worth
mentioning that the microring resonator’s sensitivity and its electro-optic tunability
do not depend on the size of the ring. As a consequence the constraints on the radius
ring can be relaxed. In the case of lithium niobate crystal, however, one should take
into account the birefringent nature of the material. By applying δE parallel to the Z
axis, the ordinary no and extraordinary refractive index ne of the microring resonator
can be achieved by way of both r13 and r33 electrooptic coefficients. For small δE it
results that the effective refractive index neff varies according to:
∂n eff r33 n 3e
∂n eff r13 n 3o
+
δE
n eff ≈ −
∂n o 2
∂n e 2
(3.18)
Since TE mode is sensitive to the ordinary refractive index only, while the TM
mode is sensitive to both, an acccurate design of the optical waveguides and microring
resonators is needed to achieve the desired performance. In particular, it is necessary
to estimate the applied electric field at the LN stage (δE LN ). It consequently requires
3.9 Lithium Niobate and Hybrid Solutions
141
at least simulations depending on the geometry starting from the external applied
voltage δV using the continuity of the vertical component of the electric displacement
field D. To simplify the description and standardize the way of setting the operational
parameters, an effective thickness d eff is often introduced so that δE LN = δV /d eff .
The shift of the resonance wavelength, due to the induced in modification of the
effective index, therefore results in:
δλ = −
λ ∂n eff r13 n 3o
λ ∂n eff r13 n 3o
∂n eff r33 n 3e
∂n eff r33 n 3e δV
+
δ E LN = −
+
n g ∂n o 2
∂n e 2
n g ∂n o 2
∂n e 2
deff
(3.19)
where ng is the group refractive index. while the tunability T defined as frequency
shift per voltage δν/δV is consequently estimated.
Ring Resonators in LN by Proton Exchange
One of first examples of ring resonators in lithium niobate was presented in 1985
(Mahapatra and Robinson 1985) by exploiting proton-exchanged in Z-cut Lithium
niobate crystals. Thanks to the high refractive index obtained by this doping technique, a ring resonator with a finesse close to 6 at a wavelength of about 790 nm was
reported and as high as 22 at 1.3 μm was achieved with a Rung radius of 1500 μm
operating only along the extraordinary polarization state. In order to achieve this
result, an e-beam was exploited to pattern the suitable on a Cr thin film deposited
on the surface. The patterned sample was then immersed in benzoic acid carried out
at 249 °C for 30 min. A scheme of the ring resonator is reported in Fig. 3.99: at
that time this result was pioneering especially for the realization of resolved bended
Fig. 3.99 A scheme of the ring resonator obtained by proton exchange in LiNbO3
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3 Materials, Fabrication and Characterization Methods
Fig. 3.100 Device structure of a wavelength-tunable microring resonator on LN. Left: scheme of
the index distribution of Ti-diffused ridge waveguide; Right: scheme of the device
microstructures. Relative high losses were deriving mainly by the significant roughness of the optical circuit, limited by the spit size of the e-beam (close to 0.25 μm,
relatively high respect the waveguide width close to 2 μm).
Recently, advances on this topic have been reported by exploiting the annealed
proton exchange (APE) method on LN crystals. By making use of Cr film as electrodes, a tunability of 2 pm/V has been obtained by applying 150 V, getting a measured
extinction ratio is approximately 13 dB (Siew Shawn et al. 2016).
Microring Resonators on Ti-Indiffused LN Crystals
Wavelength-tuneable microring resonators have been realized also on Ti-indiffused
substrate with integrated microheater allow wavelength tuning by way of the thermooptic effect (Wang et al. 2007). In this case ridge structures have been patterned on
the Ti-indiffused waveguide to increase the lateral index contrast and a ring radius
of 100 μm. A scheme for the presented resonator is reported in Fig. 3.100.
The performances of this typology of ring resonators have been tested by varying
the physical parameters such as the ring radius and the current injected in the microheater to achieve wavelength tuning. In particular Zhang and coworkers found that
the FSR curves present a trend that is in agreement with FSR equation relating to
the round-trip length (2π · R + 2 · L) and the effective index of guided mode neff
respectively. In particular this measured FSR in function of R is in coherent with
the FSR equation. Slight mismatch from the fitting curve has been ascribed to the
dependence of neff on the wavelength and microring radius. In lithium niobate the
ordinary refractive index (for TE) is higher than the extraordinary refractive index
(for TM): as a consequence, for TE polarization the authors reported aa smaller FSR
than TM polarization for various microring radiuses. In any case for both polarizations, the resonant wavelength shift approximately has shown a linear increase with
the current. In particular the experimental tuning rates for TM and TE polarizations
has been estimated to be 2.54 × 10−2 nm/mA and 3.40 × 10−3 nm/mA respectively.
3.9 Lithium Niobate and Hybrid Solutions
143
It is worth citing that the corresponding currents values required for the resonant
wavelength shift of FSR value have been settled to be 55 and 400 mA.
Microring Resonators by Ion Implantation in LN Crystals
Fluorine ion implantation has been combined with high-ridge planar structuring to
realize sub-100 μm radius microrings on Z-cut LiNbO3 wafers (Majkic et al. 2009).
Ridge geometry allowed efficient optical confinement of transverse-electrically (TE)
polarized waves. Planar waveguides were first produced by implantation of fluorine
ions into the Z-cut LiNbO3 wafers at room temperature, at implantation energy equal
to 14.5 meV and fluence of 2.5 × 1014 ions/cm2 respectively. Single-mode waveguides with a thickness of 1.35 μm and separated from the substrate by a 2 μm wide
optical barrier have been therefore produced. Post annealing at 300 °C allowed to
recover the crystal properties after the implantation and was followed by a photoresist deposition. After the deposition and the sub-μm gap between the microring and
waveguide was granted by patterning the photoresist with laser writing and then
transferring the pattern on the implanted substrate by Ar+ sputtering, producing
microrings with radius R = 80 μm, 3.2 μm width and 1.2 μm height. To perform
electro-optic tuning, the Cr/Al lower electrode was deposited in close proximity to
the microring outer rim, whilst the upper electrode above the microring. A buffer
layer of PVA was used to optically isolate the waveguides from the upper electrode.
A scheme of the realized microring resonator is reported in Fig. 3.101.
The device was fully characterized at a wavelength of 1.5 μm showing optical
resonances with a modulation depth of 11 dB, separated by a 2.0-nm FSR for TE
waves. Resonances were not observed with TM polarized light, presumably due to
smaller index contrast and higher propagation losses.
Fig. 3.101 a Optical micrograph of the microring resonator device, prior to applying the PVA
buffer layer and the upper electrode. MR: microring; BW: bus waveguide; CR: coupling region;
LE: lower electrode encircling 88% of the ring. b Microring waveguide cross-section, simulated
optical intensity profile of the first TE mode (light gray), and the equipotential lines (1-V separation)
upon application of an electrode voltage difference of 10 V (black) (Majkic et al. 2009)
144
3 Materials, Fabrication and Characterization Methods
Fig. 3.102 a Measured TE wave transmission spectrum of the fabricated microring resonators.
b Measured transmission spectra upon applying a bias voltage of 10, 0, and 10 V on the electrodes.
Marked points represent: (1) maximum-slope point, (2) maximum transmission, and (3) minimum
transmission upon applying a 10-Hz sinusoidal modulation voltage (Majkic et al. 2009)
The final performances can be summarized as follows: electrooptical tunability
of 10 pm/V, full-width at half-maximum spectral width of 0.5 nm and a measured
microresonator’s FSR of (2.03 ± 0.02) nm respectively. the modulation depth at the
strongest resonances was 14 dB. The resonator finesse was F = = 4 ± 0.4 and the
corresponding quality factor Q = 3100 ± 300 (Majkic et al. 2009). The measured
TE wave transmission spectrum of the fabricated microring resonators is reported in
Fig. 3.102. It is worth mentioning to recall that the resonance shift depends on the
change of the effective index but is independent of the resonator’s perimeter L =
2π r. Thanks to the LN birefringence and the ring’s axial symmetry, in the proposed
configuration the δneff for TE waves depended mostly on the vertical component of
the applied electric field (Ez ) and with approximation only electro-optical coefficient
r13 could be considered.
Zhao et al. fabricated ridge waveguides on lithium niobate using implantation of
O+ ions combined with Ar ion beam etching, reporting 2 dB of losses.
Microring Resonators by Argon-Milling (ICP-Etching)
Micro-ring resonators with coupling waveguides have been efficiently realized by
exploiting the Argon Milling (ICP-etching) technique described in Sect. 3.9. A typical
result of a microring with a coupling waveguide is reported ion Fig. 3.103. The
micro-structuring process has been achieved by the laser lithography system in a
negative-tone photoresist film deposited on a LiNbO3 crystal. Coupling gaps, as
narrow as 200 nm width, have been realized by a double step lithography process
where initially a coupling waveguides have been written in the photoresist film by
moving the sample with the translation stages followed by the photoresist developing
and hardening. In a second step, a second lithography process has been added on
a newly deposited photoresist film and the rings in order to achieve fine written
3.9 Lithium Niobate and Hybrid Solutions
145
Fig. 3.103 Scanning
electron micrographs of a
microring resonator with a
coupling waveguide:
a photoresist mask on a
LiNbO3 wafer written by the
laser lithography system;
b final structure transferred
onto a LiNbO3 crystal
surface by Ar+ ion
ICP-etching (Ar-milling)
(Poberaj et al. 2009)
structures by accurate and precise steering of the laser beam by way of the acoustooptic deflectors. The final structure transferred onto a LiNbO3 crystal surface by
Ar+ ion ICP-etching (Ar-milling) respectively, bringing a microring with a coupling
waveguide on a LiNbO3 that after after Ar+ ion etching has an etching depth of about
400 nm.
Ring Resonators in LN: Performances Comparison
In the following table a comparison among the performances of LN based micro-ring
devices is reported. The previously quoted fabrication techniques as well as some
key design parameters are listed such as the operating wavelength, the ring radius
together with the λFSR and the best value achievable. The data have been taken
from the references already cited in the previous sections for further details: it is
worth mentioning that the waveguide propagation losses are highest in the case of
crystal ion slicing and the best values are achieved in Ti-indiffused case. λFSR is
below 2.0 nm even if 4.0 has been demonstrated in F implantation (Table 3.8).
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3 Materials, Fabrication and Characterization Methods
Table 3.8 Properties of LN based microring resonators
Fabrication
technique
λ [μm]
n
Curvature
radius [μm]
Prop. losses
[dB/cm]
λFSR [nm]
Max. λ∗FSR
[nm]
Proton
exchange
0.79
~0.01
1500
1.4–4.2
0.027
~0.1
Titanium
indiffusion
1.5
≤0.04
100
–
1.42
1.0
Fluorine
implantation
1.5
0.17
80
7.8
2.0
4.0
Crystalion
slicing
1.5
0.65
100
17
1.66
14
Although these results could have been considered promising but still in the need
of improvement, LN crystals can be exploited also in other configurations such as
thin slices on insulators. In this case the performances have been drastically increased
and the real potentialities of LN have been exploited. In the following sections details
on ring resonators based on lithium niobate on insulators will be therefore provided.
3.9.2 Ring Resonators Based on Lithium Niobate
on Insulators (LNOI)
The first demonstration micro-resonating device based on a LNOI structure have been
published since 2007, with the pioneering work of Guarino and coworkers (Guarino
et al. 2007). They were able to demonstrate a LN based microring resonator with a
radius of 100 μm whose tunability can be driven by the electrooptic effect. To achieve
this result, they realized LN thin films by implanting z-cut lithium niobate wafers
with He+ ions followed by bonding to another lithium niobate wafer, covered by a
metallic electrode and a benzocyclobutene (BCB) layer of approximately 2.5 μm
thickness as described in the previous sections. This planar structuring method of
BCB-bonded LNOI samples is suitable for high-density integration on a single chip
and therefore has been later optimized. However in the initial work of Gaurino, Ar+
ion etching has then exploited to reduce the film thickness to about 60 nm. Rings and
waveguides were then realized by standard photolithographic techniques to achieve
a 0.4 μm ridge structure. To reduce scattering looses and guarantee a good optical
insulation between the chromium electrode and the core so that the applied electric
field could be considered parallel to the z-axis, a 0.85 μm-thick SiO2 layer was
finally deposited to cover the above mentioned device. A scheme of section of the
LN microring resonator is reported in Fig. 3.104.
In particular a straight waveguide was integrated as well at a distance (gap) of
0.2 μm from the ring. An image of the final devices reported in Fig. 3.105.
An example of the achieved transmitted spectrum and relative geometry is
presented in Fig. 3.106 at λ = 1.55 μm for both TE (electric field direction mainly
3.9 Lithium Niobate and Hybrid Solutions
147
Fig. 3.104 Schematic
cross-section of an
electro-optically tunable
microring resonator based on
BCB-bonded LN
Fig. 3.105 Structured lithium niobate microring resonator. Scanning electron microscopy images
of a lithium niobate microring resonator with radius R = 100 μm and b zoom of the coupling region
between the waveguide and the ring. The gap size is approximately 0.2 μm (Guarino et al. 2007)
Fig. 3.106 Transmission spectrum of a 100 μm-radius ring resonator. The measured normalized
transmitted light at the through port for both TE (left) and TM (right) modes using a tunable source
in the λ = 1.55–1.57 μm region is shown. The free spectral range is 1.66 nm and the finesse 5. The
modulation depth is approximately 7 dB (Guarino et al. 2007)
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3 Materials, Fabrication and Characterization Methods
parallel to the film) and TM (perpendicular to the film) polarisations of the waveguide
respectively. An extinction ratio at the resonant wavelengths close to 7 dB, a free
spectral range of the resonator of about λFSR ≈ 1.66 nm has been found. The
resonator finesse was approximately F = λFSR /δλFWHM ≈ 5 and the corresponding Q value is Q = 4 × 103 . This value is probably limited by implantationinduced defects and scattering losses. The propagation losses were measured to be
approximately 4 cm −1 .
This LN based ring resonator was characterized by a high-refractive index contrast
in the stack (n ≈ 0.65), requiring stringent geometrical conditions to a single mode
propagation such as a waveguide width ≈1 μm. At that time the technology was
not optimized not easy to be achieved). It was however demonstrated that a 4 μm
multimode waveguide could be used because of high losses of higher modes than
the fundamental mode propagation. In the configuration presented by Guarino and
coworkers, low bending losses have been obtained. Simulations suggested that they
remain negligible even at ring radii as low as 10 μm. The electro-optical shift of the
resonance curve is reported in Fig. 3.107 showing λ = 105 pm-shift in response
to an applied voltage of V = 100 V, corresponding to a frequency tunability of
0.14 GHz/V.
As an order of magnitude, for δV = 100 V a TM tunability of 0.3 GHz/V and
TE tunability 0f 0.1 GHz/V are expected and have been experimentally confirmed
in a LN based microring resonator with a radius of 100 μm. Similarly resonance
shifts of the order of 100 pm and 30 pm have been measured for TM and TE mode
respectively (Guarino et al. 2007).
Disruptive advances in the lithography procedures have been achieved by
exploiting laser lithography instead of standard mask alignment techniques. This
approach allowed to overcome the initial limitations encountered that somehow
constrained the microring radius to be not less than 100 μm.
By using laser lithography, only two years later the pioneering work of Gaurino,
Koechlin and coworkers in Koechlin (2009) demonstrated that the optical waveguides
Fig. 3.107 Electro-optic
shift of the resonance curve.
Resonance curve at a
wavelength around 1.555 μm
(blue) and the corresponding
electro-optically shifted
curve (red) by applying a
voltage V = 100 V to the
device electrodes. The shift
corresponds to an
approximate tunability of
0.14 GHz/V (Guarino et al.
2007)
3.9 Lithium Niobate and Hybrid Solutions
149
surface quality could have been strongly improved allowing the realization of smaller
curvature radii. They have been able to realize racetrack microring resonators with a
curvature radius of 20 μm and a 10-μm long coupling region with a gap of 200 nm
has been reported. In this case transmission measurements showed that a FSR value
of 7 nm can be achieved as well as a quality factor Q of around 10,000. Finally a
Transmission resonance dip with a width of 0.15 nm (FWHM) at a wavelength of
1544.8 nm (Poberaj et al. 2012).
The micro-resonators milled in LNOI samples (Diziain et al. 2015) have been
realized. LNOI wafers consisted of a 750 nm thick Z-cut LiNbO3 membrane bonded
on a 1200 nm thick SiO2 layer deposited by plasma enhanced chemical vapor deposition (PECVD) on a LN substrate. The argon ion beam etching has been used to thin
the sample (as an order of magnitude, the etching rate of LN is around 10 nm/min for
an Ar + beam with an energy of 400 eV and a current density of 0.3 mA/cm2 ). The
gross removal of material to get the final disk configuration have been then finely
tuned by scanning the FIB on the LNOI surface and achieve a precise ring shape.
With this two-steps approach, two types of self-suspended micro-resonators have
been prepared: a Photonic Crystal (PhC) cavity in a 373 nm thick LiNbO3 layer and
a micro-disk in a 512 nm thick membrane respectively.
Devices using 600 nm thick X-cut LN thin films on 2 μm of silicon dioxide (SiO2 )
on silicon substrates have been proposed by Zhang et al. (2017). They used a standard
electron beam lithography to define patterns in hydrogen silsesquioxane (HSQ) resist
with multipass exposure. The patterns were then transferred into the LN thin film by
commercial reactive ion etching (ICP RIE) set-up. LN etching was perfomed with an
Ar+ plasma to get a ridge configuration eith a final height of hrib = 350 nm of LN with
a hslab = 250 nm thin LN slab. After cleaning and removal of the resist, the devices
have been cladded by depositing 1.5 μm of SiO2 using plasma-enhanced chemical
vapor deposition (PECVD). The final configuration therefore achived is depicted in
Fig. 3.108.
Fig. 3.108 a Scanning electron microscope (top) and optical microscope (bottom) images of
a microring and micro-racetrack resonators of various lengths. Inset: Close-up of the etched
waveguides. b Simulated optical modes in straight and bent waveguides (Zhang et al. 2017)
150
3 Materials, Fabrication and Characterization Methods
Fig. 3.109 a Resonance linewidth in the best devices is as narrow as 38 MHz, corresponding to
loaded QL = 5 × 106. The laser is modulated by a precise frequency source at 500 MHz for
calibration. Inset: Transmission spectrum in logarithmic scale indicating that the resonator is nearly
critically coupled. b Ring-down measurement of the same device. c Measured quality factors for
different resonators on several chips. d Extracted propagation loss for racetrack resonators. All the
measurements are conducted around 1590 nm (Zhang et al. 2017)
Despite of the high values of Q-factor, as depicted in Fig. 3.109, the proposed
configuration was still suffering from sidewall scattering losses. As the same authors
underlined, increasing the waveguide width from 800 nm to 2.4 μm can lead to a Q
improvement from ~1.5 to ~4 × 106 when the reduced interaction of the light and
the etched sidewalls can be achieved, basically connected only to improvements in
preparation procedures.
Recently, all-pass microring resonators have been monolithically integrated in Zcut LNOI from small, low-loss, high-index contrast and single mode C-band waveguides (Krasnokutska et al. 2019). Multiple rings with radii ranging from 30 to 90 μm
have been proposed to obtain an FSR from 1.5 to 5.7 nm respectively. To achieve
these results, a 500 nm thick LN film by smart-cut technique on 2 μm of SiO2 layer
and supported by a 500 μm LN substrate have been produced. By way of electron
beam lithography and lift-off of the e-beam evaporated metal layer, a hard mask
defining the photonic components have been obtained. The components underwent
a dry etching in a reactive ion etcher and, afterwards, optical waveguides have been
cladded with 3 μm SiO2 thick film realized by plasma-enhanced chemical vapor
deposition (PECVD). The rib waveguide cross-sections, have been designed via
3.9 Lithium Niobate and Hybrid Solutions
151
focused ion beam (FIB) slicing and scanning electron microscopy (SEM). A final
sidewall angle of 75° and an etch depth of 350 nm have been finalized: optical grade
dicing has been added as a final step in order to optimize the butt-coupling. A 6 mm
chip has been therefore produced: the total input and output coupling and propagation loss is 8 dB have been obtained thank to the mode matching between the lensed
coupled fiber and the waveguide made with linear inverse tapers from 200 μm down
to 200 nm wide tips (Fig. 3.110).
The simulated and measured performances of the Q value are reported in Fig. 3.111
in both TE and TM cases respectively in function of the ring radius as well as examples
of the spectral response. In general, a Q-factor of ~9000 was achieved for the TM
mode whilst for the TE mode the Q-factor is ~1200. As the radius of the ring increases,
the Q-factor for TM mode remains almost unchanged (Krasnokutska et al. 2019).
As far as the FSR values is concerned, as shown in Fig. 3.112, it lays in the range
between 1.6 and 5.5 depending on the ring radius. Highest values are achieved when
r is lower than 30 μm.
In order to exploit the electro-optic effect of the material, a Cr/Al (20 nm/500 nm)
electrode has been deposited directly on the upper cladding of the waveguide, with
Fig. 3.110 a Simulation of Q-factor as a function of the coupling region gap for a 30 μm radius
microring—the light red dashed lines demarcate the simulated Q-factor (~10,000) for the microring
shown in (d). b Design of a single mode LNOI rib waveguide at 1550 nm wavelength; the top width
is 650 nm, the bottom width is 840 nm and the waveguide height is 350 nm. Scanning electron
microscope pictures: c cross-section taken by FIB slicing and SEM imaging; d an etched 30 μm
radius ring with a 300 nm gap between the bus waveguide and the ring prior to PECVD SiO2
cladding; e false-color image of the coupling region after the lift-off process and prior to etching;
the false-red highlights the metal etch mask (Krasnokutska et al. 2019)
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3 Materials, Fabrication and Characterization Methods
Fig. 3.111 a Simulation of Q-factor as a function of the coupling region gap for a 30 μm radius
microring—the light red dashed lines demarcate the simulated Q-factor (~10,000) for the microring.
b Measured Q-factors of the ring resonators versus their radius for the TE and TM modes. The blue
curve corresponds to the TE mode and the red curve corresponds to the TM mode. c Spectral
response of the ring with radius 30 μm for TM mode. d Spectral response of the ring with radius
90 μm for TE mode (Krasnokutska et al. 2019)
3.9 Lithium Niobate and Hybrid Solutions
153
Fig. 3.112 a Measured FSR as the function of a microring resonator radius for the TE mode and
d for TM mode; the blue circles are measured values, whilst red line is theoretically predicted
dependence of FSR on microring resonator radius; b the simulated electrical field distribution for
the TE mode and (e) for the TM mode; c measured optical power distribution at the output of the
chip for the TE mode and f for the TM mode, where black lines schematically show the actual
waveguide dimensions (Krasnokutska et al. 2019)
a separation gap of 3 μm to prevent optical loss. The bottom electrode, serving as a
ground plane, is made from Cr (10 nm), Au (100 nm) and Cr (10 nm) respectively. By
applying a DC voltage inn the range [0; −55] V across the top and bottom electrodes
of the microring resonators, the resonance shifts with the applied voltage have been
determined with an average EO tunability of 3 ± 0.04 pm/V. Microrings with radii
≥60 μm experience a DC voltage bias offset meanwhile, rings with radii ≤50 μm
have a constant tunability of ~3 pm/V even at lower voltages (<10 V) (Fig. 3.113).
The microring design was tailored depending on the radius: in the case of 30 μm
microring resonator small bending loss were needed requiring high-index contrast
single mode waveguides at 1550 nm. To obtain wide bandwidth resonances, a geometry with a 300 nm gap was chosen and get high overcoupling conditions in the rings.
This is a strategy commonly used to relax the need of a very fine wavelength tuning. In
the particular case they obtained a 3 dB resonance badwidth. The Q-factor measurements have shown that it is possible to achieve small and high performance microring
Fig. 3.113 a Simulation results of electrical field. b Spectrum of the optical resonances of a 70 μm
when voltage from −55 to 0 V is applied. c Shift in resonance of a 50 μm microring resonator when
−10 V is applied (Krasnokutska et al. 2019)
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3 Materials, Fabrication and Characterization Methods
resonators for the TM mode—critical for electro-optic and nonlinear applications.
On the contrary, the TE mode bending losses can significantly limit the Q-factor of
the smaller radius microring resonators. In this case in fact the index contrast of the
TE fundamental mode is lower than that of the TM fundamental mode. It is important to underline that in this type of microring resonator Voltage bias offsets can be
present, even as high as 50 V in microring resonator with radius close to 50 μm.
Respect other polymers, BCB has been played the role of a key factor: apart from
his low refractive index (n ≈ 1.55), high transparency in the visible and infrared
region, it presented excellent adhesion and easiness to be flatted.
Recent results obtained by the group of Loncar at the Harvard University demonstrated quality factors of up to 107 , thanks to Ar+ plasma etching to physically sculpt
micro-resonators from lithium niobate films that were 600 nm thick and grown on
a 2 μm-thick SiO2 wafer. By etching a total of 350 nm of lithium niobate they left
behind a 250 nm-thin lithium niobate slab and were able to prepare an integrated
waveguide-coupled micro-ring and racetrack resonators with a bending radius of
80 μm and various “straight arm” lengths and waveguide widths. The optical Qfactors of this devices using a tuneable telecom external cavity diode laser and the
propagation losses of less than 3 dB/m allows light to propagate across a metre-length
path while only losing about half their optical power. The advances obtained respect
the previous lithium niobate devices is definitively significant because the previous
ones lost more than 99% over the same distance. This opens up a wide range of applications, including ultralow-loss quantum photonics, coherent microwave-to-optical
conversion and active topological photonics (Zhang et al. 2017).
Finally even the laser writing technique has very recently demonstrated suitable
to design an integrated optical ring resonator to be implemented in LiNbO3 with a
2.5 mm radius and an operating wavelength of 1550 nm (Pagano et al. 2020). A free
spectral range of 71.54 pm and a quality factor of ~5 × 105 were achieved. In this
sense, the suitable determination of a splice angle (in this case 1.44°), shape and
length for segments demonstrated to be key parameters in the ring design. For this
purpose, an ad hoc software was implemented and in summary, a 250 sided polygon
side showed a suitable coupling performance and established a new layout approach
for middle range rings.
It is worth mentioning that the so called self-suspended micro-resonators patterned
in Z-cut lithium niobate on insulator substrates have been also proposed as hybrid
configuration. In this case the fabrication technique consists of two single steps,
focused ion beam milling for the micro- and nano-structuring and subsequent SiO2
etching for the realization of thin self-suspended membranes. The fabrication process
of a free-standing photonic crystal cavity and a suspended micro-disk is described and
the linear and nonlinear optical properties of the micro-resonators are investigated
at telecommunication wavelengths. The whispering gallery modes of the micro-disk
are measured experimentally and compared to an analytical model. The fundamental
transverse-electric polarized mode of the photonic crystal cavity is measured and
compared to three dimensional finite difference time domain simulations. Second
harmonic generation enhancement due to the field confinement in the cavity mode
is demonstrated. These results are promising for the use of Z-cut lithium niobate
3.9 Lithium Niobate and Hybrid Solutions
155
Table 3.9 Comparison between different types of tunable rings (Krasnokutska et al. 2019)
Material
Radius of a ring (μm)
FSR (nm)
EO tuning (pm/V)
SOI PN junction30
7.5
8000
12.6
26
SOI on LN with
integrated electrodes31
15
11,500
7.15
12.5
SOI on LN32
15
14,000
7.15
3.3
A1N33
60
500,000
n.a.
0.18
X-cut LNOI34
n.a.
50,000
n.a.
7
Z-cut LNOI35
100
4000
1.66
1.05
Z-cut
LNOI36
Q-factor
50
2800
3.2
2.15
Z-cut LNOI (this work) 70
7500
2.5
3
self-suspended membranes as platforms for highly efficient miniaturized photonic
devices for telecommunication applications.
In Table 3.9 a comparison between microring resonator achieved in LNOI on both
X and Z cut microring resonators is reported respect other technologies. Although
silicon has reported very high tuning with large FSR, it is worth mentioning that the
optical transparency for this material prevents its application in some spectral ranges.
Recent works in hybrid Si on LN have been proposed to solve this problem but still
requires extra fabrication steps that complicate the fabrication procedures. For these
reasons LNOI photonics presents a promising alternative for getting tunable ring
resonators as complementary tools to silicon based devices.
Further refinements have been achieved developing new receipts. Either advance
plasma etching combinations techniques as well as femtosecond laser have been
successfully implemented. Despite the more complicated receipts they optimized
the final results especially to face the know limitation of ion beam etching. It can
inherently leave behind a surface roughness on the order of a few nanometers, which
can limit the final Q-factor of a freestanding LN microdisk to ~106 recently been It
has been proposed to proceed with a first patterning a chromium (Cr) thin film coated
on the top surface of LNOI into a hard mask with a femtosecond laser, followed by the
chemo-mechanical polish (CMP) for structuring the LNOI into the microdisk (Wu
et al. 2018). The CMP lithography (CMPL) can enable ultrahigh performance LNOI
photonic structures, opening the venue toward large scale, low loss, reconfigurable
PICs for numerous applications. The performance of on-chip integrated photonic
structures has approached that of the bulk optics fabricated in traditional ways such
as polishing and coating (Wu et al. 2018) (Fig. 3.114).
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3 Materials, Fabrication and Characterization Methods
Fig. 3.114 Schematic of the fabrication flow of the chemo-mechanical polish lithography.
a Depositing a thin layer of Cr on the top of the lithium-niobate-on-insulator (LNOI) wafer.
b Patterning the Cr layer by femtosecond laser ablation to form a hard mask. c Conducting chemomechanical polishing (CMP) on the sample to transfer the pattern from the Cr mask to the LNOI.
d Chemically removing the remaining Cr mask and performing a secondary CMP to further smooth
the sidewall near the top surface. e Schematic illustration of the CMP principle and the instrument
(Wu et al. 2018)
3.9.3 Ring Resonators Based on Lithium Niobate
on Insulators in Hybrid Configuration with Nitrides
and Semiconductors
Hybrid configurations to couple semiconductors, glass compounds, polymers and
other crystals such as lithium niobate have proven to be extremely advantageous to
overcome some specific problems that are material-dependent. Among those solutions free standing microrings BCB bonded LNOI with nitrides stacks have been
proposed (Poberaj et al. 2012).
As a matter of fact thin-film LiNbO3 on insulator has recently proved as a
promising alternative to achieve lower mode areas boosting the electro-optic efficiency. In this frame of reference, monolithic LN nanophotonic circuit has been
addressed as the new challenge of high-speed modern telecommunication and in
hybrid platforms where an easy-to-etch material (e.g. Si and SiN) is used as a device
layer bonded to non-etched thin LN films. These heterogeneous platforms are very
promising and for this reason great efforts are currently made to optimize them
in order to get the best compromise between electro-optic bandwidth, modulation
efficiency, optical confinement and operating wavelengths respectively.
3.9 Lithium Niobate and Hybrid Solutions
157
LN Hybrids with Nitrides
Starting from the BCB bonding procedures already presented in the previous section,
hybrid solutions have been realized coupling LN rings to nitrides. In this case LN
rings have been obtained by fully etching BCB/LN structures until the BCB layer
interface. In this way isolated microrings have been obtained, laying on the top
of the substrate free to be moved and transferred onto any other host substrate.
They have been therefore placed and aligned with high accuracy and precision using
submicrometer positioning actuators.
By using this approach LiNbO3 microrings coupled to gallium nitride (GaN) have
been achieved with small radius (close to 20 μm). GaN has been chosen because
its low absorption in the near infrared wavelength range and a good refractive index
matching with LiNbO3 respectively. The vertical structure LN/GaN showed a good
refractive index match, optimized by using a sapphire substrate covered with a 100nm thick layer of SiN and waveguides (Koechlin et al. 2010). Koechlin and coworkers
(2010) have demonstrated that free-standing LiNbO3 microring with a radius of
20 μm, positioned on a straight GaN waveguide can be achieved. The widths of the
coupling waveguide and of the microring have been settled to 1.1 μm and 3.0 μm,
respectively, both structures having a height of 600 nm (Kochlin et al. 2010). These
authors characterized the polarized transmission. The transmission spectrum has
shown as sharp resonance dips with a linewidth of 0.15 nm FWHM and an extinction
ratio of up to 18 dB, separated by a FSR = 7.9 nm at 1.55 μm respectively. These
types of structures have demonstrated to have a finesse close to 53 and quality factor
Q 10,000 and propagation losses close to 17 dB/cm for the zero-order TE mode in
the LiNbO3 microring. The measured resonance dip was found at 1555.28 nm with
a linewidth of 0.15 nm FWHM and an extinction ratio of 18 dB.
Both standalone and other hybrid LiNbO3 platforms such as Si-LiNbO3 , Si3 N4 LiNbO3 ) have been also demonstrated to be very active (Boes et al. 2018). Si3 N4 LiNbO3 have attracted great attention because of good index matching, high mode
confinement inside LiNbO3 (Jin et al. 2016; Zhang et al. 2017) as well as ultralow
propagation loss of Si3 N4 , high power handling capabilities. Last but not least,
Si3 N4 has insulating properties, and a wide optical transparency window. Passive
devices have been optimized in Si3 N4 -LiNbO3 -based structures made low loss optical
waveguides and vertical mode transition structures from Si3 N4 to LiNbO3 material
and push–pull Mach-Zehnder interferometer (MZI) modulation. As far as microring
resonators, recent advances have been confirmed with the first hybrid Si3 N4 -LiNbO3 based tunable microring resonator where the waveguide has been formed by loading
a Si3 N4 strip on an electro-optic (EO) material of X-cut thin-film LiNbO3 (Ahmed
et al. 2019). A sketch of the realized structure is reported in Fig. 3.115.
The hybrid Si3 N4 -LiNbO3 microring exhibited a high intrinsic quality factor
of 1.85 × 105 , with a ring propagation loss of 0.32 dB/cm, resulting in a spectral linewidth of 13 pm, and a resonance extinction ratio of ~27 dB within the
optical C-band for the transverse electric mode. Using the electro-optic effect of
LiNbO3 , a 1.78 pm/V resonance tunability near 1550 nm wavelength has been finally
demonstrated. In Fig. 3.116 a sketch of the preparation procedure is reported.
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3 Materials, Fabrication and Characterization Methods
Fig. 3.115 a Schematic of the tunable hybrid Si3 N4 -LiNbO3 micro-ring resonator with integrated
electrodes (not drawn in scale). b Simulated TE mode field profile of a hybrid Si3 N4 -LiNbO3 waveguide formed by a 200 nm × 1.2 μm Si3 N4 loading strip at 1550 nm. c Simulated bending loss as a
function of bending radius for the TE mode. The bending loss is presented as decibel (dB) per 90°
bend (Ahmed et al. 2019)
Fig. 3.116 a SEM image of the bilayer lift-off process. b SEM image of the microring coupling
section. c SEM image of a hybrid Si3 N4 -LiNbO3 microring with a bending radius of 300 μm,
waveguide thickness of 200 nm, and waveguide width of 1.2 μm. The inset shows the zoomed
section of the boxed region (Ahmed et al. 2019)
3.9 Lithium Niobate and Hybrid Solutions
159
Fig. 3.117 Hybrid microring resonator characterization. a The measured transmission spectrum of
the passive microring at the through port for TE mode using a tunable laser near the 1550 nm. The
free spectral range is 0.58 nm, and the resonance extinction ratios are up to 27 dB. b The Lorentz
fitting (red curve) of the resonance dip at 5 1551.98 nm, which corresponds to an intrinsic Q of 1.83
× 10. c The resonant spectra as a function of the applied voltage for TE mode at wavelengths near
1551.410 nm (black curve) of a micro-ring resonator; the red and blue curves are the corresponding
electro-optically shifted curves by applying a voltage of −50 V and 50 V to the device electrodes,
respectively. The measured tunability is 1.78 pm/V. d The resonant wavelength shift as a function
of the applied DC voltage (Ahmed et al. 2019)
Some results of this integrated microring resonator is depicted in Fig. 3.117.
In this case the measured transmission spectrum of the passive microring at the
through port for TE mode using a tunable laser near the 1550 nm is shown. The free
spectral range is 0.58 nm, and the resonance extinction ratios are up to 27 dB. The
resonant spectra as a function of the applied voltage for TE mode at wavelengths
near 1551.410 nm are presented together with the corresponding electro-optically
shifted curves by applying a voltage of −50 V and 50 V to the device electrodes,
respectively.
LN Hybrids with Semiconductors
As already pointed put in the previous sections, the crucial technological step to
realize an Integrated Optics Circuit and in LNOI and photonic devices in general
relies on the way used to pattern LiNbO3 thin films. Recent advances on this topic
come mainly on the exploitation of optimized techniques and protocols to achieve
a better resolution, an improved surface and cut edge quality. On this framework
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3 Materials, Fabrication and Characterization Methods
of reference, femtosecond laser, chemo-mechanical polishing for patterning waveguides have recently demonstrated to provide better results in the LNOI realization.
To this aim even Si-LN and Si/LNOI structures have been proposed to improve integrated ring resonators. In particular Hybrid silicon and LiNbO3 electro-optical ring
modulator operating at gigahertz frequencies consisting of a 15 μm radius silicon
microring and an ion-sliced LiNbO3 thin film bonded together via benzocyclobutene
has been successfully achieved (Chen et al. 2014). A sketch of the proposed device
is reported in Fig. 3.118. A Scanning electron micrograph of the silicon microring
resonator after slab patterning and doping is reported in Fig. 3.119.
These devices have been operating in the TE optical mode and exhibited an optical
loaded quality factor of 14,000 and a resonance tuning of 3.3 pm/V respectively (Chen
et al. 2014). In particular an electrical-to-optical 3 dB bandwidth has been measured to
be 5 GHz together with a digital modulation with an extinction ratio greater than 3 dB
demonstrated up to 9 Gb/s. High-speed and low-tuning-power chip-scale modulators
that exploit the high-index contrast of silicon with the second-order susceptibility of
LiNbO3 have therefore achievable. Optical transmission measurements were carried
out to characterize the electrical tuning of optical resonances. TE-mode light from
Fig. 3.118 Schematic of the hybrid silicon and LiNbO3 ring modulator (Chen et al. 2014)
Fig. 3.119 a Scanning electron micrograph of the silicon microring resonator after slab patterning
and doping; b top-view optical micrograph of the fabricated device (Chen et al. 2014)
3.9 Lithium Niobate and Hybrid Solutions
161
Fig. 3.120 Measured optical
transmission of a single
resonance as a function of
applied voltage (Chen et al.
2014)
a tunable infrared continuous-wave laser source has been therefore coupled through
the input and output fiber-to-chip cantilever couplers of the modulator. DC voltage
was consequently applied to the top electrode of the modulator while the bottom
electrode is grounded. An example of the measured optical transmission of a single
resonance as a function of applied voltage is reported in Fig. 3.120. The total optical
insertion loss were found to be close to 4.3 dB. The resonance shift is 66 pm for a
change in DC bias from −10 to 10 V can be there seen indicating 3.3 pm/V tuning,
which is equivalent to a V π L of 9.1 V cm. The measured quality factor is 14,000,
the FWHM is 13.7 GHz, and the group index is 4.0. At 1551.856 nm, the optical
transmission intensity varies by 5.2 dB with a −5 to 5 V voltage swing, as indicated
by the dashed arrow (Chen et al. 2014).
3.9.4 Microring Modulators Based on Lithium Niobate
and Chalcogenide Glasses on Silicon
Chalcogenide glasses are amorphous materials containing at least one of the
chalcogen elements such as Se, Te and S. Although they have been mainly used
in optical memories and IR lens systems thanks to their thermal stability, and transparency to a large range of wavelengths. Waveguide structures in chalcogenides have
been already been demonstrated as well as applications in nonlinear optics. Although
some constraints in achieving high confinement has been initially evidenced in the
past due to the low refractive index, chalcogenide glasses appeared to be attractive
to create hybrid solutions. In this frame of reference, the first feedback optical filter
fabricated in ring shaped As2 S3 on LN crystals has been proposed. Vertically integrate
waveguides with a core material of As2 S3 , a chalcogenide glass with a refractive index
of 2.4 compared with 2.2 for LN have been therefore obtained with low-loss bend
radii of the order of 100 μm by Solmaz and coworkers. The mode confinement has
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3 Materials, Fabrication and Characterization Methods
been adjusted between the As2 S3 and the LN materials by varying the As2 S3 waveguide thickness and width (Solmaz et al. 2009). Lithography and reactive-ion etching
have been exploited to design the final configuration, where standard Ti-indiffused
waveguides have been deposited with 470 nm thick As2 S3 by RF magnetron sputtering. The fiber-to-fiber insertion loss of a typical waveguide is 2.5 ± 0.5 dB. A
protective layer of SiO2 and Ti is covered on the chalcogenide thin film to prevent
dissolution of As2 S3 in photoresist developer. Contact photolithography has been
used to pattern on the titanium and a subsequent reactive-ion etching step forms the
As2 S3 ring structure. The taper design helps to reduce the effective index mismatch
between the Ti-diffused and the As2 S3 waveguides and thereby increase the coupling
into the ring. The taper length of 750 μm together with a ring diameter of 581.6 μm
together generated a final circumference of 4.827 mm and free-spectral range (FSR)
of approximately close to 25.4 GHz, with a calculated power coupling ratio and
roundtrip loss are 10.6% and 2.08 dB, respectively, for TM polarization respectively.
Other heterogeneous microring modulators based on lithium niobate and chalcogenide glasses on silicon have been realized by bonding on silicon substrates and
rib-loaded with a chalcogenide glass Ge23 Sb7 S70 . Single-mode submicron waveguides and microring modulators in the telecom C band have been made by using
400-nm-thick film of Y-cut LN bonded to a 2 μm thick layer of SiO2 on a Si substrate
to form the slab region of the ridge optical waveguide. The LN thin films were then
rib-loaded with a 0.35 μm × 1.3 μm strip of index-matched chalcogenide to get a
single-mode waveguides at 1550 nm wavelength. Bending losses could be considered negligible in this geometry thanks to the high radius of the microring modulator.
The crystal orientation of the lithium niobate thin film has been chosen to utilize the
highest electrooptic coefficient of LN, r 33 = 31 pm/V: the microring modulator have
been designed for a tunability of 3.8 pm/V. A final performance of 1.2 dB/cm waveguide propagation with quality factor close to 1.2 × 105 has been achieved, with a
tuning rate equal to 0.4 GHz/V and 13 dB extinction ratio respectively. A scheme of
the realized structures is depicted in Fig. 3.121 (Rao et al. 2015), together with the
section of the device.
Fig. 3.121 Schematic of the new platform depicting the chalcogenide (ChG) rib, lithium niobate
(LN) core slab, lower optical cladding of silicon dioxide (SiO2), silicon substrate (Si), and the gold
metal electrodes for: a microring modulators; b optical TE mode profile at 1550 nm—the thin gold
stripes are the 100-nm-thick regions of the gold electrodes (Rao et al. 2015)
3.9 Lithium Niobate and Hybrid Solutions
163
Fig. 3.122 a Measured transmission spectrum (blue) around one under-coupled microring resonance, and the corresponding theoretical fit (red). b Measured transmission spectrum (blue) around
one critically coupled MRM resonance and the corresponding theoretical fit (red). c Measured
transmission power spectrum of the critically-coupled MRM devices. d Optical modulation (green)
following the electrical drive signal (blue) at sub-kHz frequencies. The drive signal clipping observed
is a measurement artefact from the limitation of the measurement range of the oscilloscope used,
and doesn’t affect the extraction of any parameters from the measured data (Rao et al. 2015)
These responses have been obtained at wavelength in the range 1530–1565 nm:
in the case of 200 μm radius, these devices were under-coupled to minimize the
coupling loss. It is worth mentioning that the propagation loss of 1.2 dB/cm in the
LN waveguides rib-loaded with ChG is significantly lower than those observed on
Ta2 O5 microring modulators that showed instead loss of 5 dB/cm (Rabiei et al. 2013).
The critically-coupled microring modulators have a lower loaded Q of 8.6 × 104 , an
unloaded Q of 1.26 × 105 , and a maximum potential extinction ratio of over 15 dB.
The measured transmission spectrum under-coupled microring resonance as well as
around one critically coupled MRM resonance are reported together wit the optical
modulation in Fig. 3.122.
3.10 Microring Modulators in LN, LNOI and Hybrids:
Limits and Improvements
The optimization of the final performances needs to look after every constraint and
verify what can be improved and what instead represents and intrinsic limit. Several
studies have been made on this topic, the most comprehensive has been very recently
made by Bahadori et al. (2020). In a microring resonator, it is expected a high impact
164
3 Materials, Fabrication and Characterization Methods
of the curvature of microring/race-track resonators on the electro-optic tuning with
a coefficient so-called the filling factor. Bahadori and coworkers have calculated this
contribute depending on the crystal cut. By referring to Fig. 3.123 for the reference system and geometries therein considered, the electro-optic perturbation under
rotation is summarized in Table 3.10.
In Fig. 3.123 in fact it is shown the rotation a straight waveguide and its side
electrodes by an angle ϕ respect the crystal axis (in this case Y-axis). It results that
the applied lateral DC field still strongly interacts with the transverse electric (TE)
Fig. 3.123 Schematic of a straight LN waveguide with two electrodes on the side. The applied DC
field between the two electrodes is exactly in the extraordinary direction of the crystal. Under the
rotation, the applied DC field is no longer in the extraordinary direction. The 1, 2, 3 axes are aligned
with the LN crystal coordinate system such that axis 3 is the extraordinary direction (optic axis).
The axes under rotation by ϕ are denoted by 1 , 2 , 3 (Bahadori et al. 2020)
Table 3.10 Derived relations for the electro-optic perturbation under rotation for the LN crystals
Electro-optic perturbation under rotationa
(0)
Crystal
n eff (φ)/n eff
X-cut
cos3 φ +
2
22
2
33
r22
r33
sin φ +
Y-cut
cos2 φ +
2
11
2
33
r13
r33
cos φ sin2 φ
Z-cut
1
r23
r33
cos φ sin2 φ
It is worth noting that in this derivation the impact of rotation of the DC [ε] tensor on the applied
DC field inside the LN waveguide has been ignored. DC field is exactly aligned with the Z-axis, the
dielectric tensor [ε] corresponds to the dielectric perturbation tensor [ε] (Bahadori et al. 2020)
a
11 = 22 = 4.889 = o (ordinary, optical). 33 = 4.569 = e (extraordinary, optical). r13 =
r23 = 8.6 pm/V, r22 = 3.4 pm/V, r33 = 30.8 pm/V Z-cut assumes a vertical DC field
3.10 Microring Modulators in LN, LNOI and Hybrids: Limits and Improvements
165
mode of the waveguide although the r 33 coefficient cannot be fully harnessed to
produce maximum net electro-optic effect.
It clearly emerges that electrodes are closer to the waveguide, guaranteeing a
higher optical confinement of the TE mode and the reinforcement of the interaction
between the TE optical mode and the lateral DC electric field respectively (Bahadori
et al. 2020). This configuration has proven to have a significant impact when X
and Y cut LN based microring resonators devices because of the stronger electrooptic perturbation effects under the same applied voltages. Instead, the electro-optic
performances of Z-cut waveguides are not improved by the rotation of the waveguide
and the electrodes. It is worth mentioning that in Z-cut waveguides TM modes are
commonly used to achieve high electro-optic effect. In this case electrodes are placed
at higher vertical distance above the waveguide hence limiting the strength of this
perturbation due to the lower optical confinement of TM modes (Bahadori et al.
2020). Their work has shown also that the upper bound of the filling factor for a singlepair electrode arrangement in a microring modulator is ~0.25 which is achieved
when the electrodes are symmetrically extended by 90° about the extraordinary
direction. In general, a microring modulators have shown to present an upper bound
on their electro-optic performance (~50% filling factor) corresponding to a specific
arrangement of metal electrodes surrounding the microring. In the case of lithium
niobate, it yields nearly identical results for X-cut and Y-cut designs although this
limitation does not exist (i.e., 100% filling factor is possible) with Z-cut microring
modulators. It is worth mentioning that filling factor ~100% is achievable in Xcut and Y-cut modulators provided that a race-track configuration with segmented
electrodes is set-up. By exploiting the crystal properties of the material, it is possible
to optimize the design and consider the effect of the so-called rotated configuration.
These effects of the electro-optic performances are impacting on the final
microring response but can be overcome by a suitable tailoring of the resonator
design. Some studies have been performed to propose new configurations, as depicted
in Fig. 3.124 (Bahadori et al. 2020).
In this case of a microring resonator with one electrode inside and another electrode outside of the ring is reported. The tuning efficiency can be estimated by
quantifying the shift in the resonance λres , that in this case is given by:
λres =
EO
· FSRnm
2π
(3.20)
where is the variation in the phase shift (λ), and EO stands for Electro-Optic.
Due to the curvature of the microring resonator and electrodes (in Fig. 3.125a)
it is clear that the applied DC field inside the ring deviates from the extraordinary
direction when moving along the ring from the angle ϕ = 0. As reported in Bahadori
et al. (2020), the total induced electro-optic phase shift is given by
EO
2π
·R
=
λ
φ1
n eff (φ)dφ
φ0
(3.21)
166
3 Materials, Fabrication and Characterization Methods
Fig. 3.124 a Schematic of a microring resonator in Y-cut LN. The curvature of the ring and
electrodes causes the applied DC field inside the LN waveguide to deviate from the extraordinary
direction (3 axis). b Electrode arrangements for X-cut or Y-cut microring modulators with arbitrary
extent originated from the extraordinary axis, and c its filling factor (Bahadori et al. 2020)
That corresponds to a tuning efficiency:
λres
=
VDC
λres n (0)
eff
·
ng
VDC
· ff
(3.22)
It is worth mentioning that, as underlined by Bahadori et al. (2020), the term in
parentheses is equivalent to a uniform electro-optic perturbation in the extraordinary
direction.
λres n (0)
eff
·
(3.23)
pEO =
ng
VDC
Similarly to a straight waveguide at the state of zero where: rotation, this term
represents the impact of the curvature of microring/electrodes. The so-called filling
extent of the electrodes (i.e., the fraction of the microring exposed to electro-optic
perturbation) is given by:
3.10 Microring Modulators in LN, LNOI and Hybrids: Limits and Improvements
167
Fig. 3.125 a Symmetric extension of electrodes about the ordinary axis and b its filling factor.
c Symmetric extension about the extraordinary axis, and d its filling factor
1
f f (φ0 , φ1 ) =
2π
φ0
φ0
n eff (φ)
n (0)
eff
dφ
(3.24)
By taking in to account these equations and the results summarized in Table 3.11.
The filling factors for X and Y configuration can be estimated in function of θ. It
results that the maximum possible value for the filling factor is 0.253 for X-cut and
0.246 for Y-cut (Bahadori et al. 2020). This result fixes a basic constraint in the
curvature of the microring resonators and the relative electro-optic performance in
X-cut or Y-cut thin-film LN platform respectively.
In Table 3.11 a summary of performances in terms of tunability actually achievable by microring modulators based on thin-film lithium niobate have also been
quoted in Bahadori et al. (2020). Although the X-cut and Y-cut modulators showed
to suffer from rotation effects as previously quoted, they provide higher electrooptic tunability for the resonance respect other microring configurations. In the case
of Z-cut structures, only hybrid systems have been suitable alternatives for a good
tunability.
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3 Materials, Fabrication and Characterization Methods
Table 3.11 Literature review on the demonstrated tunability of X-cut, Y-cut, and Z-cut microring
modulator (Bahadori et al. 2020)
Author
Structure type
LN type
Mode
Tunability (pm/V)
Ahmed et al. [23]
Hybrid LN/SiN
Zhang et al. [24]
Partially etched LN
X-cut
TE
2.8
X-cut
TE
Rabiei et al. [16]
Hybrid LN/Ta2 O5
X-cut
4
TE
4.5
Chen et al. [25]
Hybrid LN/Si
X-cut
TE
3.3
Wang et al. [4]
Partially etched LN
X-cut
TE
2.4
Wang et al. [10]
Partially etched LN
X-cut
TE
7
Ahmed et al. [26]
Hybrid LN/SiN
X-cut
TE
1.78
Rao et al. [9]
Hybrid LN/Sia
Y-cut
TE
3.2
Mahmoud et al. [15]
Partially etched LN
Y-cut
TE
0.32
Chen et al. [21]
Hybrid LN/Si
Z-cut
TM
12.5
Wang et al. [27]
Partially etched LN
Z-cut
TM
1.565
Guarino et al. [20]
Partially etched LN
Z-cut
TM
1.05
Lee et al. [7]
Hybrid LN/Si
Z-cut
TE
2
Siew et al. [28]
Partially etched LN
Z-cut
TM
2.15
Krasnokutska et al. [19]
Partially etched LN
Z-cut
TM
3
Reprinted under Common Creative License
a With chalcogenide glass
Examples of devices that can be therefore obtained and provide for excellent
compromises are reported in Figs. 3.126 and 3.127. In the first case a modal electrooptic efficiency of about 2.26 × 10−5 V−1 and pEO close to 15.64 pm/V.
The following chapter deals with the building blocks of ring resonator devices
which include bends and couplers.
3.10 Microring Modulators in LN, LNOI and Hybrids: Limits and Improvements
169
Fig. 3.126 a Cross-section of the LN waveguide with its dimensions listed in the inset table.
b Electrode arrangement used in the X-cut microring structure. The two pairs of electrodes have
reverse polarity; hence each pair contributes a filling factor of ~0.24 and the overall filling factor is
~0.48. c COMSOL simulation for the DC E-field distribution for V DC = 1 V. The DC E-field inside
the LN waveguide is almost horizontal. d COMSOL simulation of the fundamental TE00 optical
mode of the waveguide (electric field). e Calculated optical effective index and f group index of the
waveguide. g Change of effective index under different voltages (Bahadori et al. 2020)
170
3 Materials, Fabrication and Characterization Methods
Fig. 3.127 a Schematic of a race-track resonator with a single pair of electrodes in X-cut or Y-cut.
b Schematic of a race-track resonator with two pairs of electrodes. c X-cut microring modulator
with double-pair electrodes under rotation. d Calculated filling factor under rotation showing an
optimal angle of 17°. e Race-track modulator under rotation. f Normalized filling factor for the
race-track resonator under rotation (Bahadori et al. 2020)
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Chapter 4
Building Blocks of Ring Resonator
Devices
Ring resonator devices comprise a bus waveguide and a ring which is made out of
bend waveguides in the basic configuration. The material used for realizing the ring
resonator filter already imposes restrictions onto the waveguide type and thus on the
performance of the ring resonator. It is therefore important to analyze the building
blocks of the envisaged ring resonator with respect to the wanted performance of the
filter in advance once the material has been chosen.
The part where the bus and the ring come close to one another can be regarded as
a coupler, also in the basic configuration, where the interaction path (coupler length)
of the optical field in ring and coupler is extremely short. The performance of the
ring resonator depends on the power coupling factor as one parameter besides several
other factors already discussed in previous chapters. Several coupling schemes can
be applied including vertical couplers, directional couplers, MMI couplers and Ycouplers. A detailed summary of the simulation and design of directional couplers and
MMI couplers also with respect to polarization dependence is presented in Darmawan
et al. (2005).
In order to fabricate ring resonators with low loss, it is essential to know the
bending loss of the waveguides which depends directly on the used bending radius,
which supplies the FSR of the ring resonator filter if this type of waveguide is used
for fabricating the ring.
A fact which should be taken into account in the designing stage is the coupling
of the bus waveguides to the outside world. Here several concepts exist like tapering
the waveguides in vertical, horizontal (or both) directions to match the mode field
profile of the bus waveguides to an optical fiber.
This chapter provides an introduction into the various building blocks making up
a ring resonator filter.
© Springer Nature Switzerland AG 2020
D. G. Rabus and C. Sada, Integrated Ring Resonators, Springer Series
in Optical Sciences 127, https://doi.org/10.1007/978-3-030-60131-7_4
179
180
4 Building Blocks of Ring Resonator Devices
4.1 Couplers
4.1.1 Directional Couplers
An important device used to couple light into and from ring resonators is the directional coupler. This type of coupler is preferably used to realize splitting ratios other
than 3 dB. One of the first papers to deal with directional integrated optical couplers
is presented in Marcatili (1969b).
Directional couplers have been studied extensively in the past and have found their
way into many integrated optical devices like for example optical switches (Forber
and Marom 1986) and vertical coupler beam splitters (Raburn et al. 2000).
The well-known equations which describe the input and output field of the coupler
shown in Fig. 4.1 are given by
E3
E4
1
= (1 − γ ) 2
√
√ 1 − κ −j κ
E1
√ √
.
·
E2
−j κ 1 − κ
(4.1)
The relation between the in- and output intensity of a symmetrical directional
coupler is given using
I3
I4
1−κ κ
I
= (1 − γ )
· 1 ,
I2
κ 1−κ
(4.2)
where γ is the power loss coefficient, κ is the power coupling factor. If both waveguides have the same propagation constant which is the case in this configuration and
the light is inserted into input port 1, then after a length L c the energy will have
coupled into the other waveguide and can be detected at output port 4.
The coupling behavior dependent on L c for light inserted at input port 1 is
expressed by
π
x ,
2L c
1
π
E 4 (x) = j E 1 (1 − γ ) 2 sin
x ,
2L c
1
E 3 (x) = E 1 (1 − γ ) 2 cos
I3 (x) = E 3 (x) · E 3 (x) and I4 (x) = E 4 (x) · E 4 (x).
Fig. 4.1 The directional
coupler
(4.3)
(4.4)
(4.5)
4.1 Couplers
181
Fig. 4.2 Coupling behavior
of a symmetrical directional
coupler
The coupling behavior for a coupler with L c = 450 μm, E 1 = 1, E 2 = 0 is shown
in Fig. 4.2. The intensity at both output ports is normalized to the sum of the output
intensities
Intensity at output port 3 =
I3
I3 + I4
(4.6)
Intensity at output port 4 =
I4
I3 + I4
(4.7)
The power coupling factor κ is taken from the diagram (Fig. 4.2) for a specific
coupling length x.
For example, the power coupling factor κ is equal to κ = 0.9 for a coupler with a
length of 360 μm.
The separation between the waveguides in the directional coupler is the critical
element regarding the fabrication. The resolution of the photolithography used (standard photolithography using a quartz/chromium mask, electron beam lithography,
etc.) defines the minimum coupling gap. The fabrication of the gap depends mainly
on the waveguide width and the etch depth in the gap. An example of a fabricated
coupler is shown in Fig. 4.3. The etch depth in the gap is lower in this example than
on the outer side of the coupler waveguides, which is due to the lower etch rate in the
gap. The dry etching process is strongly dependent on the etch gases and conditions
used and has to be modified if performed with other RIE systems to achieve similar
results.
Integrated optical devices require directional couplers to provide the desired power
splitting ratio, independent of wavelength or polarization. In wavelength division
multiplexing systems, where ring resonator add drop filters are deployed, it is necessary to achieve a constant splitting ratio for all used wavelength channels. It is often
impossible to achieve broadband polarization-insensitive performance, especially
in planar integrated devices, unless several design consideration are incorporated
and tradeoffs taken into account as is explained in Sect. 3.7. A wavelength- and
polarization-insensitive directional coupler configuration is demonstrated in Little
182
4 Building Blocks of Ring Resonator Devices
Fig. 4.3 SEM photograph of
the input region of a
directional coupler, gap =
0.8 μm
and Murphy (1997) and Murphy et al. (1999). Design rules towards polarization
insensitive directional couplers employed in ring resonator filters are discussed and
presented in Chin (2003).
4.1.2 Multimode Interference Couplers
A multimode interference (MMI) coupler consists of a broad center waveguide which
supports several modes depending on the width and the layer sequence of the waveguide (Fig. 4.4). The self-imaging principle is used in MMI couplers for realizing
various coupler configurations including a 2 × 2 coupler to be used in ring resonator
devices. Self-imaging is a property of multimode waveguides by which an input
field profile is reproduced in single or multiple images at periodic intervals along the
propagation direction of the guide (Soldano and Pennings 1995).
Between these intervals, the input field is reproduced with only a fraction of the
input intensity, divided symmetrically in the multimode section. A SEM photograph
of the input region of a 2 ×2 MMI coupler is shown in Fig. 4.5.
An atomic force microscope (AFM) photograph of the input region of an MMI
coupler is shown in Fig. 4.6 (Rabus 2002). The gap between the two input waveguides
is 2.4 μm.
The main advantage of MMI couplers compared to directional couplers is the
fabrication tolerance with respect to the splitting ratio which can be for example
3-dB in the case of 2 ×2 couplers used in ring resonators. If other coupling ratios
Fig. 4.4 Top view of an
MMI coupler
4.1 Couplers
183
Fig. 4.5 SEM photograph of
the input region of a 2 ×2
coupler
Fig. 4.6 AFM picture of the
input region of an MMI
coupler (Rabus 2002)
are required, directional couplers are favored. The multimode section should support
more than three modes to assure an appropriate interference signal of the input mode.
Finite difference time domain or beam propagation tools (Weinert and Agrawal
1995) are needed to calculate the behavior of MMI couplers which are commercially
available.
The fundamental beat length of MMI is related to the waveguide parameters
(step-index MMI section) by Soldano and Pennings (1995):
Lπ =
π
4n eff · w2
∼
,
=
β0 − β1
3λ0
(4.8)
184
4 Building Blocks of Ring Resonator Devices
where β 0 and β 1 are the propagation constants of the fundamental and first order
lateral modes, respectively, λ0 is the wavelength, neff is the effective index and w is
the width of the multimode section.
The 3 dB length of MMI couplers can also be approximated by the formula given
in van Roijen et al. (1994):
L 3 dB =
λ0
3
n eff · w2
≈2
,
4 n eff0 − n eff1
λ0
(4.9)
where λ0 is the wavelength, neff0 and neff1 are the effective indices of the fundamental
and first order mode.
The usage of short couplers with defined splitting ratio is essential in ring
resonators for achieving a high FSR due to a short roundtrip length. One of the
first fabricated MMI couplers on InP having the shortest length at that time of only
107 μm for a 3 dB coupler are demonstrated in Spiekman et al. (1994). The width
of the MMI is only 9 μm. A ridge waveguide design is used with an InGaAsP core
with a bandgap wavelength of 1.3 μm and a thickness of 600 nm. An InP cap having
a thickness of 300 nm is grown on top.
Extremely short InP–InGaAsP MMI 3-dB couplers with lengths between 15 and
50 μm are presented in Ma et al. (2000b).
Ring resonators ideally require a tunable coupler in order to adjust the coupling
factor to the roundtrip loss in the case of passive resonators and to realize specific
filter characteristics in the case of multiple coupled ring resonators. MMI couplers
with a tunable splitting ratio are demonstrated in Nagai et al. (1999), Leuthold and
Joyner (2000, 2001) and Jiang et al. (2005). MMI couplers are usually fabricated
in semiconductor materials which enable the realization of strong guiding waveguides. Recently MMI couplers are proposed using weak guiding structures (West
and Honkanen 2005) and fabricated in polymer materials (Mule’ et al. 2004; Rabus
et al. 2005b).
4.1.3 Y-Couplers
Y-couplers are a well-known class of integrated optical devices and have been used
in several integrated systems to guide and manipulate light. Quite a lot of research
has been performed on digital optical switches (DOS) in polymers using cascaded
Y-couplers to create integrated 1 × N splitters (Bernhard 2002; Hauffe 2002). An
example of a Y-coupler is shown in the schematic in Fig. 4.7.
This example of a Y-coupler comprises single mode waveguides for in- and out
coupling with width w, a taper and a coupling region. The taper region is designed
in such a way, that the width at the end is slightly less than 2 times the width of a
single mode waveguide. This assures, that only the fundamental mode is allowed to
propagate in the beginning of the taper and in the end into the two output waveguides
and not the next higher mode which would cause additional losses, as it is not
4.1 Couplers
185
Fig. 4.7 Schematic of a
symmetric Y-coupler
supported by the geometry of the single mode waveguides. In the coupling region,
both output waveguides have to be treated using coupled mode theory to describe
their behavior. This region is of importance when it comes to design a symmetric
Y-coupler with equal power splitting in both output arms. If the angle α is chosen
too small, power from one arm is able to couple to the other one being the cause for a
different splitting ratio than intended. On the other hand making the angle too large
causes additional losses. Therefore, a tradeoff has to be found for realizing a specific
Y-coupler. Usually S-bends are used to separate the output arms and realize a certain
distance between them. Due to manufacturing tolerances like proximity effect and
etching, a sharp branching angle is not achieved in most cases and a compromise
has to be made to find the optimum angle. An example of a fabricated Y-coupler in
polymers is shown in Fig. 4.8 (Rabus et al. 2005b).
Y-couplers have found their way into ring resonators for example in ring lasers,
where they have been specially designed to increase the output power. An example of
an improved Y-junction splitter used in ring resonator lasers can be found in Burton
et al. (1994). The design uses only rectangular sections which make it similar to an
MMI coupler avoiding sharp tips at waveguide intersections, which are a challenge to
fabricate. For more details on ring resonator lasers, see Sect. 5.6. Due to the fact that
Y-couplers can be regarded as standard optical components which can be simulated
Fig. 4.8 Polymer Y-coupler
186
4 Building Blocks of Ring Resonator Devices
with several commercially available BPM and FDTD software, further treatment of
these devices will not be given.
4.2 Bends
Bends are inevitable building blocks of state-of-the-art integrated optical circuits
and have therefore been always of interest in the optics community. One of the first
papers dealing with the analysis of bends is described in Marcatili (1969a). Since
then, many methods have been proposed and developed to describe the behavior of
the mode field and lower the losses in bends for example, Neumann and Richter
(1983), Bienstman et al. (2002), and Melloni et al. (2001).
One method of describing a waveguide bend is to use a conformal transformation
which is presented in Heiblum and Harris (1975). The curved waveguide is translated
into an equivalent straight waveguide with a transformed index profile.
By using a cylindrical coordinate system (x, ρ, φ), propagation of light in circularly
curved waveguides can be described in terms of modal propagation (Fig. 4.9). A mode
in such a structure is given by Smit et al. (1993):
E Circ = Uγ (r )e±γφ φ .
(4.10)
This mode has as an equi-phase front which propagates in the angular direction
φ. γ φ is regarded as a complex angular propagation constant and is described as:
γφ = αφ + jβφ ,
(4.11)
where α φ is the attenuation coefficient, this time in angular direction, and β φ is the
real angular propagation constant in rad−1 .
Fig. 4.9 Curved waveguide transferred to a straight waveguide using conformal transformation.
Curved waveguide with real index profile (left). Equivalent straight waveguide with transformed
index profile (right)
4.2 Bends
187
Using a conformal mapping technique (see also Chin and Ho 1998), the problem
of solving the wave equation in cylindrical coordinates can be transformed to rectangular coordinates by performing the following steps (Heiblum and Harris 1975;
Smit et al. 1993):
u = Rt ln
r
Rt
(4.12)
with Rt a freely selectable reference radius. Equation (4.10) can then be written as
∂2
2 2
2
+
{k
n
(u)
−
γ
}
Ut (u) = 0,
t
t
∂u 2
(4.13)
where
u
n t (u) = n{r (u)}e Rt
γt =
γφ
Rt
(4.14)
(4.15)
u
r (u) = Rt e Rt
(4.16)
The angular propagation and attenuation constants can now be derived using
(4.15) as follows:
βφ = βt Rt ,
(4.17)
αφ = αt Rt .
(4.18)
The radiation loss can then be expressed by
−α π φ
= 10π αφ log10 e.
Aφ = −20 log10 e 2
(4.19)
With this transformation an ordinary straight waveguide problem is obtained,
which can be solved with the effective index method by using a staircase approximation for the transformed index profile in the u-direction (Fig. 4.9 right). The index
profile n(r) is transformed into an index profile nt (u). The shape of the transformed
profile can be qualitatively understood by considering that the longer path length
of the light travelling in the outside bend has to turn up in the straight waveguide
problem as a slower phase velocity, hence the higher index there. The center of
gravity of the mode profile in a curved waveguide moves outward, an effect that
increases by decreasing the radius of the bend.
188
4 Building Blocks of Ring Resonator Devices
An approximation can be made when Rt is chosen to be equal to the outer edge
of the waveguide and u/Rt 1 in the vicinity of the waveguide, then
r∼
= Rt + u,
(4.20)
which leads to a transformed index profile
u
∼
.
n t (u) = n(Rt + u) 1 +
Rt
(4.21)
A simple method for estimating bend radii of deeply etched rib waveguides
(Fig. 4.9) is presented in Pennings et al. (1991). This method can be used for rib
waveguides, where the rib is etched completely through the guiding layer. The effective index method (EIM) is used in this reference to describe the rib waveguide by
a one dimensional refractive index profile with an effective index nrib under the rib
and an effective index of 1 next to the rib (air). This one dimensional refractive index
profile can now be treated as a straight slab waveguide with a propagation constant
of
β = kn straight·
(4.22)
All modes with a refractive index nstraigth smaller than the refractive index of
the substrate nsubstrate are treated as below the cut of wavelength and are lost into the
substrate. The straight waveguide problem is solved again by applying the conformal
transformation method as discussed before with the refractive index of the bend nbend
related to the angular propagation constant γ by
n bend =
αφ
Re(γφ )
=
.
kR
kR
(4.23)
The imaginary part of the angular propagation has been neglected due to the high
index contrast between the waveguide and the surrounding air, which leads to a
strong confinement of the mode in the waveguide and results in low radiation losses
in the bend. The radius R is defined as being the length up to the outer side of the
waveguide bend. Using the cutoff condition R = Rco when nbend = nsubstrate and the
approximation
n straight − n bend =
w
1
n rib
2
R
(4.24)
leads to the equation for the cutoff radius, which depends only on parameters of the
straight waveguide
Rco =
w · n rib
.
2(n straight − n bend )
(4.25)
4.2 Bends
189
Fig. 4.10 Architectures of
waveguide bends
The main cause for losses in bends is of course the bending losses themselves
(4.19). One way to minimize the bending loss is by increasing the radius. This is of
course limited when designing ring resonators with certain parameters and a specified
filter performance. Therefore one way to reduce the bending loss is by changing the
refractive index of the material on the outer side of the waveguide. This can also
mean the complete removal of the material on the outer side of the waveguide and
forming a trench. An analysis of this idea is presented in Neumann (1982b) and
Seo and Chen (1996). Schematics of proposed waveguide geometries are shown in
Fig. 4.10. Seo et al. not only suggested to use trenches on the outer side of the curved
waveguide to reduce the bending losses, but analyzed also the slope of the rib with
regard to the transition losses which can be lowered this way.
Another type of loss which is especially important when it comes to the design of
racetrack shaped ring resonators is the transition loss which occurs at the interface
between a straight waveguide and a bend. One of the first publications dealing with
the reduction of these transition losses is (Neumann 1982a). As described earlier,
the center of the mode field in the curvature shifts with increasing radius to the outer
side of the waveguide in the bend. This distance d of the mode shift in a waveguide
having a width w1 can be described by the following equation:
d=
π 2 n 2eff w
.
λ2 R
(4.26)
One method of reducing the transition losses is therefore to apply an offset between
the curved and the straight waveguide sections which is equal to a distance d. A
schematic of a racetrack shaped ring resonator employing offsets at the respective
interfaces is shown in Fig. 4.11. A fabricated racetrack shaped ring resonator in the
material system GaAs–AlGaAs (Fig. 4.12) employing such offsets is presented in
Van et al. (2001). Here, fabricated racetrack shaped ring resonators with offsets up to
0.08 μm are demonstrated. The parameters for the racetrack shaped ring resonators
are a waveguide width of 0.52 μm, a coupling gap of 0.2 μm, an average bending
radius of 4.7 μm, and straight-section length of 10.24 μm.
The transmission from a straight to a curved waveguide for the case of rib channel
waveguides is given by Subramaniam et al. (1997)
1 Note
that w can either be the actual width of the waveguide or the width of the mode, depending
on the type of waveguide used.
190
4 Building Blocks of Ring Resonator Devices
Fig. 4.11 Schematic of a
racetrack shaped ring
resonator with offsets
between the curved and
straight waveguide junctions
Fig. 4.12 Racetrack shaped
ring resonator with lateral
offsets between curved and
straight waveguide
sections Van et al. (2001)
−d 2 2
d
e 2w2 1 + (k·n·w)
2R
TSC (d) = 4 w2
1 + (k·n·w)
2R 2
2
,
(4.27)
where w represents the mode width and n the effective refractive index of the rib in
the center of the waveguide. Minimum transition loss is achieved when:
(a) The amplitude distributions of the two modes are matched
(b) The phase distributions are matched.
Condition (b) is satisfied, condition (a) is a cause for the transition losses which
can be evaluated using (4.27) or can be approximated by Neumann (1982a)
αSC-losses = 4.343
d 2
w
(dB)
where w is either the width of the waveguide or the width of the mode.
These transition losses can be lowered by choosing the appropriate offset, trench
or different material with a lower refractive index on the outer side of the waveguide
4.2 Bends
191
in the bend and in addition selecting the right widths of both the straight and the bend
waveguides (Smit et al. 1993).
Bends are not only used as “connecting” elements in integrated optics, but can also
serve themselves as polarization rotators. An analysis of polarization rotation in bends
is presented in Lui et al. (1998) and Obayya et al. (2001). A compact polarization
converter based on bends is demonstrated in van Dam et al. (1996). Polarization
rotation can be of importance when designing ring resonator filters and depends on
several influencing factors like type of material used, waveguide geometry and ring
radius.
4.3 Spot Size Converters for Light in- and Outcoupling
Spot size converters are used to reduce the fiber–chip coupling losses when single
mode fibers are butt coupled to an integrated waveguide structure or to a laser diode.
The efficiency of the spot size converter depends again on the type of material used
for realizing the integrated waveguide based device which results in possible waveguide parameters. Therefore in choosing an appropriate material for the fabrication
of a ring resonator filter for example and with it a waveguide geometry, already
sets the boundary conditions for the spot size converter. It is therefore important to
design a photonic device taking into account not only fabrication aspects, but also
the connections to the outside world.
An established way to realize a spot size converter is by incorporating tapered
structures operating close to the mode cutoff, which expands their spot size area to
enhance the optical coupling efficiency without deteriorating alignment tolerances.
The use of these designs has improved the coupling efficiency and at the same time
has enabled a more relaxed alignment tolerance of the fiber to the chip. Several
taper designs have been demonstrated, such as lateral tapers (Kasaya et al. 1993),
vertical tapers, or combinations of either lateral and vertical tapers (Yan et al. 2002) or
waveguide configurations (Hamacher et al. 2000). An example of a spot size converter
consisting of a lateral taper and a vertical coupling to a waveguide underneath is
shown in Fig. 4.13.
Here an approach is applied which relies on an adiabatic coupling between a
strong confined waveguide mode and a weak waveguide mode in a guiding layer
1 μm beneath the actual waveguide. The rib of the waveguide is laterally tapered
down from 2 to 0.5 μm forcing the light to couple between the two modes. For a
better lateral confinement of the weakly guided mode a second rib is etched in the
tapered region only. An example of the integration of this spot size converter with a
ring resonator is shown in Fig. 4.14.
A tradeoff between overall chip size and length of the taper region on both sides has
to be found. A longer taper with a gradual enough taper slope will of course exhibit
a lower loss. An optimization of compact lateral, vertical, and combined tapered
spot size converters using the beam-propagation method is presented in Haxha et al.
(2006).
192
4 Building Blocks of Ring Resonator Devices
Fig. 4.13 Schematic of a
spot size converter
(Hamacher et al. 2000)
Fig. 4.14 Ring resonator
with integrated SOA and
spot size converter
4.4 Gratings for Light in- and Outcoupling
In integrated optics based devices, such as those here presented in this book, the
optical coupling efficiency is a key parameter to optimize the final device performance. In order to decrease the insertion losses, several designs have ben proposed,
especially to match the external laser output, normally in the form of single optical
fibers, to the integrated optical waveguides in the device. Among the others, grating
coupling has been demonstrated a very promising method to allow efficient optical
coupling, now implementable thanks to the advanced technologies available. This is
particular interesting when SOI or LNOI optical waveguides in microring resonators
devices are considered: grating coupling provides high alignment tolerance without
requiring cleavage and can be improved in coupling efficiency by inserting a reflectors under the buried oxide layer or silicon. It is clear that the more complex the final
4.4 Gratings for Light in- and Outcoupling
193
stuck structure is the more expensive it will be due to the need of implementing several
process steps to integrate different layers together. For these reasons, the simplest
way is always the most preferred one, not only because it is currently cheaper but
because it results to be more controllable and reproducible.
An example of a compact uniform grating structure without bottom reflector
element or silicon overlay is provided in (Nambiar et al. 2018). In one step etching
process they have achieved a relatively high efficiency. Nambiar et al. have in fact
reported a theoretical CE over 75% at a wavelength of 1550 nm and a measured
Coupling Efficiency (CE) of 47.2% at 1562 nm was obtained for a 12.4 × 12-μm2
grating coupler on silicon-on-insulator (SOI). The sketch of the device that they
have implemented is reported in Fig. 4.15. In the case of close vertical coupling
between the standard optical fiber and the wire waveguide, an adiabatic taper has
been designed by these authors to adjust the optical mode (Nambiar et al. 2018).
The final structure built is showed in Fig. 4.16, for both TE and TM fundamental mode coupling, together with the simulated and characterization results of
the Coupling efficiency in Fig. 4.17.
Nambiar et al. (2018) has provided also a detailed summary of various Silicon-onInsulator (SOI) based fiber to chip grating couplers in Table 4.1 that include uniform
as well as non-uniform (apodized) designs.
Various Adiabatic and Non-Adiabatic Tapers on SOI proposed in literature.
Features and performances are listed in Table 4.2.
Performance comparison of various SOI based polarization splitting grating
couplers (PSGCs). Columns 3 and 4 pertain to the polarization state of the coupled
waveguide modes are reported in Table 4.3. PDL denotes the minimum polarization
dependent loss.
Fig. 4.15 a Three dimensional (3-D) schematic of a Silicon-on-Insulator (SOI) based fiber to chip
surface grating coupler with adiabatic tapers; b k-space representation of the grating phase matching
condition k fr nsup corresponds propagation constant of superstrate and k fr nsup of substrate and G
is the grating reciprocal lattice. Reprinted with permission under CC license from Nambiar et al.
(2018)
194
4 Building Blocks of Ring Resonator Devices
Fig. 4.16 Top down SEM image fabricated of focusing gratings for a transverse electric (TE);
b transverse magnetic (TM) fundamental mode coupling (Nambiar et al. 2018)
Fig. 4.17 Simulated and characterization results for a TE gratings with 640 nm period. Experimental results are for 24 μm focal length and b TM couplers with 980 nm period with optimum
focal length of gratings used in experiments being 20 μm. Reprinted with permission under CC
license from Nambiar et al. (2018)
In the previous chapters, simulation, fabrication, and building blocks of ring
resonator devices have been described. The following chapter presents applications
of ring resonator devices fabricated in different material systems using different
architectures and building blocks.
4.4 Gratings for Light in- and Outcoupling
195
Table 4.1 Summary of various silicon-on-insulator (SOI) based fiber to chip grating couplers
(Nambiar et al. 2018)
SOI
coupler
Max CE
(−dB)
Bandwidth
3 dB (nm)
λmax
(m)
Uniform
(U)/apodized
(A)
[26]
3
58
1.31
[27]
2
50
1.302
[28]
1.9
23 (1 dB)
[29]
1.05
50
[11]
1.6
[10]
1.6
[15]
Fiber
tilt
angle
(θ)
Etch type
Bottom
reflector
U
12
Shallow
N
A
17
Double-etch
N
1.31
A
10
Double-etch
N
1.551
A
8
Shallow
N
63
1.515
U
10
Shallow
Y
60
1.54
U
–
Shallow
Y
1.6
80
1.53
U
13
Shallow
N
[17]
1.9
43 (1 dB)
1.524
A
15
Shallow
N
[18]
1.2
45
1.533
A
10
Shallow
N
[13]
1.08
42 (1 dB)
1.551
U
9
Shallow
Y
[13]
0.62
40 (1 dB)
1.531
A
11
Shallow
Y
[30]
2.5
–
1.325
A
33
Full
N
[31]
3.2
36 (1 dB)
1.59
A
−31
Full
N
[19]
2.16
64
1.543
A
27
Full
N
[25]
0.58
71
1.56
A
13
Full
Y
Full etch signifies SWG couplers. CE refers to the coupling efficiency
Reprinted with permission under CC license from Nambiar et al. (2018). https://doi.org/10.3390/
app8071142
Table 4.2 Summary of the features o silicon-on-insulator (SOI) based fiber to chip grating couplers,
depending on the taper design (Nambiar et al. 2018)
Taper designs
Adiabatic taper Linear [39]
Exponential
[40]
Length (m)
Initial width
(m)–final
width (m)
Coupling
efficiency
theoretical
Remarks
150–500
10–0.5
65–99%
200
10–0.5
70
Tradeoff
between the
taper length and
coupling
efficiency due to
the adiabatic
transition
(continued)
196
4 Building Blocks of Ring Resonator Devices
Table 4.2 (continued)
Taper designs
Non-adiabatic
Length (m)
Initial width
(m)–final
width (m)
Coupling
efficiency
theoretical
Parabolic [41]
200
10–0.5
80
Efficient
adiabatic [42]
120
10–0.5
98.3
Complex
non-adiabatic
[43]
15.4
10–0.56
70
Lens-assisted
[44]
20
10–0.45
−1 dB (TE)
−5 dB
(TM)
Expt.
Discontinuous
[45]
–
10–0.45
90%
Compact taper
[46–48]
15
10–0.5
92%
Remarks
Complexity in
Fabrication
Robust to
fabrication
errors,
broadband,
efficient
Reprinted with permission under CC license from Nambiar et al. (2018). https://doi.org/10.3390/
app8071142
Table 4.3 Performance comparison of various SOI based polarization splitting grating couplers
(PSGCs) (Nambiar et al. 2018)
SOI
coupler
Max CE
(−dB)
Polarization 1
(λ1 ) (m)
Polarization 2
(λ2 ) (m)
Type (1D, 2D)
focusing/non-focusing
PDL
(−dB)
[50]
2
TE0 (1.559)
TM0 (1.551)
1D non-focusing
High
[51]
5.8
TE0 (1.54)
TE0 (1.535)
2D non-focusing
0.2
[53]
5.6
TE0 (1.54)
TE0 (1.53)
2D focusing
0.4
[54]
3.2
TE0 (1.492)
TE0 (1.492)
2D focusing
0
Reprinted with permission under CC license from Nambiar et al. (2018). https://doi.org/10.3390/
app8071142
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Chapter 5
Devices
This chapter is entirely devoted to highlighting the various applications of ring
resonator devices developed to date using examples presented by the ring resonator
community. Some ring resonators have already been described in Chap. 3, therefore
only performance parameters like the free spectral range (FSR), the full width at
half maximum (FWHM), the quality factor Q and the finesse F will be given in this
chapter for selected devices.
Ring resonators have been primarily investigated to be implemented as optical
add–drop filters in optical networks. Several optical filter designs have been proposed
and realized in semiconductors and polymers, purely passive devices, ring resonators
with integrated gain sections and devices made out of active material. Optical filters
need to be tunable in order to be deployed in optical networks. This fact is even more
important, when it comes to ring resonators, as the resonances of the ring resonator
filter have to be aligned exactly to the required optical channel. Wavelength tuning
and center wavelength trimming methods will be explained in this chapter.
Ring resonators can be used for flexible dispersion compensation and several
fabricated devices will be explained.
In wavelength division multiplexing (WDM) applications, a square spectrum
response is desirable. Periodic multiplexers and demultiplexers, which have a
flat passband and a wide rejection region, can be realized integrating a modified
Mach–Zehnder interferometer (MZI) with a ring resonator.
The application of ring resonators as lasers has been demonstrated already some
time ago. It has gained attention again recently with the fact that combining ring
resonators can enhance the tunability of ring lasers. Novel concepts have been
proposed and realized using all active ring lasers and passive ring resonator coupled
configurations with integrated semiconductor optical amplifiers (SOAs).
Due to the advancing state of the art in fabrication technology, ring resonators
with very small radii have been built which opens up the possibility to use these
elements as modulators and in optical signal processing systems as logic gates and
as switching devices.
© Springer Nature Switzerland AG 2020
D. G. Rabus and C. Sada, Integrated Ring Resonators, Springer Series
in Optical Sciences 127, https://doi.org/10.1007/978-3-030-60131-7_5
199
200
5 Devices
As equally important as creating a wavelength with ring lasers and filtering out
a specific wavelength, wavelength conversion has been found to be possible using
ring resonator devices.
Finally as a new technology trend is emerging which is currently known as biophotonics, ring resonators have again found their way into this new field in the form of
sensors.
5.1 Filters
Ring resonator filters have been fabricated in many material systems as is described in
Chap. 3. State-of-the-art manufacturing technologies have enabled the demonstration
of filter characteristics and parameters useful for optical networks. The advantages of
using ring resonator filters are obvious. Ring resonators can be integrated with other
components such as lasers or SOAs to form complex photonic integrated circuits.
Ring resonators do not require facets or gratings for optical feedback and can have
very small dimensions which enables the realization of large scale photonic integrated
circuits. Several examples will be presented in this chapter highlighting various
results achieved for ring resonator filters with different geometries and materials.
5.1.1 Passive Devices
Single Ring Filters
One of the first passive single ring resonator add–drop filter with integrated
throughput and drop–port is presented in Haavisto and Pajer (1980). A thin film
of PMMA is used to fabricate the waveguides. The radius of the ring is 4.5 cm. The
waveguide widths are 10 μm, with a 17.5 μm separation from center to center. A
coupling strength of 2% is achieved. Prism coupling is used to couple in and out
of the bus waveguides. A finesse of 16 is measured. The loss in the ring is found
to be 0.05 dB cm−1 , which includes coupling and radiation losses. Due to the large
circumference of the ring, these ring resonator filters are limited in their use as
channel dropping filters.
Improvement of fabrication methods and the coming up of new material systems
(for example III–Vs) has made it possible to fabricate ring resonators with radii
far below 100 μm. One of these first ring resonators is demonstrated in Rafizadeh
et al. (1997b). Ring and disk resonators in the material system AlGaAs/GaAs with
diameters of 10.5 μm (Fig. 5.1) and 20.5 μm are presented.
An FSR of 21.6 nm and an FWHM of 0.18 nm is measured for the disk resonator
with a diameter of 10.5 μm, leading to a finesse of 120, and a cavity quality factor
Q greater than 8500. In the case of the ring resonator with a diameter of 10.5 μm,
an FSR of 20.6 nm and an FWHM of 0.43 nm is measured, leading to a finesse of
5.1 Filters
201
Fig. 5.1 SEM images of a 10.5-mm-diameter a disk and b ring (Rafizadeh et al. 1997b)
48 and a Q-factor greater than 3500. The FSR and the FWHM for the ring and disk
resonators with a diameter of 20.5 μm are 10.2 nm/10.7 nm and 0.54 nm/0.12 nm,
respectively. The FWHM is broader in the case of the ring resonator due to the loss
caused by the additional sidewall.
Similar ring resonators in glass, vertically coupled to the bus waveguides with
radii of 10 μm are presented in Little et al. (1999). An FSR of 20 nm and an FWHM
of 5.2 nm are measured, leading to a finesse of 4 and a quality factor of 300. The
low Q factor compared to the high Q factor for the similar AlGaAs/GaAs is due to
a stronger coupling, leading to a broader FWHM and therefore to a lower Q factor.
The transmission spectrum from both the throughput and the drop–port is shown in
Fig. 5.2.
These ring resonators are used as building blocks in an 8 channel add–drop filter
(Chu et al. 1999c). The ring resonators are connected in parallel to form a multichannel add–drop filter. Each ring resonator in the device has a different radius and
thus a different resonance wavelength. In the fabricated device, the first ring resonator
has a radius of 10.35 μm, while the remaining ring resonators decrease in radius by
increments of 50 nm. The parallel drop–port waveguides are separated by 250 μm.
A schematic of the 8-channel ring resonator add–drop filter is depicted in Fig. 5.3.
The transmission spectrum of the eight channel add–drop filter is polarization
dependent. The FWHMs of the resonances for TE and TM polarization, from shortest
to longest wavelengths, are 0.53, 0.63, 0.64, 0.71, and 0.92, 1, 1.06, 1.16 nm, respectively, leading to Q factors of 2500 and 1500. The average FSRs of the array is
20.1 nm and 20.2 nm for TE and TM, respectively. A junction induced crosstalk
lower than −30 dB is achieved. The channel spacing achieved with this architecture
is approximately 5.7 nm. The channel spacing can be adjusted to the required parameter by either changing the ring radius or the width of the waveguide, which results
in a different propagation constant.
202
5 Devices
Fig. 5.2 TE polarized wavelength response of a 10 μm radius ring resonator (Little et al. 1999)
Fig. 5.3 8-Channel add–drop filter
Vertically coupled ring resonators have not only been used in a parallel cascade
to form a channel dropping filter, but have also been used in a 2 × 2 cross grid array
for crosstalk reduction and spectrum cleanup in Chu et al. (1999a). A schematic of
the 2 × 2 array consisting of three ring resonators is shown in Fig. 5.4.
The three ring resonators have the same parameters and therefore filter out the
same wavelength. Resonator 1 is the first filter along the input bus waveguide.
Resonator 2 having the same resonance wavelength as resonator 1 sends the filtered
wavelength to the drop–port which increases the out-of-band signal rejection. This
ring resonator configuration corresponds to a double ring resonator leading to a
steeper roll off of the filter spectrum and consequently to a larger out-of-band rejection. Resonator 2 therefore, cleans up the drop–port spectrum. Signal power at the
resonance wavelength that is not completely filtered out by resonator 1 is filtered out
a second time by resonator 3. Resonator 3 therefore, cleans up the throughput spectrum. The add port which does not have a path to the drop–port is cross connected
to the input and throughput bus waveguide by resonator 3.
5.1 Filters
203
Fig. 5.4 2 × 2 ring
resonator add–drop node
Finally, the vertically coupled glass ring resonators have been used to realize an 8
× 8 cross grid array (Little et al. 2000). A photograph of the array is shown in Fig. 5.5.
The height of the waveguide in the ring resonators is 1.5 μm, and the waveguide
widths vary from 1 to 1.7 μm in increments of 100 nm. The ring resonators are
identical along upward directed diagonals in the array. The spacing between the bus
waveguides is 250 μm.
Vertically coupled ring resonators consisting of a dielectric material core (Ta2 O5 –
SiO2 compound glass with n = 1.8, or SiN with n = 2) and an air cladding have
been proposed, designed and fabricated by the group of Kokubun. A summary of
the work can be found in Kokubun (2005). Ring resonators with radii between 10
and 20 μm, resulting in an FSR of 10–25 nm and an FWHM 0.1–1.0 nm have been
Fig. 5.5 Photograph of a
portion of the 8 × 8
cross-grid vertically coupled
glass ring resonator array
(Little et al. 2000)
204
5 Devices
demonstrated. These device parameters lead to high Q values between 1500 and
15,000. Kokubun’s group have pushed ring resonator technology not only in terms
of ring size, but have also demonstrated polarization insensitive and tunable (center
wavelength tuning and resonance tuning) ring resonators which are addressed in the
relevant chapters of this book.
Laterally coupled ring resonators and vertically coupled disk resonators, with
PMMA cladding and without cladding have been designed and realized in Si3 N4
on SiO2 in Klunder et al. (2001). A finesse of 136 has been achieved for a laterally coupled ring resonator without cladding and with a radius of 25 μm with a
coupling gap of 750 nm. A finesse of 61 has been measured for a ring resonator with
PMMA cladding. TE polarized light is used for the characterization of the devices at
a wavelength of 1.55 μm. Vertically coupled disk resonators with a radius of 15 μm
have been fabricated. The vertically coupled disk resonators are characterized using
a wavelength of 640 nm. An FSR of 2.2 nm is measured which results in a finesse
of 31. The finesse is limited by the linewidth of the laser used for characterizing
the devices. A detailed analysis of the device performance of laterally coupled ring
resonators in the same material system is presented by the group in Klunder et al.
(2003). Here ring resonators with coupling gaps of 0.5 (not completely open, due to
fabrication imperfections), 0.75 and 1 μm have been fabricated and characterized. A
photograph of a ring resonator with a coupling gap of 0.75 μm is shown in Fig. 5.6.
An FSR of 8 nm at a wavelength of 1530 nm and a finesse of 120 are obtained
for a ring resonator with a coupling gap of 0.75 μm and air cladding. A finesse of
22 is measured for the resonator with a coupling gap of 0.5 μm with air cladding.
The values for the finesse of ring resonators with PMMA cladding are 61 and 25,
respectively.
As has been mentioned in Chap. 3, recently several groups have demonstrated ring
resonators not only in silicon, but also in GaAs and InP. One of the first racetrack
shaped laterally coupled ring resonators in the material system AlGaAs with a cavity
length of 31 μm (length of the straight sections is 6 and 4 μm) is presented in Chin
et al. (1999). A photograph of a racetrack shaped ring resonator is shown in Fig. 5.7.
Fig. 5.6 Laterally coupled
ring resonator in SiON with
a radius of 25 μm and a
coupling gap of
0.75 μm Klunder et al.
(2003)
5.1 Filters
205
Fig. 5.7 Racetrack shaped
ring resonator Chin et al.
(1999)
A gap between the bus waveguides and the racetrack of 200 nm is used. An FSR
of 20 nm and an FWHM of 1 nm is achieved in the case of the 6 μm long straight
sections, leading to a finesse of 20. An FWHM of 0.2 nm and a finesse of 100 are
obtained in the case of the 4 μm long straight sections. The racetrack shaped ring
resonators are surrounded by etched trenches which are 2.5 μm deep and 1 μm wide.
The waveguide width is 0.4 μm and is tapered to 2 μm at the facets for easier fiber
chip coupling.
Disk resonators with diameters of 5 and 10 μm in the material system GaInAsP
are presented in Ma et al. (2000). The disk resonators are vertically coupled using
polymer (BCB) wafer bonding. The measured FSR of the disk resonators is nearly
the same as for the devices described in this chapter, namely 38 nm for the disk with
a diameter of 5 μm and 21 nm/20 nm for the disk with a diameter of 10 μm. The
two values for the FSR for the 10 μm disk are due to the polarization dependence
in this disk which is also visible in the transmission spectrum having two sets of
resonance peaks. The FWHM is, as expected, therefore also polarization dependent
which leads to values of 0.25 and 0.22 nm. In the case of the 5 μm disk, the FWHM
is measured to be 0.6 nm.
Vertically coupled disk resonators also in the material system GaInAsP fabricated
by wafer bonding with radii ranging from 4 to 12 μm are presented in Dapkus et al.
(2001) and Djordjev (2002). The parameters for a disk with radius of 12 μm are: an
FSR of 10 nm, an FWHM of 0.22 nm leading to a Q factor of more than 7000. The
details of the fabrication method have been described in Chap. 3. Photographs of bus
waveguides and a disk resonator are shown in Figs. 5.8 and 5.9.
One of the smallest racetrack shaped ring resonator notch filters in InP is demonstrated in Grover et al. (2003). A radius of 2.25 μm is realized. The straight waveguides have a length of 10 μm. An FSR of 19 nm at a wavelength of 1550 nm is
measured. A photograph of a ring resonator notch filter is shown in Fig. 5.10. The
values for the finesse and the Q factor are 6 and 500. A transmission spectrum of a
notch filter is shown in Fig. 5.11.
206
5 Devices
Fig. 5.8 Bus waveguides at
the bonded interface and the
remaining transparent InP
layer after the etch of the
microdisk mesa Djordjev
(2002)
Fig. 5.9 A smooth 2.3 μm
deep microdisk mesa formed
by CH4 based RIE etch. The
bus waveguides are below
the remaining thin membrane
of InP Djordjev (2002)
A racetrack shaped ring resonator notch filter employing multimode interference
couplers is presented in Rabus and Hamacher (2001). The curved sections have
a rather large radius of 100 μm when compared to the previous examples. The
length of the used MMI coupler is 150 μm. A photograph of a ring resonator and
the transmission spectrum are shown in Figs. 5.12 and 5.13. An FSR of 0.8 nm
(corresponding to 100 GHz in the frequency domain at a wavelength of 1.55 μm)
and a finesse of 6 are measured.
Single ring resonator notch or add–drop filters have been studied extensively in
the past and have been realized in major material systems as was demonstrated in
this section. The use of single ring resonator devices as filters in optical networks is
limited by the Lorentzian like function of the transfer function. Filters employed in
optical networks require a rectangular, box-like passband shape. Multiple coupled
ring resonator devices fulfill this request and have been fabricated in several material
systems.
5.1 Filters
Fig. 5.10 One of the
smallest ring resonator notch
filters in InP Grover et al.
(2003)
Fig. 5.11 Spectral behavior
of InP racetrack shaped ring
resonator notch filter. The
solid line is experimental
data, and the dashed line is a
curve-fit Grover et al. (2003)
207
208
5 Devices
Fig. 5.12 MMI coupled
racetrack shaped ring
resonators
Fig. 5.13 Transmission
spectrum of an MMI coupled
racetrack shaped ring
resonator with a radius of
100 μm
Double Ring Filters
One of the first integrated double ring resonator filters in silicon which is also used in
a frequency-shift keying (FSK) optical transmission experiment is presented in Oda
et al. (1994). The group had previously demonstrated a double ring resonator with
an overall FSR of 40 GHz in Oda et al. (1991). In Oda et al. (1994) a double ring
resonator consisting of ring resonators with different radii is used. The use of two
ring resonators with different radius (3.33 and 3.82 mm in this case) opens up the
possibility to increase the FSR [see (2.77)]. The FSRs of the ring resonators are 14.29
and 12.50 GHz at a wavelength of 1550 nm, leading to an overall FSR of 100 GHz
or 0.8 nm. The finesse achieved is 200 for this configuration. A 10 GHz spaced,
8-channel, 622 MB s−1 FSK direct detection distribution experiment over 40 km is
demonstrated using this double ring resonator configuration. A similar double ring
resonator consisting again of two ring resonators with different radius is presented
by the same group in Suzuki et al. (1995). The double ring resonators consist of two
ring resonators with FSR’s of 12.5 and 14.29 GHz, whose ring radii are 1.75 and
2.0 mm, respectively. The designed overall achieved FSR is again 100 GHz (98 GHz
measured). The finesse is 138. In these two ring resonator experiments thin film
heaters are integrated to be able to match the resonances of the two rings. Matching
5.1 Filters
209
of the resonances in multiple coupled ring resonators is of utmost importance to
achieve an optimum device performance and to realize the designed filter response.
The tuning of the resonances and the center wavelength of ring resonator devices
will be addressed in Sect. 5.2.
A double ring resonator where the ring resonators and the bus waveguides are
coupled to one another by multimode interference couplers is presented in Rabus
and Hamacher (2001). The radius of the curved sections is 100 μm. The length pf
the MMI coupler is 150 μm, leading to an FSR of 0.8 nm at a wavelength of 1550 nm.
A photograph of an MMI coupled double ring resonator is shown in Fig. 5.14.
Vertically coupled double ring resonators in the material system Ta2 O5 –SiO2 are
presented in Kokubun et al. (2002). Double ring resonators with a finesse of 39.8,
an FSR of 16.7 nm and an FWHM of 0.42 nm have been designed, fabricated and
characterized. Due to the double ring resonator structure, a box-like filter response
is obtained.
The design and characterization of a polarization independent double ring
resonator filter with a designed FSR of 50 GHz (47.6 GHz measured) at a wavelength
of 1550 nm by use of SiOx Ny technology is presented in Melloni et al. (2003a). The
photograph of a double ring resonator is shown in Fig. 5.15.
The coupling between the ring resonators is realized by directional couplers with
coupling coefficients of 0.4, 0.28, and 0.4 for realizing a Butterworth type filter
response. A 15 dB extinction ratio and a bandwidth at −1 dB of 7.4 GHz are measured.
The transmission spectrum of a double ring resonator filter is shown in Fig. 5.16.
Double ring resonator filters are a first step to enable the realization of box-like
filter functions. Using double ring resonators as was demonstrated by the examples
in this chapter also makes enlargement of the FSR possible. In order to improve the
roll-off and out-of-band rejection, multiple coupled ring resonator filters are required.
Fig. 5.14 MMI coupled
double ring resonator
210
5 Devices
Fig. 5.15 Photograph of a double ring resonator filter Melloni et al. (2003a)
Fig. 5.16 Drop–port TE (solid curves) and TM (dashed curves) measured spectral responses of the
double-ring filter. a Response over a 4-nm span and b detail of the response centered at 1551.2 nm.
The dotted curve in (b) is the theoretical response Melloni et al. (2003a)
Multiple Coupled Ring Filters
Serially coupled, racetrack shaped, AlGaAs–GaAs triple ring resonators with radii
of 4.5 μm and straight sections with lengths between 0 and 10 μm are demonstrated
in Hryniewicz et al. (2000). A photograph of a triple ring resonator is shown in
Fig. 5.17.
The waveguide width, bus waveguide–ring resonator gap and inter ring resonator
coupling gap is between 0.18 and 0.32 μm. The box-like filter response of a triple
ring resonator is shown in Fig. 5.18.
Parallel cascaded third- and fifth-order disk resonators in the material system
GaInAsP/InP are presented in Ma et al. (2001). Photographs of the realized devices
are shown in Fig. 5.19.
The disks have diameters of 10 μm and are only coupled to the bus waveguides and
not to each other. The coupling gap between the bus waveguide and the disk resonator
is about 0.15 μm. The distance between two adjacent resonators is 23.85 μm, leading
to a π /2 phase shift. The chosen distance between the resonators introduces in-phase
5.1 Filters
211
Fig. 5.17 Serially coupled
triple ring
resonator Hryniewicz et al.
(2000)
Fig. 5.18 Transmission
spectrum at drop–port of
triple resonator
filter Hryniewicz et al.
(2000)
responses among the parallel cascaded disk resonators. A box like filter response
is obtained due to the constructive interference formed at the drop–port which can
be seen in the spectral response of a fifth-order disk filter in the measurement of
the drop–port in Fig. 5.20. The FSR of the fifth-order filter is about 20 nm and the
FWHM is approximately 3.5 nm.
Parallel, vertically coupled triple ring resonators in the material systems GaAs–
AlGaAs and GaInAsP–InP are demonstrated in Grover et al. (2002). A photograph
of a triple ring resonator is shown in Fig. 5.21.
The width of the single mode waveguides is 0.8 μm. The waveguides are tapered
to a width of 2 μm at the facets to improve fiber chip coupling. The radius of the rings
is 9.55 μm. The distance between the rings is chosen to be 20 μm (center-to-center).
The achieved overall FSR of the triple ring resonator is 34 nm. The transmission
spectrum of the GaAs–AlGaAs ring resonator is shown in Fig. 5.22.
212
Fig. 5.19 Photograph of third- and fifth-order disk resonators Ma et al. (2001)
Fig. 5.20 Measured filter
responses of fifth-order
cascaded microdisk
resonator filter for TM
polarization Ma et al. (2001)
Fig. 5.21 Photograph of a
vertically coupled triple ring
resonator filter. The ring
resonators are on the lower
level Grover et al. (2002)
5 Devices
5.1 Filters
213
Fig. 5.22 Response of the
drop–port of a parallel,
vertically coupled triple ring
resonator Grover et al.
(2002)
The increase in the FSR in the case of the third-order ring resonator filter compared
to a single ring resonator device is due to the Vernier effect (see Sect. 2.2.2). The
cavities which interfere with one another are each of the ring resonators and part of
the ring resonators with the bus waveguides. Fabrication tolerances can introduce an
unwanted Vernier effect also and have an influence on the device performance. A
difference in the radius of the rings of 0.04% is reported for this device.
Vertically, serially coupled triple ring resonators are presented in Yanagase et al.
(2002). The ring resonators are fabricated in the material system Ta2 O5 –SiO2 . A
photograph of a triple ring resonator is shown in Fig. 5.23.
The bus waveguides and ring resonator 2 are in the lower layer and ring resonators
1 and 3 are located in the upper layer. The coupling strength between the resonators
and the resonators with the bus waveguides is controlled by the thickness of the
buffer layer. This is one of the advantages of using a vertically coupled ring resonator
configuration. One triple ring resonator configuration presented by the authors has
the following parameters: the radius of ring resonator 1 and 3 is 22.78 μm resulting
in an FSR of 10 nm, the radius of ring resonator 2 is 39.32 μm leading to an FSR of
6 nm. The measured overall FSR expanded to 25.8 nm (theoretical value: 30 nm),
which is larger than the FSR of each of the ring resonators. In determining the value
for the overall FSR, one has to take into account different values for the propagation
constant in the buried ring resonator and the ring resonators on top. A transmission
spectrum of the response of the drop–port of a single resonance is shown in Fig. 5.24.
The mentioned shape factor is defined here as the width of the bandwidth at −1 dB
divided by the width of the bandwidth at −10 dB.
214
5 Devices
Fig. 5.23 Vertically coupled triple ring resonator (Yanagase et al. 2002)
Fig. 5.24 Measured filter
response of a triple ring
resonator with radii of
28.52 μm for resonators 1
and 3 and 39.32 μm for
resonator 2 (Yanagase et al.
2002)
One of the first and so far only demonstration of 6 and 11 serially coupled ring
resonator filters using the material HydexTM1 which is a glass based material, is
presented in Little et al. (2004). The ring resonators are laterally coupled to each
other. The outer rings are vertically coupled to the bus waveguides. A photograph
of a serially coupled sixth-order ring resonator is shown in Fig. 5.25. The width and
thickness of the cores of the waveguides are approximately 1.5 μm. The vertical gap
1 See
www.nomadics.com for more information.
5.1 Filters
215
Fig. 5.25 Example of a
sixth-order ring resonator
filter fabricated with 17%
index contrast Hydex Little
et al. (2004)
between the bus waveguides and the outer ring resonators varies from 200 to over
1000 nm depending on the desired filter linewidth. The gaps between the laterally
coupled ring resonators vary from 500 to 1400 nm depending again on the application. The drop–port response of first-, third-, and 11th-order ring resonator filters
is shown in Fig. 5.26. Filters with high quality factor and large out of band rejecFig. 5.26 Measured
response for first-, third-, and
11th-order ring resonator
filters similar in fabrication
to the device shown in
Fig. 5.25. The responses
have been normalized to
their 3-dB bandwidths. The
dashed curve is the
theoretical fit to the
11th-order filter Little et al.
(2004)
216
5 Devices
tion have been realized. As can be seen, maximal flatness of the filters response is
obtained by increasing the number of coupled ring resonators. Polarization independent resonances can be achieved by this technology by choosing the correct aspect
ratio for the waveguides.
The examples in this section have demonstrated that fabrication methods of ring
resonator filters in several material systems are available for realizing devices with
adjustable performance parameters suitable for implementation in future all-optical
networks. In order to increase the device functionality of ring resonator filters, gain
can be introduced into the cavity. Examples of devices with gain inside the ring
resonator are presented in the following section.
5.1.2 Devices with Gain Section
Ring resonator lasers have of course been around quite some time and examples will
be presented in Sect. 5.6. This chapter focuses on ring resonator filters with integrated
gain sections for realizing improved and loss reduced filter functions.
One of the first devices with gain inside the resonator is presented in Djordjev et al.
(2002b). Disk resonators with gain region, vertically coupled to the bus waveguides
are used to demonstrate gain trimming of the resonant response. The fabrication of
the devices has been described in Sect. 3.4.7. The response from the throughput port
of a disk with a radius of 10 μm is shown in Fig. 5.27.
The device has an FSR of 10 nm. A quality factor of 5700 and a finesse of 40
are measured. The coupling coefficient is estimated to be 3.6%. As can be seen in
Fig. 5.27 it is possible with active devices to adjust the response of the disk resonator.
When the applied current supplies enough gain inside the resonator to equal the
Fig. 5.27 Gain trimming of
the transmission response of
a disk with radius
10 μm Djordjev et al.
(2002b)
5.1 Filters
217
internal losses, the resonator becomes lossless and the obtained filter spectrum is
ideal.
Racetrack shaped ring resonators with integrated SOAs are presented in Rabus
et al. (2002c). A minimum radius of 100 μm which is one magnitude larger than the
ones presented in the previous paragraph is used. Single, double and triple serially
coupled ring resonator add–drop filters with integrated SOAs are demonstrated. The
fabrication details and the layer sequence of the devices have been described in
Sect. 3.4.7. A photograph of a serially coupled triple ring resonator with SOAs is
shown in Fig. 5.28. The output port is transferred to the right side of the chip via
another half circle for a better accessibility when measuring the transfer response.
The devices realized have FSRs of 12.5, 25, and 50 GHz at a wavelength of 1550 nm.
The lossless filter response of a single ring resonator with an FSR of 25 GHz is
shown in Fig. 5.29.
The radius of the ring resonator is 363 μm and the length of the SOA is 400 μm.
The length of the couplers is 200 μm (gap = 0.9 μm), which results in power coupling
factors of 0.17. The y-axis has been normalized to the fiber–chip coupling loss. The
on–off ratio is measured to be more than 22 dB. The FWHM is determined to be
0.012 nm. The finesse of the ring resonator is F = 17, leading to a Q factor of more
than 130,000. The filter response is measured by sweeping the external cavity laser
(ECL) signal with a resolution of 4 pm. The SOA is operated at a current of 90 mA
Fig. 5.28 Serially coupled triple ring resonator with integrated SOAs
218
5 Devices
Fig. 5.29 Single ring resonator with two straight input/output waveguides and directional couplers
(length = 200 μm, gap = 0.9 μm), r = 363 μm, gain length = 400 μm, FSR = 25 GHz
which provides lossless operation of the ring resonator as is seen in the transmission
spectrum. The response from the drop–port on resonance is as high as the response
from the throughput port off-resonance.
The response from the drop–port of a double ring resonator with integrated
SOAs is shown in Fig. 5.30. The double ring resonator is made up of two straight
input/output waveguides, two 3 dB MMI couplers for the outer couplers (length =
150 μm, width = 6 μm) and a directional coupler in the center (length = 150 μm,
gap = 1 μm), r = 347 μm, SOA length = 500 μm which results in an FSR of
25 GHz.
The driving current for each SOA is 50 mA. The shape factor which is defined in
this case as L 1 divided by L 2 , achieved for this configuration is 0.5. The FWHM is
measured to be 0.04 nm, leading to a finesse of 5.
The drop–port response of a triple serially coupled ring resonator is shown in
Fig. 5.31.
The measured triple ring resonator has a radius of 323 μm. The length of an
SOA is 400 μm. The length of the couplers is 325 μm with a gap of 0.8 μm for
the outer couplers and 1 μm for the couplers in the center. The achieved FSR is
25 GHz. The driving current for each of the three SOAs is 50 mA. The steep roll-off
can be seen from the measurement. The two ripples result from a slight resonance
mismatch between the three ring resonators. The on–off ratio for the fabricated triple
ring resonator is more than 18 dB including the ripples.
Ring resonators integrated with SOAs have not only been fabricated in the serially
coupled configuration, but have also been demonstrated in the parallel architecture.
The photograph of a parallel coupled triple ring resonator is shown in Fig. 5.32.
5.1 Filters
219
Fig. 5.30 Drop–port response from a double ring resonator with two straight input/output waveguides, two MMI couplers and a directional coupler (length = 150 μm, gap = 1 μm), r = 347 μm,
SOA length = 500 μm, FSR = 25 GHz
Fig. 5.31 Filter response of the drop–port of a triple ring resonator with r = 323 μm, length of the
couplers = 325 μm, gain length = 400 μm, FSR = 25 GHz
220
5 Devices
Fig. 5.32 Photograph of a fabricated triple coupled ring resonator in a parallel configuration
The ring resonators have a radius of 117 μm, a coupler length of 200 μm (gap =
0.9 μm) and a gain length of 300 μm. An FSR of 50 GHz is realized. The driving
current for each SOA is 50 mA. The distance between the resonators was chosen to be
equal to half of the circumference of a single ring resonator. The filter characteristic
of the drop–port of the parallel, triple coupled ring resonator is shown in Fig. 5.33.
The ripples are due to a slight resonance mismatch due to fabrication tolerances.
The resonances can be matched when integrated platinum resistors (see Sect. 5.2) in
the ring resonators or adjusted SOA currents are used.
Another example of the integration of ring resonators with SOAs is presented in
Menon et al. (2004). In this example, a vertically stacked asymmetric twin waveguide
structure is used to integrate the SOA with the passive waveguides. The ring resonator
is racetrack shaped and is designed as a notch filter with only one input/output bus
waveguide. A photograph of the fabricated chip as well as a schematic of the design
Fig. 5.33 Drop–port response of a parallel coupled triple ring resonator with integrated SOA,
length of the couplers = 200 μm, r = 117 μm, gain length = 300 μm, FSR = 50 GHz
5.1 Filters
221
Fig. 5.34 Schematic of the microring resonator with integrated SOAs at the input and in the ring.
Upper left inset: Scanning electron microscope image of the fabricated devices with and without an
SOA in the ring. Lower right inset: Refractive index profile and layer structure of the ring resonator
with integrated SOA Menon et al. (2004)
is shown in Fig. 5.34. In addition to the SOA in the resonator, another SOA has
been integrated on the side of the input port. Details on the fabrication have been
described in Sect. 3.4.7. The racetrack shaped ring resonator has an FSR of 0.25 nm.
A multimode interference coupler is used as in the previous example to couple into
and from the ring. The length of the MMI is 685 μm and the width is 12 μm. The
length of SOA1 is 1000 μm and the length of SOA2 is 500 μm. The overall length
of the resonator is 3020 μm. The availability of an SOA inside a ring cavity enables
the tuning of parameters of the resonator like the FWHM, the extinction ratio and
thus also the Q factor and the finesse. The tuning of these parameters is shown in
Fig. 5.35.
A fabricated ring resonator employing an SOA, an MMI and total internal reflection (TIR) mirrors is demonstrated in Kim et al. (2005). Details on the layout and a
photograph of a TIR based ring resonator are shown in Fig. 5.36.
An FSR of 2 nm at a wavelength of 1568 nm is obtained. The on–off ratio achieved
is 14 dB, an FWHM of 0.3 nm is measured leading to a finesse of more than 6, and
a Q factor of more than 4900. The length achieved for the MMI coupler is one
of the shortest reported. The SOA current dependable tunability of the resonance
characteristic of the device is shown in Fig. 5.37.
All integration schemes have in common that they require temperature stabilization. Another effect which takes place is the resonance shift due to increase in
SOA current. This is due to the current dependency of the refractive index of the
SOA. Despite these unwanted effects, SOAs inside ring resonators offer tunability of
222
5 Devices
Fig. 5.35 Measured extinction ratio and FWHM as a function of the ring SOA2 current Menon
et al. (2004)
Fig. 5.36 Total internal reflection mirror-based GaInAsP ring resonators integrated with optical
amplifiers Kim et al. (2005)
essential parameters and enable lossless switching devices, which can also be used
for lasers, wavelength converters and nonlinear operation. Examples will be given
later on in this chapter.
5.2 Tunability Methods
223
Fig. 5.37 Tuning of the
resonator extinction ratio via
the SOA current Kim et al.
(2005)
5.2 Tunability Methods
Tunability is essential for the system application of optical filters. In the case of
periodic filters, like ring resonators, it is important to fit the transmission curve to
the defined channel spacing (e.g., ITU-Grid). Several tunability methods exist either
for trimming the center wavelength of the filter after processing or for tuning the
resonance wavelength when the ring resonator add–drop filter is in operation. These
methods including examples are briefly explained in the following chapters. The
physical mechanisms behind these methods are:
Thermo-optic tuning. Thermo-optic tuning is realized by heating the component
for example by fabricating a metal heater on top of the waveguide in the ring resonator.
The refractive index of the material is changed through the heat which in turn shifts
the resonances. The heating process is fairly slow but can be used to trim resonances
in for example a double ring resonator because it is very difficult to fabricate ring
resonator devices with exactly the same resonant wavelength. By adding heating
elements and using the same, negligible additional loss is obtained. On the other
hand, using heaters, limits the density of devices to maintain thermal isolation, and
requires significant power consumption to maintain the tuned status.
Another used tuning mechanism is electro-optic tuning. Here an electric field
is applied to change the properties of the material, which means either the refractive index or the absorption. Changes in the refractive index are realized by using
a bandgap wavelength of the material which is far away from the signal wavelength so as not to interfere with it. This effect is quite small compared to the effect
produced by the heating elements. The refractive index increase is maximized when
ring resonators with narrow peaks and low losses are used. The change in the refractive index by using the electro-optic effect is weak in III–V materials like InP, but has
the advantage of being fast compared to the thermo-optic effect described before.
One has to be careful when applying higher voltages which lead to significant losses.
Changes in the absorption of the material are obtained, when the bandgap wavelength
224
5 Devices
is closer to the signal wavelength. Only a small electric field is necessary to induce
a large loss. This can be used advantageously in switching devices which shall be
explained in the following chapter.
Carrier injection (or free carrier injection for example in InP) is another means of
changing the refractive index, absorption or gain. Introducing gain in ring resonators
is an advantage of using carrier injection. As is and will be demonstrated in the
following chapters, gain can be used to change the response of ring resonators, the
extinction ratio, the Q factor and the maximum transmission. Ring resonators can
be switched between dropping and transmitting a signal by changing the loss/gain
inside the cavity. When gain is introduced into the ring resonator, attention has to be
paid to design and fabricate a heat sink which is necessary to suppress the unwanted
thermo-optic effect.
5.2.1 Wavelength Tuning
Wavelength tuning is essential for realizing optical filters to be implemented in
optical network. Tunability offers the network suppliers flexibility when designing
and operating a network.
Thermo-Optic Tuning
A common and well-known method of tuning semiconductor and polymer based
integrated optical devices is by using temperature. The simplest way is to heat the
entire device and thus change the resonance spectrum in the case of ring resonators.
This method is of course only useful for materials with a large temperature coefficient.
A more effective way is to use local heating elements on top of the waveguides in the
ring resonator for changing the refractive index and so for changing the resonance
wavelength of the device. A detailed theoretical analysis with implementation on
thermal tuning in ring resonators is described in Geuzebroek (2005).
One of the first papers dealing with the integration of such heating elements in
ring resonators made in silicon is presented in Katila et al. (1996) and Heimala et al.
(1996). The ring resonator is made out of silicon nitride (Si3 N4 ) rib waveguides
with a height of 40 nm. The silica undercladding layer and the silicon nitride layer
thicknesses are 3 μm and 300 nm, respectively. The diameter of the ring is 2 mm.
The resistors are made out of a phosphorous doped polysilicon layer. Aluminum
with a thickness of 900 nm is used to create the bondbads. The layout and the layer
sequence are shown in Fig. 5.38.
Temperature tuning of the entire chip is used in Rafizadeh et al. (1997a) to tune
a disk resonator. A temperature tuning of 1.3 nm per 10 °C is obtained. An overall
tuning range of 6.3 nm over a temperature range of 50 °C is demonstrated. The
tunability is mainly due to physical thermal expansion of the cavity.
Triple ring resonators incorporating thermo-optic phase shifters for wavelength
and passband shape tuning are demonstrated in Madsen and Zhao (1997) and
Coppinger et al. (1999). In Madsen and Zhao (1997), double and triple serially
5.2 Tunability Methods
225
Fig. 5.38 a The schematic layout and b the cross-section (A–A) of the temperature-controlled ring
resonator Katila et al. (1996)
coupled ring resonator filters in silicon with chromium heating elements inside the
ring resonators are presented. A minimum bend radius of 4 mm is achieved leading to
an FSR of 0.066 nm. The response of the filter is adjusted by the integrated heating
elements and is analyzed by a developed algorithm. Triple serially coupled ring
resonators integrated in a silica waveguide technology with diameters of 8.5 mm are
presented in Coppinger et al. (1999). The FSR of the filter is 7.5 GHz and a bandwidth of 1.5 GHz is measured. The application of this rather large ring resonator
filter is the filtering of microwave signals to obtain a microwave transfer function.
The integrated phase shifters (heating elements) cover part of the waveguide in the
ring. As will be explained in the following paragraph in more detail using another
ring resonator example, these heating elements are used to match the resonances of
each ring to one another which leads to an improved pass-band of the filter. Once
the desired passband characteristic is achieved, the power of the heating elements is
increased by the same amount which enables wavelength tuning of the entire filter.
Another method applied successfully to achieve wavelength tuning is by using
platinum as a heating element inside a GaInAsP/InP based ring resonator (Rabus
226
5 Devices
et al. 2002b). The platinum layer which enables the local heating of waveguide
segments of the ring resonators via the thermo-optic effect is deposited directly on
the waveguides. Before the platinum is deposited, the entire device is covered with a
SiNx layer. This layer assures that no metal will diffuse into the waveguide material
and no waveguide mode couples to the metal and increases the propagation losses.
A photograph of a part of a Pt-resistor in a ring resonator is shown in Fig. 5.39. The
pads for contacting the Pt-resistor are composed of layers of titanium, platinum and
gold. A triple ring resonator with integrated Pt-resistors is shown in Fig. 5.40.
The Pt-resistors have two functions. The first function is the tuning to specific
wavelengths. The second function is the resonance matching of multiple coupled
ring resonators to each other. A demonstration of resonance matching of a double
ring resonator is shown in Rabus et al. (2002a).
The tunability of a single ring resonator notch filter is shown in Fig. 5.41. The
Pt-resistors enable a finer tuning to a specific wavelength and so an improved on–off
ratio is obtained.
The second feature of the Pt-resistors, the resonance matching, is demonstrated
with a double ring resonator (r = 200 μm, upper and lower coupling factors κ 0,2 =
0.5, middle coupling factor κ 1 = 0.055, coupler lengths = 150 μm). The unmatched
transmission spectrum of the double ring resonator is shown in Fig. 5.42. The upper
curve shows the response of the throughput port and the lower curve that of the
drop–port. This device has not been antireflection coated, which leads to Fabry–Perot
resonances in the straight waveguides. The resonances are visible in the transmission
spectrum of the throughput port. The typical filter characteristic of the double ring
resonator is not disturbed despite the Fabry–Perot resonances. It depends on the
application, if antireflection coating is required. The contrast of the throughput port
is 16 dB and that of the drop–port 13 dB. The simulated filter response reveals a
difference of the effective refractive index of about 0.0003, which is also the origin
of the different contrast values. According to the calculation, the refractive index is
lower in the upper ring. This is mainly due to fabrication tolerances which occur
during the deep etching on the outer side of the waveguide in the curvatures. The
physical lengths of the resonators are the same. In order to match the resonance
frequency in both ring resonators, the upper Pt-resistors are used. A voltage of 0.5 V
Fig. 5.39 SEM picture of waveguide with platinum layer
5.2 Tunability Methods
227
Fig. 5.40 Triple ring resonator with integrated platinum heaters on top of the waveguides in the
curvatures and adjacent contact pads
Fig. 5.41 Tunability of a single ring resonator notch filter with Pt resistors
228
5 Devices
Fig. 5.42 Unmatched
transmission spectrum of a
double ring resonator. Dotted
line—simulation, solid
line—measurement
is applied to match the resonance frequency. The temperature coefficient of InP can
be approximated in this example to (see Sect. 3.4):
dn
≈ 0.0001 K−1
dT
(5.1)
The local temperature increase is therefore approximately 3 K. The result of the
resonance matched double ring resonator is shown in Fig. 5.43.
The tuning to a specific wavelength can be performed after the frequency matching
in such a way, that both of the Pt-resistors in the two rings are used. The driving voltage
of the Pt-resistors is different in both ring resonators due to the previous frequency
Fig. 5.43 Resonance matched double ring resonator. Dotted line—simulation, solid line—measurement
5.2 Tunability Methods
229
matching but has to be increased by the same amount in order to shift to a specific
wavelength.
A tunable racetrack shaped ring resonator notch filter in SOI is demonstrated in
Kiyat et al. (2006). Details of the ring resonator and the used waveguide are shown
in Fig. 5.44. A directional coupler with a coupling gap of 0.8 μm and a length of
48 μm is used, which results in a coupling factor of 0.45. The FSR of the ring
resonator is determined to be 248 pm. The FWHM is measured to be 40 pm leading
to a Q-factor of 38,000 and a finesse of 6.2. A heater electrode made out of nickel is
used for tuning the resonance wavelengths of the filter. The electrode covers part of
the waveguide in the curvature as in the previous example where platinum is used
as the electrode material. The resistance of the heating element including the bond
pads is 170 . The tuning of the resonance wavelength against power consumption
is shown in Fig. 5.45.
Electro-optic Tuning
Fig. 5.44 Schematic views showing critical dimensions. a Top view of SOI resonator and b crosssectional view of SOI rib waveguide Kiyat et al. (2006)
Fig. 5.45 Shift in resonance
wavelength as function of
applied power (dotted line
with arrows indicate the
tuning parameters for
reaching the FSR) Kiyat
et al. (2006)
230
5 Devices
As already cited in Chap. 3, the electro-optic effect can be used to tune the resonance
wavelength by tailoring the refractive index. In materials such as Lithium Niobate,
high efficiency can be achieved. As far as semiconductors based ring resonators,
one of the first electro-optic tunable, racetrack-shaped ring resonator notch filters in
GaInAsP/InP is presented in Grover et al. (2004). The racetrack shaped ring resonator
filter is also one of the smallest reported, with a radius of curvature of 2.25 μm and
straight sections with a length of 1 μm leading to an FSR larger than 30 nm. The
electrodes are made on top of a BCB layer which is used to planarize the device
after the waveguides have been etched. The top contact (p-side) is made out of
deposited Ti–Pt-Au. The bottom contact is made out of deposited Pd-Sn-Au-Pd-Au
after the chip has been thinned. The change of the refractive index and the tuning of
the resonance wavelength of the ring resonator filter with applied electric field are
shown in Fig. 5.46.
The quadratic electro-optic coefficient can be calculated from the measurement
and is determined to be −9.8 × 10−1 cm2 V−2 . A tuning range of 0.8 nm which
corresponds to 100 GHz at a wavelength of 1550 nm is realized.
A narrowband, widely electro-optically tunable filter based on a whispering
gallery mode cavity using LiNbO3 is demonstrated in Savchenkov et al. (2003).
The device has an FSR of 10 GHz and can be used in microwave photonics communication systems. The obtained tuning speed of the filter is approximately 10 ns. The
actual spectrum shifting time is determined by the 30 MHz bandwidth of the filter
and does not exceed 30 ms. A channel crosstalk suppression of −20 dB for a 50 MHz
channel spacing is measured.
Fig. 5.46 Effective refractive index versus electric field, assuming all the bias appears across the
core. Corresponding value of the resonance wavelength is shown on the right side. Refractive index
in the absence of electric field is obtained from simulations. Quadratic fit provides us the quadratic
electro-optic coefficient for the waveguide. Value of the coefficient for the waveguide is a lower
bound for the quadratic electro-optic coefficient of the core Grover et al. (2004)
5.2 Tunability Methods
231
Carrier Injection Tuning
One of the first vertically coupled disk resonators with a radius of 10 μm using carrier
injection for increasing the refractive index and tuning the resonance of the resonator
is demonstrated in Djordjev et al. (2002b). The device has an FSR of 10 nm and a Q
value of 5500. The fabrication of the device has been explained in Sect. 3.4.7. The
tunability of the device is 1.1 nm (mA)−1 . The refractive index change is n = −2.1
× 10−3 . The linewidth of the resonances is 0.28 nm. A transmission measurement
of the tuning of the disk resonator is shown in Fig. 5.47.
The vertically coupled disk resonator can also be used as an on/off switch. A
demonstration of the switching behavior is shown in Fig. 5.48. The switch is operated
by changing the drive current from 200 to 400 μA requiring a voltage of only 0.1 V.
A contrast between the on and off state of 10 dB is achieved.
Fig. 5.47 The free carriers
injected into the disk
resonator change the modal
refractive index, which
blue-shifts the resonant
wavelengths Djordjev et al.
(2002b)
Fig. 5.48 Switching
behavior of a disk at a
wavelength of 1598 nm.
Change in the drive current
by I = 200 μA is enough
to toggle the switch from the
off to the on state. The
voltage change required for
this transition is V =
0.1 V Djordjev et al. (2002b)
232
5 Devices
Fig. 5.49 Schematic drawings and SEM images of: a a disk vertically coupled to a single air-guided
bus waveguide, type 1, and b a disk built on a buried bus line, type 2, respectively. The SEM image
in (b) shows a stain-etched cross-sectional view of a buried bus waveguide section Choi et al. (2004)
Two different types of tunable disk resonators vertically coupled to bus waveguides are presented in Choi et al. (2004): a disk resonator coupled to air-guided rib bus
waveguides and another one fabricated on buried hetero-structure bus waveguides.
Diagrams and SEM photographs of both types of resonators are shown in Fig. 5.49.
The disk resonators have a radius of 12 μm. The two types of disk resonators have Q
values of 8000 and 3000, respectively. A tunability of 1.5 and 2.1 nm is demonstrated
at a current of 3 mA due to free carrier injection.
5.2.2 Center Wavelength Trimming
In the previous chapter, examples of tuning mechanisms have been presented which
enable the selection of resonance frequencies inside a ring resonator filter. Postfabrication methods which enable the permanent fitting of the entire resonance
spectrum to a desired resonance frequency grid are explained in this chapter.
5.2 Tunability Methods
233
Ring resonators once fabricated offer practically no way to change the resonance
spectrum besides heating the entire sample and thus changing the refractive index
which in turn shifts the resonance spectrum. Therefore it is highly desirable to have
methods which can be applied after the ring resonator filters have been fabricated to
change the resonance spectrum. One way is to use a UV sensitive polymer overlay
to change the resonance spectrum (Chu et al. 1999c). Polysilane is used as a polymer
overlay to change the resonance spectrum of vertically coupled glass ring resonators
with a radius of 19 μm. The FSR of the device before UV exposure for TE and
TM polarized input light is 10.54 and 10.56 nm, respectively. Dip coating of the
resonator is used which results in a thickness of the polymer of 2 μm. An Hg-lamp
UV source (Toshiba Lightec TOSCURE 251), having a center wavelength of 370 nm
and an irradiance of 38 mW cm−2 is used for the UV exposure. The trimming of
one resonance using TM polarized input light is shown in Fig. 5.50. The wavelength
shifts obtained for the resonances are 7.62 and 9.14 nm for TE and TM polarized
input light. No change has been observed to a device after UV exposure which was
measured again after one month.
A similar polysilane UV trimming technique has been used in Suzuki et al. (2002)
to trim the resonance wavelengths of a vertically coupled 1 × 8 filter array. A radius
of 15 μm is used for all rings in the array. The ring resonators are made on a SiO2
substrate. The ring and bus waveguides are made out of Ta2 O5 / SiO2 compound glass.
The cores of the ring resonator waveguides are covered by polysilane with a thickness
of 10 μm using dip coating. The change of the refractive index of polysilane versus
UV exposure time is shown in Fig. 5.51.
The authors report, that the center wavelength change which is caused by the index
change of the polysilane overcladding is due to the effect of oxidation or humidity
Fig. 5.50 The detailed TM
spectra around one resonance
after three different UV time
exposures (Chu et al. 1999c)
234
5 Devices
Fig. 5.51 Measured
refractive index change of
polysilane versus UV
exposure time Suzuki et al.
(2002)
absorption during UV exposure of the polysilane. The authors also report on an aging
effect which makes hermetic packaging of the device after UV trimming necessary.
A polysilane overcladding has also been used in Sparacin et al. (2005) to trim
the resonance spectrum of Si3 N4 ring resonators fabricated on a 3 μm SiO2 undercladding layer on a (100) silicon substrate with a diameter of 100 μm. The ring
resonators are designed for a wavelength of λ = 1550 nm. The difference to the
aforementioned polysilane trimming method which utilizes dip coating is that the
used polysilane is brought on to the ring resonators using a vapor phase technique.
The polysilane used is (PECVD 6M2S). The UV exposure is carried out with a
MINERALIGHT® handheld lamp (model UVGL-25) emitting at a wavelength of λ =
254 nm at an intensity of 1.7 μW cm−2 . The refractive index decreased exponentially
by ~4%, from 1.52 to 1.46 at a wavelength of λ = 1550 nm. The overall spectrum
shift obtained is 12.8 nm for the TE mode and 23.5 nm for the TM mode.
Another UV trimming method is presented in Haeiwa et al. (2004) where the
refractive index of the waveguide material SiN is exposed to UV light which imposes
a refractive index change in the material. The refractive index change of an SiN film
versus UV exposure time is shown in Fig. 5.52. The UV light source used is an Ar
ion second harmonic generation laser with a wavelength of 244 nm and an output
power of 100 mW.
Details on the used ring resonator can be taken from the inset in Fig. 5.52. The
maximum refractive index change is n = −1.3 × 10−2 , leading to a center wavelength shift of −11.4 nm. This UV induced index change is reported to be stable for
more than 1200 h without any further treatment. A side effect of the UV induced
index change is that coupling strength and loss inside the ring resonator are affected
due to the absorption of UV radiation, changing the performance of the ring resonator
5.2 Tunability Methods
235
Fig. 5.52 Refractive index
change of SiN film by UV
irradiation and calculated
center wavelength
shift Haeiwa et al. (2004)
filter. The FWHM in the presented example changed from an initial value of 0.34 to
1.02 nm after UV irradiation for 24 h.
A different approach of trimming the resonance spectrum of SiN ring resonators is
demonstrated in Wang et al. (2005). Oxygen plasma treatment is used to convert the
ring resonator material into SiOx Ny changing the refractive index and thus affecting
the resonance spectrum. The refractive index of SiOx Ny depends on the amount of
oxygen incorporated in the SiN layer and can be tuned over a large range between
1.45 (SiO2 ) and 2.0 (Si3 N4 ). A schematic of the used ring resonators is shown in
Fig. 5.53. The radius of the ring resonator filter is r = 25 μm. The length of the
zero-gap coupler is 4 μm. The waveguide width is 1 μm for the bus waveguides
and 2.5 μm for the ring resonator waveguides. An overall change in the resonance
wavelength of 8.9 nm is demonstrated.
In the previous examples, tuning of semiconductor based ring resonators has been
addressed. In the following example, a polymer ring resonator notch filter fabricated
by soft lithography (Poon et al. 2004) is tuned via a photo-bleaching technique of
CLD-1 chromophores. The radius of the ring resonator is 207 μm, and the height
and width of the waveguides are approximately 1.6 and 1.4 μm, respectively. The
coupling gap is 430 nm wide. The trimming is performed using a visible broadband
light source which is focused on one part of the ring resonator. The wavelength shift
achieved is 8.73 nm after an exposure time of 1.75 h. The stability of chromophores,
as it is well known, can degrade the performance of this material by the presence
of oxygen. Therefore hermetic sealing and an inert gas atmosphere are needed for
practical applications.
Tunability of the resonance spectrum of ring resonators by changing the refractive index with different methods has been presented, highlighting several practical
examples. These methods have only affected the FSR and have had sometimes as a
side effect, changed the shape of the resonances which is seen by an increase/decrease
of the FWHM. A way of definite tuning of the resonance shape is by implementation
of tunable couplers.
236
5 Devices
Fig. 5.53 Ring resonator filter [inset: (upper-left) SiN waveguide structure; (upper-right) photograph of fabricated ring resonator filter] Wang et al. (2005)
5.2.3 Tunable Couplers in Ring Resonators
Tunable couplers have been fabricated and demonstrated as has been described in
Sect. 4.1. Their implementation in ring resonators is so far limited by the size and
technologies used. A widely used technique for realizing tunable couplers in ring
resonator filters is by applying heaters on top of the waveguides in the coupling
region. This also affects the resonance spectrum which is also shifted and has to be
compensated with another heater inside the ring cavity.
Tunable couplers enable the exact matching of the coupling coefficient to the loss
inside ring resonator filters realizing a critically coupled state with maximum on–off
ratio. One of the first disk resonators on an SOI platform, employing tunable couplers
is presented in Lee and Wu (2005). Micro-electromechanical system (MEMS) actuated deformable waveguides are used to tune the shape of the resonance. The
layout and an SEM photograph of the MEMS disk is shown in Figs. 5.54 and 5.55,
respectively.
The disk has a radius of 10 μm and the gap is 1.4 μm wide when no voltage is
applied. A voltage of 70 V is needed to obtain a zero-gap coupler. One advantage of
using MEMS couplers is the elimination of electron beam lithography to define the
coupling gaps smaller than 500 nm. In this example a single standard lithographic
step is required to pattern both the disk and the bus waveguides simultaneously.
Another MEMS approach is described and demonstrated in Nielson et al. (2004),
where a MEMS parallel plate structure is placed above the ring resonator enabling
switching by lowering the plate and elevating it thus creating a change in the effective
5.2 Tunability Methods
237
Fig. 5.54 Schematic structure of the disk resonator with deformable waveguides. a At zero bias,
the disk is completely uncoupled since the suspended waveguides are far away from the disk. b With
voltage applied on the electrodes, the waveguides are bent toward the disk, increasing the coupling
between the waveguides and the disk Lee and Wu (2005)
Fig. 5.55 SEM photograph
of MEMS actuated disk
resonator Lee and Wu (2005)
refractive index and a change in resonance wavelength. A detailed theoretical analysis
of tunable couplers in ring resonators is presented in Kaplan (2006). Tunable couplers
are one possibility of realizing perfectly matched ring resonator filters apart from
gain implementation inside the ring cavity as was described in Sect. 5.1.2. Due to the
advancing state-of-the-art of manufacturing technologies, it will only be a matter of
time until tunable couplers are widely incorporated in ring resonator filters realizing
various types of devices.
238
5 Devices
5.3 Dispersion Compensators
In classical optics, “dispersion” is used to denote the wavelength dependence of
the refractive index in matter (dn/dλ, where n is the refractive index and λ is the
wavelength) caused by interaction between matter and light. In communication technology, “dispersion” is used to describe any process by which an electromagnetic
signal propagating in a physical medium is degraded because the various wave
components (i.e., frequencies) of the signal have different propagation velocities
within the physical medium.
Material dispersion causes different wavelengths to travel at different speeds due
to the variation of the refractive index of the fiber core with wavelength. However,
part of the light also travels in the cladding of the fiber, which has a different refractive
index. This portion of the light propagates therefore right through the cladding at
different speeds to the core—an effect known as waveguide dispersion. Material
and waveguide dispersion are combined to give an overall effect called “chromatic
dispersion.”
Chromatic dispersion is caused by a variation in the group velocity of light traveling within a fiber with changes in optical frequency. A data pulse always contains a
spectrum of wavelengths. As the pulse travels along the fiber, the shorter wavelength
components travel faster (negative dispersion) than the longer wavelength components (positive dispersion). This effect broadens the pulse and causes it to interfere
with neighboring pulses and distort the transmission signal. The allowed chromatic
dispersion in an optical network is inversely proportional to the square of the transmitted bit rate, so as data rates increase, dispersion tolerances decrease dramatically.
While 2.5 Gbit s−1 networks can tolerate 16,000 ps nm−1 of dispersion, 10 Gbit s−1
networks can tolerate only 1200 ps nm−1 and in 40 Gbit s−1 networks, the tolerance
drops to only 60 ps nm−1 of dispersion. In addition, 40 Gbit s−1 systems require a
wider modulation spectrum. A 12 GHz wide spectrum is typical for 10 Gbit s−1 ,
for 40 Gbit s−1 , it can be as high as 50 GHz, which means the total dispersion per
channel is higher. Chromatic dispersion has a fixed, stable component in addition to
a dynamic one. Most of the fixed dispersion is caused by the fiber and is predictable
as a function of the type of fiber and the distance. In addition, the optical components
present in the optical path add a smaller, fixed contribution. A dynamic contribution
must be added to the fixed one. Since many passive components do not have a simple
flat or linear dispersion curve, laser drift (caused by aging or temperature change)
can lead to dispersion fluctuations that are nonlinear and hard to predict.
Another important type of dispersion is the polarization mode dispersion (PMD).
PMD is caused by light traveling faster in one polarization plane compared to another.
Fundamentally, it is caused by the core of the fiber not being perfectly round in
cross-section and by birefringence which is introduced by mechanical forces. As a
result, the optical thickness is not absolutely identical on every possible axis. PMD
is a special case for modal dispersion or intermodal dispersion, which is caused by
multimode propagation of light. Each mode travels with a different group velocity.
The modes can be higher order modes of the same polarization, or modes of different
5.3 Dispersion Compensators
239
polarization, as is it is the case for PMD. Intermodal dispersion is of no concern under
single mode operation.
Finally, there is structural dispersion also known as quadratic dispersion which is
effectively the second derivative of the transmission phase with respect to frequency.
Structural dispersion is determined by the architecture and layout of the photonic
integrated circuit.
Ring resonators can be used as dispersion compensators and examples presented
in literature will be highlighted in this chapter. Practical dispersion compensators
should have a limited tunability, uniform insertion loss upon tuning of dispersion
and should enable the operation at multiple wavelengths. Ring resonators can be
used to enhance the physical length by forcing the light to traverse the physical
distance many times. Resonant enhancement, however, comes at the price of finite
bandwidth. A large enhancement results in a narrower bandwidth. Ring resonators
allow large compensation for multiple wavelengths simultaneously in a so far limited
frequency range.
The building block of a multistage dispersion compensator using ring resonators
is shown in Fig. 5.56. The group delay of a ring resonator follows a periodic curve.
Cascading multiple loops enables synthesization of various delay curves.
A tutorial overview on ring resonators used as dispersion compensators highlighting various configurations is given in Schwelb (2004).
Dispersion compensators utilizing ring resonator architectures have been investigated by Madsen and coworkers extensively and some examples will be given in the
following section. One filter type is of special interest, the optical all pass filter (APF).
APF’s are devices that allow phase correction or equalization without introducing
any amplitude distortion (Lenz and Madsen 1999). One of the first experimental
demonstration of a multistage all pass filter dispersion compensator that uses ring
resonators in planar waveguides is demonstrated in Madsen et al. (1999). A two stage
optical filter consisting of two parallel coupled ring resonator notch filters with a bend
radius of 2.2 mm is realized. Ge-doped silica waveguides on a silicon substrate are
used for the waveguides. A coupling gap of 3 μm is used for the directional couplers.
The phase shifter inside the ring resonators is made out of chrome with a resistance
of 55 , which is deposited on the upper cladding of each ring. The FSR of the device
is 12.5 GHz. The parameters of the filter are: D = 4200 ps nm−1 , ±5 ps group delay
ripple, <3 dB loss, and a 4.5 GHz passband width. The filter is used in a transmission
experiment using 320 km of fiber. The filter is capable of compensating negative
and positive dispersion. Due to the birefringence of the used waveguides, the filter
Fig. 5.56 Single ring
resonator filter building
block of multistage
dispersion compensator
240
5 Devices
is polarization dependent and therefore to avoid PMD, either TE or TM polarized
input light is used.
Four stage ring resonator dispersion compensating filters are presented in Horst
et al. (2000). Ring resonators with an FSR of 25, 33, and 50 GHz are fabricated in
SiON technology. Metal heaters are deposited on top of the waveguides to allow for
tunable phase shifting. A dispersion of −415 ps nm−1 over a usable bandwidth of
22 GHz for a filter with an FSR of 50 GHz is obtained. The filter is as the previous
example polarization dependent which means that accurate polarization control has
to be maintained.
A new architecture combining ring resonators and MZIs to be used for dispersion
compensation is presented in Madsen et al. (1999). A schematic of a single stage ring
resonator filter with an MZI design is shown in Fig. 5.57. The MZI design enables
a tunable APF by incorporating phase shifters in the ring and the MZI. The phase
shifter in the MZI enables a tunable coupling ratio while the phase shifter in the ring
resonator is for resonance tuning.
Four stages of the ring resonator/Mach–Zehnder combination are cascaded
yielding a dispersion of 1800 ps nm−1 and a passband of 14 GHz, which is greater
than 50% of the FSR. A low group delay ripple of 15 ps peak is achieved. The device
is realized in Ge-doped silica planar waveguides. The directional coupler lengths are
477 μm. The radius used is 1 mm, and the FSR of the filter is 25 GHz (at 1490 nm).
A device consisting of ring resonators coupled to arms of an MZI are used in
Madsen et al. (2004) to compensate and emulate PMD. A photograph of a similar
realized device is shown in Fig. 5.58. The device which is used for PMD measurements consists of a directional coupler, which is fed into an MZI which has ring
resonators attached at each arm. A schematic of the used configuration is shown in
Fig. 5.59.
The experimental device based on Ge-doped silica waveguides is a four stage
all pass filter. The radius of the ring resonators used is 350 μm, leading to an FSR
of 74.4 GHz. A discrete polarization beam splitter (PBS) on the output side and a
linearly polarized input signal with the polarization aligned to either the TE or TM
axis is used in the measurement setup. The authors demonstrate a differential group
delay (DGD) tuning range over 100 ps for 10 Gbit s−1 and 25 ps for 40 Gbit s−1
Fig. 5.57 Ring resonator
with asymmetric
Mach–Zehnder
interferometer
5.3 Dispersion Compensators
241
Fig. 5.58 A two-section planar waveguide chip with three-stage all-pass filters in the upper and
lower arms of each section Madsen et al. (2004)
Fig. 5.59 Experimental device Madsen et al. (2004)
data. Second order PMD with a tuning range of 255 ps2 and third order PMD with a
range of 2430 ps3 are also demonstrated.
Ring resonators combined with MZIs can not only be used for dispersion
compensating optical devices. Other applications will be addressed in the following
chapter.
5.4 Mach–Zehnder Interferometers Combined with Ring
Resonators
MZIs are well known and have found their way into integrated optics. A basic MZI
consist of two waveguides of different lengths, which are joined at both ends using
3 dB couplers. A schematic is shown in Fig. 5.60.
The transfer characteristic has a periodic sin2 shape over wavelength assuming
that the two 3 dB couplers are wavelength independent regarding their coupling
behavior. The distance between the minima and maxima in terms of wavelength
depend on the length difference in both arms of the MZI. The 3 dB bandwidth of the
filter in the frequency domain is given by
242
5 Devices
Fig. 5.60 Layout of a basic MZI
f =
c0
2n eff L
(5.2)
where L is the length difference between both arms.
Optical filters deployed in optical networks are required to have a “box-like” filter
response as was described earlier. One way to do this is by using multiple coupled
ring resonators. MZIs can also be modified to realize a more rectangular transfer
function by introducing a ring resonator into one of the arms. A ring resonator has
one 2π phase shift per FSR. In order to obtain passband flattening of the transfer
characteristic of the MZI, two ring resonator phase shifts per FSR of the MZI are
required. This means that the FSR of the ring resonator has to be half of the FSR of
the MZI. Translated into length requires the circumference of the ring to be twice as
large as the delay length of the MZI.
A periodic multi/demultiplexer with a square spectrum response having an FSR
of 200 GHz is presented in Kohtoku et al. (2000). A schematic of the device layout
including design parameters is shown in Fig. 5.61. The device is fabricated on an InP
substrate. MMI couplers are used in the device which enables lower manufacturing
tolerances regarding the splitting ratio. The circumference of the ring resonator is
876.6 μm leading to an FSR of 100 GHz which is half of the FSR of the MZI.
Fig. 5.61 Configuration of the periodic multi/demultiplexer with a ring resonator Kohtoku et al.
(2000)
5.4 Mach–Zehnder Interferometers Combined with Ring Resonators
243
A suitable coupling ratio for the coupler in the ring resonator has to be chosen to
obtain a rectangular transfer characteristic with a large rejection bandwidth and a
high extinction ratio. The MMI coupler in the ring resonator has a splitting ratio of
15:85. The transmission characteristic of the device is shown in Fig. 5.62.
In the following example, a balanced MZI with one arm coupled to a ring resonator
in AlGaAs-GaAs is presented (Absil et al. 2000b). The motivation in using a balanced
MZI is by realizing a notch filter and thus introducing a zero pole filter when speaking
in terms of the Z-transformation (see Chap. 2). When the round-trip loss in the ring
resonator is small compared to the waveguide coupling strength, the ring resonator
introduces a phase shift of π at resonance. The resonant phase shift is independent
of the coupling coefficient, and minimum transmission occurs. A photograph of the
device is shown in Fig. 5.63. The amplitude transfer response of this kind of device
is given by Absil et al. (2000b):
t − e−(α+ jβ)2π R − jφ
1
,
1+
e
T =
2
1 − te−(α+ jβ)2π R
t = 1 − κ 2,
(5.3)
where φ is the phase imbalance between the two arms of the MZI. The Y-splitters
are assumed of having a 3 dB splitting ratio with a wavelength independent loss. The
device has only one input and one output port coupled to 3 dB Y-splitters. The transfer
spectrum obtained is slightly deviated from the theoretical notch filter response due
to an imbalance in the arms of the MZI of only 110 nm. The spectrum is shown in
Fig. 5.64.
Fig. 5.62 Transmission spectra of the fabricated device with 200 GHz FSR. The solid line indicates ports 1–3. The dashed line indicates ports 1–4. The dotted line indicates the reference
waveguide Kohtoku et al. (2000)
244
5 Devices
Fig. 5.63 SEM micrograph
of the fabricated MZI in
GaAs–AlGaAs (Absil et al.
2000b)
Fig. 5.64 Measured Mach–Zehnder transmission spectrum and analytical fit showing imbalanced
arms (Absil et al. 2000b)
These two examples show how different transfer functions can be realized with a
ring resonator coupled to one arm of an MZI. The response depends on the length of
the arms (balanced/unbalanced), on the type of response desired and on the coupling
coefficient from one arm to the ring resonator.
Recently a novel geometry for ring resonators coupled to an MZI has been
demonstrated in polymer in Paloczi et al. (2003). A photograph of the proposed
and fabricated device is shown in Fig. 5.65. The device is realized in SU-8. The ring
resonators are racetrack shaped and have a bending radius of 100 μm. The straight
coupling sections have a length of 50 μm. The designed coupling gap is 750 nm.
The ring resonators have an FSR of 2.2 nm for TE polarized light at a wavelength
5.4 Mach–Zehnder Interferometers Combined with Ring Resonators
245
Fig. 5.65 Novel design of
ring resonators coupled to an
MZI. The size of the device
is approximately
1.2 mm Paloczi et al. (2003)
Fig. 5.66 Experimental data (dotted) and the theoretical fit (line). The fitting parameters used for
the fit were: polarization 93% TE and 7% TM, effective indices 1.48475 for TE and 1.48555 for
TM, power coupling coefficients 0.46 for TE and 0.85 for TM, and waveguide loss of 30 dB cm−1
Paloczi et al. (2003)
of 1550 nm. Complicated phase properties and a periodic spectral response of the
absolute field amplitude are observed. The transmission spectrum of the device is
shown in Fig. 5.66.
MZIs with ring resonators have also been demonstrated to be used for all optical
switching (Heebner et al. 2004).
Optical switching in ring resonators will be described in Sect. 5.8. Ring resonators
coupled to MZIs have also been investigated for implementation as modulators
Tazawa and Steier (2005).
The properties of ring resonator modulators are addressed in the following chapter.
5.5 Modulators
Wavelength division multiplexing (WDM) and dense WDM systems require modulators to generate the required optical signals to be transmitted. Electro-optic (EO)
modulators based on an MZI are used for fulfilling this task so far. Resonator based
modulators are of increasing interest as they can be operated in principle with a
246
5 Devices
lower driving voltage and have a more compact design which is a prerequisite for
integrated devices. One of the earliest resonator based modulators is of course the
Fabry–Perot resonator. Ring resonator modulators have recently gained attention
due to the improvement of fabrication technologies which enable very small devices
as was demonstrated in previous chapters, and due to improved and novel material
properties. In contrast to MZI based EO devices, ring resonator modulators have a
rather small bandwidth which limits their applications so far to systems requiring
a modest radio frequency (RF) bandwidth but operate at high carrier frequencies.
A single wavelength is used as the input signal for a ring resonator modulator. The
operating wavelength of the ring resonator modulator is tuned, so that the steepest
slope of one of the resonances in the throughput port spectrum is used. Applying a
voltage through an electrical field in the ring resonator induces a shift in the position
of the resonance peak, resulting in an intensity change at the throughput port.
The main bandwidth limitation is the time which is needed to build up the optical
field in the ring resonator. The time of one roundtrip in the resonator is given by (see
also Chap. 2):
τRoundtrip =
2π Rn g
c0
(5.4)
The total time needed for a ring resonator to build up a resonance (also referred
to as cavity ring-down time) is given by
τCav = m ·
2π Rng
c0
(5.5)
The cavity ring-down time can be related to the quality factor Q of a ring resonator
by Leinse (2005)
τCav =
λQ
2π c0
(5.6)
The cavity ring-down time can also be written in terms of the finesse F of the ring
resonator using (2.31) to:
τCav =
F Rn g
c0
(5.7)
Instead of using the group refractive index, the effective refractive index can also
be used. The group refractive index takes into account the wavelength dependency
of the effective refractive index and therefore a more accurate value for the cavity
ring-down time is obtained. The relationship between the bandwidth of the filter
spectrum response and the maximum transmission capacity is analyzed theoretically
and experimentally in Suzuki et al. (2001). A vertically coupled ring resonator add–
drop filter with a radius of 20 μm is used for the experiment. An FWHM of 0.75 nm is
5.5 Modulators
247
obtained. A pulsewidth of 3.4 ps is measured at the output port of the ring resonator,
when an input pulse of 1.2 ps with a sech pulse shape from a fiber laser is inserted at
the input port. A maximum transmission capacity of 50 Gbit s−1 is estimated for this
type of ring resonator filter. Linear and nonlinear pulse propagation in ring resonator
filters is analyzed theoretically in Melloni et al. (2003b). In particular, the so-called
slow wave structures consisting of a chain of directly coupled ring resonators are
investigated.
In the following paragraph a relationship between the bandwidth and the driving
voltage based on Rabiei et al. (2002a) is given.
Since the traditional switching voltage V π in MZI based modulators cannot be
used for a ring resonator modulator a switching voltage of V fwhm is defined, which
is the voltage required to shift the resonant wavelength by the FWHM. Sometimes
other definitions are used which define the voltage needed for a specific extinction
ratio (e.g., V 10 dB or V 20 dB).
The modulation bandwidth BW of a ring resonator is given by
BW =
1
2π τLifetime
,
(5.8)
where τ Lifetime is the finite lifetime for the photons in the resonator. Using the
frequency relationship for the FWHM
ωFWHM =
1
.
τLifetime
(5.9)
The bandwidth can be rewritten as
BW = vFWHM
(5.10)
The index change neff required to shift the resonance by vfwhm is given by
n eff
vFWHM
,
=
n eff
v
(5.11)
where neff is the effective refractive index of the ring resonator and v is the optical
frequency. The index change relation for EO materials is given by
n ef =
V
1
K n 3EOr33 ,
2
d
(5.12)
where K is the confinement factor, V is the applied voltage, nEO is the refractive
index of the EO material, and d is the distance between the electrodes. Using these
equations, the relationship between the bandwidth and the driving voltage is obtained,
yielding the fundamental limitations of these kind of modulators:
248
5 Devices
BW
K vn 3EOr33
.
=
VFWHM
2n eff d
(5.13)
The polymer based ring resonator modulator presented in Rabiei et al. (2002a) has
a bandwidth of 2 GHz and a transmission experiment has been carried out demonstrating an open eye diagram at 1 Gbit s−1 . Detailed expressions for the modulation
bandwidth and drive voltage for optical resonator based modulators can be found in
Gheorma and Osgood (2002). Ring resonator-based travelling wave modulators are
also analyzed theoretically in Tazawa and Steier (2006). Theory on ring resonator
modulators, device design, and characterization is presented in Rabiei (2003) and
Leinse (2005). In Leinse (2005), modulators consisting of a ring resonator coupled
to an MZI are also demonstrated.
Polymer ring resonator modulators with diameters of 50, 70, and 150 μm are
demonstrated in Rabiei et al. (2002b). The modulators have FSRs of 1100, 770, and
300 GHz at a wavelength of 1330 nm. The fabrication and layer sequence of the ring
resonators has been described in Sect. 3.5.1. The bandwidth of the devices is 18,
16, and 12 GHz, respectively. The authors propose a multiwavelength ring resonator
modulator and filter configuration for implementation in WDM systems shown in
Fig. 5.67.
In order for the system to be realized, the FSRs of each of the ring resonator
modulators and filters have to be greater than the wavelength spectrum used in the
WDM system. Each ring resonator has to be frequency hence wavelength stabilized
to modulate or filter out the correct wavelength with high extinction ratio. The device
consisting of several ring resonators is feasible with current state-of-the-art manufacturing methods and as was described in a previous chapter, wavelength stabilization
can be performed with several methods.
Modulators based on ring resonators on silicon on insulator are presented in
Pradhan et al. (2005) and Xu et al. (2005). A ring resonator notch filter is used with
a rib waveguide structure. Photographs of the ring resonator and the metal contacts
are shown in Fig. 5.68.
Electro-optic modulation of the refractive index is achieved by a p–i–n junction
integrated with the ring resonator. The p- and n-doped regions are on the inner and
outer side of the ring waveguide having a concentration of 1019 cm−3 . The width and
height of the ring and bus waveguides are 450 and 250 nm, respectively. A coupling
Fig. 5.67 Integrated WDM system using microring modulators and filters Rabiei et al. (2002b)
5.5 Modulators
249
Fig. 5.68 SEM and microscope images of the fabricated device. a Top view SEM image of the
ring coupled to the waveguide with a close-up view of the coupling region. b Top view microscope
image of the ring resonator after the metal contacts are formed. The metal contact on the central
p doped region of the ring goes over the ring with a 1 μm thick silicon dioxide layer between the
metal and the ring Xu et al. (2005)
gap of 200 nm is realized. The diameter of the ring resonator is 12 μm leading
to an FSR of 15 nm. The FWHM of a resonance around 1550 nm is measured to
be 0.04 nm. The cavity ring down time for this type of modulator using (5.6) is
calculated to be τ cav = 33 ps. The performance of the device is demonstrated using
a nonreturn-to-zero (RZ) signal at 0.4 Gbit s−1 and an RZ signal at 1.5 Gbit s−1 .
Vertically coupled disk modulators on InP are demonstrated in Sadogopan et al.
(2005). The operation of the device is based on a depletion width translation mechanism which involves the transfer of optical energy between two waveguides at the
resonance of a ring or disk resonator that couples the two waveguides. A photograph
of a fabricated ring modulator as well as a sketch of the cross-section is shown in
Fig. 5.69.
The fabricated device has an outer radius of 12 μm and an inner radius of 8.5 μm.
The 3 dB modulation BW of the device is 8 GHz. A wavelength shift of 0.2 nm at a
driving voltage of 0.9 V leads to an extinction of the signal wavelength of 10 dB. The
device shows open eye diagrams at 10 Gbit s−1 which demonstrates the functionality
at these speeds.
Ring and disk resonators with a high Q-factor enhance the coupling between
waveguides, thus a low voltage modulation of the resonator Q can modulate the power
transfer, enabling high speed operation. Examples of techniques for fabricating ring
and disk resonators modulator circuits have been demonstrated in this chapter and
ongoing research will enable faster and smaller devices.
High-speed modulation of a compact silicon ring resonator based on a reversebiased pn diode is demonstrated in Gardes et al. (2009), where a high speed ring
resonator modulator based on the carrier depletion effect in an asymmetric pn diode
structure is fabricated and characterized. The modulator exhibits a DC on/off ratio
of 5 dB at −10 V, and a 3 dB bandwidth of 19 GHz.
250
5 Devices
Fig. 5.69 SEM photograph
of fabricated ring modulator.
The cross-section of the
device shows the
three-dimensional coupling
which is necessary for the
depletion
mechanism Sadogopan et al.
(2005)
One of the first experimental demonstration of interdigitated PN silicon modulator
integrated in a ring resonator is presented in Ziebell et al. (2011). Here, to increase
the modulation efficiency, an alternative solution is used to change the orientation of
the diode and consequently to use interdigitated PN junctions orthogonally oriented
to the direction of light propagation (i.e. waveguide direction). In such configuration,
the optical mode propagates through successive depleted regions, which maximizes
the interaction between the light and the regions where refractive index variation
occurs.
The structure was integrated in a ring resonator with a radius of 50 μm. High
modulation was obtained in both TE and TM polarizations, with a DC extinction
ratio larger than 10 dB. V π L π as low as 2.5 V × cm was obtained in both TE and TM
polarizations. Excess optical loss lower than 1 dB were measured. Finally, high-speed
operation was analyzed thanks to 10 Gbit s−1 eye diagram measurements. A clear
open eye diagram was obtained, with 4 dB extinction ratio using 5 V peak-to-peak
RF signal.
High speed coupling-modulation of a ring resonator is demonstrated by Li et al.
(2011), showing that an extinction ratio improvement from <1 to >20 dB with 40 Gb/s
non-return-to-zero (NRZ) signals can be achieved utilizing a 25 times smaller driving
voltage. The obtained tolerance to active ring propagation loss is increased from
5.5 Modulators
251
5 dB cm−1 to more than 25 dB cm−1 with less than 5% modulation bandwidth
reduction. The authors convincingly describe of obtaining 160 Gb/s NRZ signal
with approximately 4 V drive voltage and less than 5 dB insertion loss in optimizing
their structure.
Hagan et al. (2020) present high-speed performance of a thulium doped fiber
amplifier(TDFA)-band ring resonator modulator and detector. The authors present
steady-state measurements of the defect-mediated (DM) detector showing 1.97 μm
wavelength responsivities of 0.04 and 0.14 A/W at −15 and −30 V, respectively.
The DM detector exhibits a maximum electrical bandwidth of 16 GHz at −15 V
and about half of this at −30 V. The authors have demonstrated high-speed operation of a mid-infrared (MIR) SOI-based MRR modulator operating without an integrated modulation driver at a detector-limited bandwidth of 12.5 GHz. Combined in
an optical link with a transfer-impedance-amplifier (TIA)-less high-speed detector
operating with a maximum bandwidth of 16 GHz, open eye-diagrams up to 12.5
Gbps have been demonstrated.
These examples clearly demonstrate the potential of using integrated ring
resonators as elements for telecom applications highly needed to massively increase
the bandwidth of current optical networks.
5.6 Lasers
Semiconductor ring lasers have been investigated in the past and have recently
gained attention again because they can be readily integrated with other optoelectronic devices and do not require gratings or facets for optical feedback. Ring lasers
avoid spatial hole burning by traveling wave operation, which results in single mode
operation and reduced sensitivity to feedback. Different types of active and passive
coupling configurations have been used in ring resonator lasers including Y-splitters,
directional couplers and multimode interference couplers. MMI couplers have
attracted widespread attention, because they allow increased fabrication tolerances
compared to directional couplers as has been described in Chap. 4.
Ring lasers have been described in detail in literature, therefore only brief highlights will be given and different types of laser configuration will be discussed in the
following chapter.
5.6.1 All Active Lasers
In this chapter ring resonator-based lasers fabricated using gain material for realizing
ring and bus waveguides are described. These ring lasers will be referred to as all
active ring lasers.
252
5 Devices
One of the first demonstrations of the principle of a ring resonator laser is presented
in Weber and Ulrich (1971). A rhodamine 6G2 doped polyurethane film which serves
as the waveguide is coated on the surface of a cylindrical glass rod with a diameter
of 5 mm providing the ring resonator geometry. This film is pumped with a N2 laser
having a wavelength of 337 nm emitting a beam with a sheet like output characteristic,
enabling the pumping of only a short width of approximately 0.2 mm of the film
coated glass rod. In using this pump method, a ring resonator laser is obtained.
A prism coupler is used to couple light out of the ring resonator. One of the first
integrated ring resonator lasers is presented in Liao and Wang (1980). The ring laser
is made in the material system GaAs–GaAlAs and has a straight branching waveguide
serving as the output. The output waveguide is in principle a Y-splitter. A ring radius
of 100 μm is realized. The lasing wavelength observed is around 873 nm under pulse
operation. The threshold of the laser is above 300 mA. In order to prevent the output
waveguide from acting as a second cavity, it was made 3 mm long and the facets
have been scratched to lower or eliminate the reflectivity.
One of the first continuous wave (cw) operating integrated disk resonator lasers in
the GaAs material system with integrated Y-splitter for output coupling is presented
in Krauss et al. (1990). The disk has a diameter of 84 μm and a threshold current
of 24 mA. The low threshold current is achieved by only depositing a metal contact
layer on the outer side of the disk with a width of 4 μm, forming a metal ring
and isolating the inner disk with a poly-imide layer. One of the first integrated ring
resonator lasers in GaAs/AlGaAs with a radius of 150 μm and a threshold current of
72 mA is demonstrated in Hohimer et al. (1991). A Y-splitter is used to couple out of
the ring resonator. The width of the used waveguide is 8 μm. A side mode rejection
ratio of 22 dB is measured for current values greater than 50 mA, which was one of
the highest side mode rejection ratios at that time. The laser emits at a wavelength
of 852 nm. The output power has been increased significantly for similar ring laser
devices in Hohimer et al. (1992) by tilting the output waveguide (tilt angle = 5°,
10°), eliminating a back reflection of modes which compete with the laser mode for
gain. Controlled back reflection is also investigated for unidirectional lasing in ring
resonator lasers suppressing the counter propagating wave. Ring lasers in GaAs–
AlGaAs having Y-splitters as output couplers with tilted output waveguides are also
presented in Tsai et al. (1998). Tilt angles from 0° to 15° between the waveguide
orientation and the normal of the cleaved facet are realized. Ring lasers having a
radius of 200 and 300 μm are demonstrated.
Unidirectional ring lasers using racetrack geometry are presented in Hohimer and
Vawter (1993). Inside the racetrack cavity is an equal-radius crossover S-waveguide
that is independently electrically contacted. This S bend waveguide enables unidirectional lasing. Single mode operation at wavelengths around 870 nm with an output
power greater than 10 mW is reported. This group around Hohimer has performed
extensive research on ring resonator lasers and has published numerous papers on
the subject. Therefore only an excerpt of relevant publications from this group is
presented in this chapter.
2 Formula:
C28 H31 N2 O3 Cl.
5.6 Lasers
253
One of the first ring resonator lasers in the material system GaInAsP is demonstrated in Hansen et al. (1992). The ring resonator laser has a diameter of 3 mm and
emits at a wavelength of 1.54 μm. The threshold current is measured to be 157 mA.
The ring laser is coupled to a straight waveguide with a gap of 1.5 μm. The ring
laser is fabricated using buried passive rib waveguides and two buried heterostructure active sections with multiple quantum wells. The length of the active sections is
500 μm each, placed on opposite sites of the ring laser. Continuous wave operation
is achieved with a side mode suppression of 28 dB.
InP-based ring lasers employing MMI couplers are presented and analyzed in
detail in Pennings et al. (1993, 1994) and van Roijen et al. (1994). An output power
of 9 mW under cw operation at a wavelength around 1.6 μm with a side mode
suppression of 35 dB is obtained. Two types of ring resonator geometries are analyzed
and fabricated. A schematic of the devices is shown in Fig. 5.70. Completely active
ring resonators are fabricated. Two types of MMI couplers are used, output couplers
with a width of 7 μm with lengths between 185 and 233 μm and combiners with a
width of 8 μm and lengths between 61 and 75 μm.
The use of MMI couplers in ring resonator lasers has also been investigated
and demonstrated in Krauss et al. (1994, 1995b). Racetrack shaped ring resonators
in the GaAs/AlGaAs material system with a radius of 400 μm and a length of
320 μm for the straight section and the 3 dB MMI coupler are used. The device has
a threshold current of 140 mA and emits at wavelengths around 870 nm. Ring lasers
having directional couplers, MMI couplers and Y-splitters as output configurations
are analyzed, fabricated and compared in Krauss et al. (1995a).
A square ring resonator laser in GaAs–AlGaAs with an MMI output coupler is
presented in Kim et al. (1997). A schematic of the laser is shown in Fig. 5.71. The
round-trip length of the square ring resonator laser is determined by the width of
the used waveguide. A waveguide width of 6 μm results in a 3 dB coupling length
of 283 μm and for a waveguide width of 8 μm, a 3 dB coupling length of 509 μm
Fig. 5.70 Ring laser
employing MMI
couplers—design
254
5 Devices
Fig. 5.71 Layout of square
ring resonator laser
is determined. The width of the coupling waveguide is 2 μm for the 6 μm ring
waveguide and 3 μm for the 8 μm ring waveguide. Threshold currents of 200 mA
and 250 mA are measured at lasing wavelengths around 800 nm.
A ring laser with a triangular shape in InP–GaInAsP is presented in Ji et al.
(1997). A photograph of the device is shown in Fig. 5.72. The lasing wavelength
of a presented device is around 1.26 μm with a threshold current of 64 mA (θ =
25°) under pulsed operation (100 ns pulsewidth, and 20 μs period). A side mode
suppression ratio of 25 dB is achieved. The width of the waveguide is 4 μm and the
cavity length is 300 μm. The Q of the cavity is determined by the so called structural
angle θ which defines the output angle φ. The dependence of these angles on the
output power is investigated experimentally.
Fig. 5.72 SEM fabricated triangular ring laser, cavity length 300 μm, structural angle θ and light
output angle φ are defined in the diagram Ji et al. (1997)
5.6 Lasers
255
Fig. 5.73 Schematic of photonic integrated circuit Vawter et al. (1997)
One of the first photonic integrated circuits in GaAs–AlGaAs comprising a modelocked ring laser, an optical amplifier, and a high speed photodetector is fabricated
and demonstrated in Vawter et al. (1997). A schematic of the device is shown in
Fig. 5.73.
The device is used to generate mm wave signals at frequencies of 30, 60, and
90 GHz depending on the radius of the ring laser. The radii of the used ring lasers are
860, 430, 290 μm, respectively. Passive mode locking of the ring laser is realized by
a saturable absorber, generating pulses between 1 and 10 ps.
Mode locking in ring lasers is investigated both theoretically and experimentally
in Yu et al. (1998) with respect to different configurations of intra-cavity saturable
absorbers. A schematic of the designs analyzed is shown in Fig. 5.74.
Low-threshold GaInAsP all active ring lasers are presented in Griffel et al. (2000).
The layer sequence has already been described in Chap. 3. The threshold current of
the cw operated ring laser is 66 mA with a side mode suppression ratio of 26 dB at
wavelengths around 1.6 μm.
Unidirectional bistability in circular waveguide InGaAs/GaInAsP semiconductor
lasers has been observed and demonstrated in Sorel et al. (2002). A ring diameter of
1.2 mm is used for the cw ring laser having a threshold current of 125 mA. The FSR
obtained is 0.166 nm. Three operating regimes regarding the clockwise and counter
clockwise propagating modes are observed. Operation regime one is between 125 and
Fig. 5.74 Configurations: a symmetric, b asymmetric and c dual absorber
256
5 Devices
135 mA, and both modes oscillate. Operation regime two is between 135 and 220 mA,
unidirectional operation is observed, either in one or the other direction, depending
on the driving current. The extinction ratio between the lasing and nonlasing output
is measured to be more than 30 dB. Operation regime three is above 220 mA, here the
modes randomly switch to the output ports. Bistability is imposed by two electrodes
(see Fig. 5.75), each on one side of the output waveguide. For example by applying
a short pulse to either of the two electrodes when the ring laser is operated in regime
two, changes the direction of the mode in the ring laser. Operating regimes of ring
laser in the material system GaAs–AlGaAs are also investigated by this group in
Sorel et al. (2003). A photograph of a ring laser where the contact layout can be seen
which was also used for the InP based devices is shown in Fig. 5.75. The presented
ring laser is integrated together with three photodiodes (PD) realized in a simple
manner by placing contacts on top of the active waveguides. Their position can be
taken from the photograph.
The radius of the ring lasers investigated is 1 mm. A directional coupler with a
coupling gap of 1 μm is used to couple light out of the ring. The output waveguide is
tilted at an angle of 5° to reduce back reflection of the light from the cleaved facets
below a reflectivity of 0.5%. Different operating regimes are analyzed both theoretically and experimentally. In addition to the operating regimes described previously, a
Fig. 5.75 Ring laser with
contact pad layout Sorel
et al. (2003)
5.6 Lasers
257
bidirectional regime is observed, where the two counterpropagating modes undergo
harmonic alternate oscillations.
Defined mixing of clockwise and counterclockwise ring laser modes of two ring
lasers fabricated in InGaAs/GaAs/AlGaAs is used in Cao et al. (2005) to obtain
frequency beating. The application of such integrated circuits is in ring laser gyros
and optical rotation sensors. The ring lasers in the form of racetracks have a radius
of 1 mm and a straight section length of 2 mm. Clockwise and counterclockwise
operation is achieved by integrated absorbing spiral elements coupled to the ring
waveguide located inside one ring and on the outside of the other ring. Tunability of
the lasing wavelength of each ring is realized by integrated heaters.
Single mode ring resonator laser operation using two coupled active ring lasers
is demonstrated in Hamacher et al. (2003). The ring lasers are fabricated in the
GaInAsP/InP material system. A photograph of the device is shown in Fig. 5.76.
The ring laser consists of two coupled ring resonators having a radius of 50 μm.
The ring resonators, the couplers and the bus waveguides can be driven independently by separate electrical contacts. Each ring resonator laser generates an individual slightly shifted comb like laser spectrum with respect to the driving current.
Wavelength tuning to specific single mode emission is achieved using the Vernier
effect. A measured single mode spectrum of the double ring laser configuration is
shown in Fig. 5.77. A high side mode suppression ratio of >40 dB and a maximum
output power of 6.5 mW per facet at a driving current of 250 mA is obtained.
A single mode ridge waveguide (RW) laser coupled to two ring resonators using
MMI couplers also in the material system GaInAsP/InP has been realized and
demonstrated in Bach et al. (2003). The layout of the device is shown in Fig. 5.78.
The diameter D1 and D2 of the ring resonators is 50 μm and 60 μm, respectively,
leading to an overall FSR of 18 nm. The FSR of the ridge waveguide Fabry–Perot
cavity is 0.5 nm and is small compared to the FSR of each of the ring resonators.
Therefore only the FSRs of the ring resonators will contribute to the mode selection.
The width w of the ridge waveguide is 4 μm. The facet width e inside the ring
resonators is given by
Fig. 5.76 Single mode operating double ring laser
258
5 Devices
Fig. 5.77 Single mode
output spectrum of a double
ring laser
Fig. 5.78 Layout of double ring laser. The ring resonators are also covered with BCB which is left
out for illustration purposes Bach et al. (2003)
e=
√
2 · w.
(5.14)
The ring resonators are not metal contacted and are only pumped through the
straight ridge waveguide by a lateral carrier flow over the cap layer. A measured
spectrum of such a double ring resonator laser is given in Fig. 5.79.
Ring lasers have been made with deeply etched structures to provide a stronger
confinement of the optical mode in the waveguide. This, however, comes at the
price of higher threshold currents due to surface recombination and scattering losses.
Another drawback is the fact that deeply etched structures lase in multiple lateral
modes because of the large index step. Other types of waveguide designs used for
realizing ring lasers like ridge waveguides or buried heterostructures with small index
5.6 Lasers
259
Fig. 5.79 cw laser
characteristics at room
temperature of a 700 μm
long device with 50 and
60 μm ring resonators. The
inset shows the emission
spectrum at a drive current of
450 mA Bach et al. (2003)
steps exhibit a better lateral mode confinement and have lower threshold currents. A
detailed analysis of the lateral and longitudinal mode discrimination of ring lasers is
presented in Nabiev et al. (1993).
Ring lasers with different architectures (circular, square, and triangular ring cavities) and waveguide designs having a radius down to 50 μm have been described in
this chapter. A theoretical comparison of photon recycling in circular, square, and
triangular ring laser cavities is given in Numai (2000).
Smaller devices have been fabricated by several groups and examples are given
in Sect. 5.6.3.
5.6.2 Devices with Gain Section
Merits of integrated ring resonators have been pointed out throughout this book. This
chapter demonstrates again some of them, like the integration capability with active
sections to enhance the characteristics of ring lasers.
One of the first integration of an SOA with passive silica waveguides and coupler
is demonstrated in Hibino et al. (1992). The gain in the ring resonator consists
of a GaInAsP buried heterostructure SOA. The facets of the SOA are coated with
antireflecting films made from SiO. Both facets of the SOA are coupled to lensed
optical fibers with a lens radius of 7 μm. The SOA module is inserted into the passive
integrated silica ring resonator using etched fiber grooves. The size of the module is
1.2 mm × 1.2 mm × 3 mm. The fibers are fixed to the passive waveguides using an
260
5 Devices
UV curable resin. The total resonator length is 10.2 cm leading to an FSR of 2 GHz
at a wavelength of 1.3 μm. A comb like lasing spectrum is obtained with a threshold
current of only 17 mA. The device is temperature stabilized with a Peltier cooler.
An active resonator with passive Y-coupler and outcoupling waveguides has been
realized in the material system InGaAs-GaAs in Cockerill et al. (1994). The ring laser
is made out of strained-layer InGaAs–GaAs buried heterostructure waveguides. The
integration of the passive Y-coupler is made by selective area growth. The radius of
the ring laser is 200 μm. The facets are antireflection coated to avoid back reflections.
The laser operates at a wavelength around 1 μm with a threshold current of 25 mA.
A side mode suppression of 24 dB is achieved.
Passive circular sections, an SOA and a saturable absorber in the material system
GaInAsP are used in Ohno et al. (2002) to fabricate a modelocked ring laser. The
radius of the curved sections is 100 μm. Modelocking at frequencies of 29.5, 41.2, and
61.7 GHz is obtained for three different devices with corresponding SOA lengths
of 1000, 650, and 300 μm and saturable absorber lengths of 30, 20, and 20 μm,
respectively. An MMI coupler is used for output coupling.
Ring lasers with MMI output couplers have been showed to have superior operation characteristics to devices with Y-junction couplers (examples have been given
in this chapter and in the previous chapter for both coupling versions). A further
improvement in performance of MMI coupled ring lasers as suggested in Pennings
et al. (1994) is by the use of a single active gain section in the ring, and making the
MMI coupler and outcoupling waveguides of passive waveguide material.
The realization of a racetrack shaped ring resonator laser employing an SOA as
the gain element, where the input and output waveguides, the MMI coupler and the
curved ring sections are made out of passive material is described in the following
paragraph. The passive waveguide is made from quaternary GaInAsP with a bandgap
wavelength of 1.06 μm. The ring radius is 117 μm. The length of the MMI coupler
is 150 μm. The fabrication details and the layer sequence of the passive waveguide
have already been described in Chap. 3. A photograph of the ring laser with integrated
SOA is shown in Fig. 5.80.
Fig. 5.80 Photograph of a
ring resonator laser with
integrated SOA
5.6 Lasers
261
A standard ridge waveguide laser structure was used for the 500 μm long SOA
section, which required an additional epitaxial growth step. The SOA is butt-coupled
to the passive waveguide using a self-alignment process. The detail of the SOA as
well as the fabrication process has been described in detail in Chap. 3.4.7. The butt
coupling losses have been determined to be <2 dB each. The facets of the input and
output waveguides have been antireflection coated. The ring laser has been designed
to have an FSR of 50 GHz. The ring laser is operated at T = 17 °C. The lasing
spectrum was measured using a tapered fiber and an optical spectrum analyzer. The
relationship between the lasing power in the fiber and the injection current in the
SOA is shown in Fig. 5.81.
The threshold current is as can be seen from the diagram as low as 25 mA. The
kinks in the L–I curve of the ring laser are accompanied by mode-hops and can be
explained by coupled cavity effects, the second cavity being formed by the output
path which includes the MMI coupler (Krauss et al. 1995a). The kinks have also been
observed for fabricated ring lasers which do not have an antireflection coating on
the facets of the outcoupling waveguides. The SOA does not form a cavity with the
butt-joints. This has been verified by using a straight waveguide with integrated SOA
(Fig. 5.82) where the input and output waveguides have been antireflection coated.
Fig. 5.81 Output power characteristic of a racetrack laser
Fig. 5.82 Photograph of a straight passive waveguide with integrated SOA
262
5 Devices
No lasing has been observed in such a device with a 500 μm SOA. An interesting
feature observed was that the same threshold current of 25 mA is obtained for a
device which was not antireflection coated (Fig. 5.83). The measurement has been
performed monitoring the output power directly using a photodiode. If Fig. 5.83 is
compared to the output power characteristic of the ring laser (Fig. 5.81), the fiber–
chip coupling loss which has been determined to be ~5 dB, has to be improved. This
can be done for example by using a vertical taper.
In the output power characteristic there are no kinks visible which leads to the
assumption, that the kinks in the ring laser L–I curve are mainly attributed to the
output path which includes the passive waveguides and the MMI coupler. This also
indicates that the threshold current is only dependent on the butt-joint losses. The
curved waveguide sections have negligible bending losses.
The lasing spectrum of the racetrack laser at a drive current of 162 mA is shown in
Fig. 5.84. An Advantest optical spectrum analyzer Q8384 with a maximum resolution
of 10 pm in this wavelength range is used. The measured FWHM is therefore smaller
than 1.25 GHz. The total power in the fiber is 0.6 mW per facet. As can bee seen from
the lasing spectra, the side mode suppression ratio (SMSR) is 45 dB. The spectrum
shows the designed FSR of 50 GHz of the ring resonator.
The lasing spectra covering the entire 50 nm gain spectrum is shown in Fig. 5.85.
It can be clearly seen that there is only one lasing mode.
Ring lasers fabricated by a combination of active and passive waveguide sections
enable the lowering of the threshold current as compared to all active devices, where
the whole structure needs to be electrically contacted. Special attention has to be made
Fig. 5.83 Output power characteristic of a straight waveguide with integrated SOA without
antireflection coated input and output passive waveguides
5.6 Lasers
263
Fig. 5.84 Lasing spectra of a racetrack laser at a drive current of 162 mA, showing single mode
operation with SMSR = 45 dB
Fig. 5.85 Lasing spectrum of a racetrack laser showing single mode operation over a 50 nm gain
spectrum
when joining active and passive elements. Mode field profiles of both waveguides
have to match as close as possible to minimize transition losses.
264
5 Devices
5.6.3 Passive Ring Resonator Coupled Lasers
Ring resonator coupled lasers are different from the ring lasers in the previous chapter
as the gain medium is placed outside the ring resonator cavity. Passive ring resonators
serve as optical filters which enable single mode operation and tunability of the laser.
Several examples including different architectures are described in this chapter.
Ring resonator coupled lasers offer many promising advantages over conventional
tunable lasers, including ultra wide wavelength tuning range, high side mode suppression ratio, uniform threshold and efficiency, narrow linewidth, and low frequency
chirp. The integration of active gain sections, passive waveguides and ring resonators
forming a ring resonator coupled laser has recently been proposed and analyzed in
Liu et al. (2001). A schematic of the two proposed architectures is shown in Fig. 5.86.
A detailed analysis of a single passive ring resonator coupled laser having a design
like the one shown in Fig. 5.86b, with only one gain region as the output waveguide
(the other waveguide is also passive like the ring) is given in Bian et al. (2003).
One of the first fabricated passive single ring resonator coupled lasers is presented
in Park et al. (2002a, b). A schematic of the layout of the device is shown in Fig. 5.87.
One material is used for the ring coupled laser. The ring is operated in a transparent
Fig. 5.86 Examples of
passive ring resonator
coupled lasers
Fig. 5.87 Ring resonator
coupled laser
5.6 Lasers
265
mode. Only the waveguides at the facets introduce gain into the device. The waveguides not leading to the facets act as absorbers. The ring coupled laser is made using
the material system GaInAsP on InP. Three types of devices having a radius of 5,
10 and 20 μm are fabricated. The width of the waveguides is 0.4 μm. Directional
couplers with a coupling gap of 0.2 μm are used. The bus waveguides are tapered to
a width of 2 μm having a taper length of 200 μm. The FSR of the ring resonator is
chosen large enough that a resonance is in the middle of the gain spectrum to achieve
single mode operation. The threshold of the laser is 70 mA under pulsed operation.
The lasing wavelength is measured to be 1.549 μm.
In order to achieve single mode operation, the radius of the ring resonator has to
be small, in the order of 10–20 μm. Another way to achieve single mode operation
using passive coupled ring resonators is by using a double ring architecture. The ring
resonators have slightly different radii which leads to an increase of the overall FSR
as was described in Chap. 2. Passive double ring resonator coupled lasers (DR-RCLs)
are analyzed theoretically in Liu et al. (2002).
A double ring coupled laser is demonstrated in Rabiei and Steier (2003) using
an integrated tunable polymer double ring filter, fiber coupled to an erbium-doped
fiber amplifier, serving as the gain medium. Thermo-optic and electro-optic tunable
devices are presented. The layer sequence of the device as well as the fabrication
is similar to the ones described in Chap. 3. The radius of the ring resonators is 240
and 246 μm. The overall obtained FSR is approximately 39 nm at a wavelength of
1550 nm. A layout of the double ring resonator structure is shown in Fig. 5.88.
One of several advantages of using a double ring resonator is the possibility of a
higher tuning enhancement factor using the Vernier effect. The tuning enhancement
factor is given by
T =
1
1−
L1
L2
=
R2
,
R2 − R1
(5.15)
where L 1 and L 2 are the cavity lengths of each ring and R1 and R2 the radius, respectively. The tuning range of a double ring resonator is T times the tuning range of a
Fig. 5.88 Layout of double
ring resonator structure
266
5 Devices
single ring. The polymer double ring resonator configuration has a tuning enhancement factor of 40. The transmission experiments are performed using TM polarized
input light, fed to the input port of the double ring resonator from an erbium doped
fiber amplifier which serves as the gain medium. An output power of 1 mW and a
side mode suppression ratio of 30 dB are measured for both the thermo-optic and
the electro-optic device.
One of the first integrated double ring resonator coupled lasers in GaInAsP
combining passive ring resonators with integrated SOAs is presented in Rabus et al.
(2005). A photograph of a DR-RCL is shown in Fig. 5.89. The layer sequence and
the dimensions of the waveguides are the same as is described in Chap. 3 for the
passive ring resonator and the integration of an SOA into the ring cavity.
Two configurations of DR-RCLs are investigated and the radii of the rings are
100 and 108 μm for the first configuration and 100 and 104 μm for the second
configuration. An FSR of approximately 15 and 30 nm is obtained respectively.
The coupling between the bus waveguides and the ring resonators is realized by a
codirectional coupler with a length of 500 μm and a coupling gap of 1 μm. The
coupling from the bus waveguide to the ring depends critically on the separation.
The achieved splitting ratio is 3 dB. The laser cavity consists of SOA1 and SOA2
(see Fig. 5.89) which have a length of 500 μm each and the two ring resonators.
The chip length is 2 mm. The remaining SOAs are not biased and they are used as
absorbers to suppress the lasing of sub cavity modes. The end facets of the chip are
as cleaved and are uncoated, which could be improved to increase the performance
in the future. The output of the DR-RCL is collected using a tapered fiber at SOA2.
The spectrum of the DR-RCL with an FSR of 15 nm is shown in Fig. 5.90, when
the driving currents for SOA1 and SOA2 are 110 and 90 mA, respectively. Due to the
fact that the FSR of the double ring resonator does not cover the entire gain spectrum,
another lasing mode is present. The power difference between the two lasing modes
is 13 dB. The threshold of the DR-RCL is about 30 mA when SOA1 is biased above
40 mA.
The spectrum of the DR-RCL with an FSR of 30 nm is shown in Fig. 5.91. A
side mode suppression ratio of >35 dB is obtained which is limited by the dynamic
range (−35 dB) of the used optical spectrum analyzer (OSA). The linewidth of the
Fig. 5.89 Photograph of a DR-RCL
5.6 Lasers
267
Fig. 5.90 Spectrum of a DR-RCL with an FSR of 15 nm
Fig. 5.91 Spectrum of a DR-RCL with an FSR of 30 nm
lasing wavelength is also limited by the bandwidth of the OSA which is 0.06 nm.
From calculations, the linewidth is estimated to be <2 MHz. The driving currents for
SOA1 and SOA2 are 100 and 90 mA, respectively.
The output power varies with the currents supplied to SOA1 and SOA2 (Fig. 5.92).
The threshold of the DR-RCL is about 25 mA when SOA1 is biased above 40 mA.
An output power exceeding 1 mW is demonstrated in Bian et al. (2006). The
resonance wavelength of the rings can be tuned by the integrated platinum resistors
on top of the passive waveguides in the ring resonators. Varying the current of one
heater results in a shift of resonance wavelength of the corresponding ring resonator
due to the thermo-optic effect and the lasing can jump from one mode to the next
one where the transmission peaks of the double ring resonators overlap. Figure 5.93
268
5 Devices
Fig. 5.92 PI-curve of the DR-RCL with an FSR of 30 nm changing the current at SOA2
Fig. 5.93 Wavelength tuning by applying a current between 0 and 30 mA to the integrated Platinum
heater
shows a series of lasing spectra when varying the heater current between 0 and 30 mA.
When the current of the integrated heater is changed, the laser produces 20 different
modes, which are spread uniformly over a 17 nm wavelength range.
Another architecture for a double ring resonator coupled laser is analyzed theoretically in Chung et al. (2005). The device consists of a coupled ring reflector and
an active straight waveguide providing lasing activity. A schematic of the proposed
device is shown in Fig. 5.94.
The properties and formulas describing the behavior of coupled ring reflectors
have been addressed in Chap. 2. The radius of the ring resonators is chosen to be
different enabling a larger FSR for the coupled device utilizing the Vernier effect.
5.6 Lasers
269
Fig. 5.94 Schematic of a ring resonator reflector coupled laser
Two different ring radii enable an enhanced tuning factor as is described in this
chapter. The reflective properties are obtained by allowing inter ring coupling.
A tunable laser based on a coupled ring reflector laser is fabricated and demonstrated in Choi et al. (2005). The device is fabricated by using a buried heterostructure
waveguide design in the material system GaInAsP/InP. A photograph of the device
is shown in Fig. 5.95.
The radius of the used ring resonators is 130 and 140 μm, giving an FSR for
each of the rings of 0.8 nm and 0.75 nm. The overall FSR is determined to be 12 nm.
Tuning of the device is realized through the free carrier injection (FCI) method which
shifts the resonance wavelengths by the free carrier plasma effect. The tunability of
the device is shown in Fig. 5.96. Carriers are injected into the ring resonator having
an FSR of 0.75 nm leading to a shift of the resonance wavelength of 0.8 nm which
corresponds to 100 GHz at a wavelength of 1550 nm.
Examples of ring resonator coupled lasers with different architectures have been
presented in this chapter and due to this relative new research field, an improvement
of the device parameters is expected in the coming years. Technological progress
will also add to advancement in device performance.
Ring resonator based devices both active and passive can be used for wavelength
conversion as will be demonstrated in the following section.
Fig. 5.95 Photograph of a fabricated coupled ring reflector laser. Photograph courtesy of Prof.
Dapkus, University of Southern California, Department of Electrical Engineering—Electrophysics,
VHE 314, Vivian Hall of Engineering, Los Angeles, CA 90089, USA
270
5 Devices
Fig. 5.96 Measured tuning
characteristics. Photograph
courtesy of Prof. Dapkus
5.7 Wavelength Converters
The four wave mixing (FWM) effect can be applied to passive and active ring
resonators, enabling efficient wavelength conversion for all-optical communication
systems. Ring resonators based on GaAs or InP combine both advantages of a high
nonlinear susceptibility and a high linear gain. In contrast to other active resonant
structures like distributed feedback (DFB) lasers or SOAs, ring resonators enhance
both, the optical power of the signal wavelength at frequency ωS and that of the
converted wavelength at ωC . Maximum conversion efficiency is achieved, when ωS
and ωC fit one of the resonance wavelengths of the ring resonator. No stop-band has
to be taken into account. Operating at wavelengths not being one of the resonance
wavelengths of the ring resonator results in a reduced conversion efficiency. The
internal optical field enhancement and the FSR can be designed by the radius and
the power coupling ratio between the ring resonator and the bus waveguides.
A passive GaAs racetrack shaped ring resonator is used in Absil et al. (2000a) to
demonstrate wavelength conversion by four wave mixing with an improved conversion efficiency compared to a straight waveguide. A photograph of the device is
shown in Fig. 5.97. The increase in efficiency is attributed to the increase of the
interaction length and the enhancement of optical power inside the ring resonator
cavity. Optical propagation losses limit so far the overall performance. A spectrum
of the FWM measurement is shown in Fig. 5.98. The ring resonator used in the
experiment has a radius of 4.2 μm. A coupling strength of 0.27 is obtained for the
directional coupler.
The properties of an all-optical wavelength converter with reshaping characteristics, based on FWM in a passive GaAs–AlGaAs ring resonator notch filter are
investigated in Mikroulis et al. (2004). A detailed theoretical analysis of the static
and dynamic reshaping characteristics of the wavelength converter is carried out.
5.7 Wavelength Converters
271
Fig. 5.97 Optical
micrograph of a
racetrack-shaped resonator
with defined ports Absil
et al. (2000a)
Fig. 5.98 Optical spectra for on-resonance (solid curve) and off-resonance (dotted curve)
cases Absil et al. (2000a)
Improved conversion efficiency is expected in ring resonators fabricated as allactive ring resonators. An active ring resonator architecture used for wavelength
conversion is demonstrated in Hamacher et al. (2003). A photograph of an electrically
contacted ring resonator is shown in Fig. 5.99. The ring resonator has a radius of
182 μm including two 160 μm long MMI couplers which can be electrically driven
separately to couple the light from the straight bus waveguide into the ring and vice
versa.
In analogy to FWM in DFB lasers the ring cavity itself can be used as the pump
signal source. A proper choice of the driving currents provides a sufficient side mode
suppression ratio of greater than 35 dB. An ECL acting as a cw signal source is used
in the FWM experiment. The result of this experiment with a cw output power of
2 dB m measured in the feeding fiber is shown in Fig. 5.100. A conversion efficiency
272
5 Devices
Fig. 5.99 All active ring
resonator
Fig. 5.100 Optical cw
spectrum measured at the
throughput port exhibiting a
conversion efficiency of −
5 dB (relation of the
intensities in the feeding
fibers)
of −5 dB is derived from the measurement of the output power. Taking into account
that the input signal will be increased due to the high power enhancement of the
active ring structure, the conversion efficiency can be corrected by a factor of 8 dB,
resulting in an “effective” conversion efficiency of 3 dB.
Instead of selecting a single mode laser spectrum by using a ring resonator with a
small radius and/or a proper choice of driving currents as mentioned in the previous
example, it is also feasible to obtain a mode selection by injection locking. If the
frequency of the master laser (in the test set-up a second ECL, amplified by an
erbium-doped fiber amplifier) is close enough to the ring resonator’s free-running
frequency and the signal amplitude is large enough, the device is locked to the master
frequency over a certain bandwidth. This approach may be favored for practical use
in a real system in order to realize a well controlled resonator of specified FSR for
FWM and to control the pump signal by injection locking in a separate device (master
laser).
5.7 Wavelength Converters
273
To demonstrate the FWM capabilities of an all active device, an all-optical cw
channel switching experiment is performed. In this experiment the cw signal at ωS
is kept fixed at a resonance wavelength of the ring resonator of 1567.9 nm. For
maximum conversion efficiency the injection locked pump wavelength ωP is chosen
to fit one of the resonances of the ring resonator. When the detuning of the pump
wavelength is changed stepwise by multiples of the FSR, the converted signals at ωC
= 2ωP − ωS fit the resonances of the ring resonator as well. In this way the conversion
efficiency can be kept at a maximum level over a tuning range of multiples of the
FSR, which is verified in the experiment. Due to a high coupling factor of 0.7, the
enhancement effect of the ring is limited and a conversion efficiency of approximately
−20 dB is obtained. The result of the measurement is shown in Fig. 5.101, where
λC is the converted wavelength, λP is the pump wavelength and λS is the signal
wavelength.
Wavelength conversion can also be performed using passive ring resonators with
integrated SOAs (Fig. 5.80) as the pump laser and inserting a signal wavelength
Fig. 5.101 All optical channel switching experiment in cw operation using injection locking. The
signal wavelength is fixed and the pump wavelength routes the conjugated signal
274
5 Devices
into the bus waveguide placed on a resonance of the ring resonator. A spectrum
of the ring resonator operating as a laser without signal and pump wavelength is
shown in Fig. 5.102. The result of an FWM experiment using this racetrack shaped
ring resonator with integrated SOA is shown in Fig. 5.103. The ring resonator has
a radius of 117 μm. A directional coupler with a gap of 1 μm and a length of
150 μm is used for coupling into and from the resonator. The overall FSR is 0.4 nm
which corresponds to 50 GHz at a wavelength of 1550 nm. A conversion efficiency of
approximately —6 dBm is achieved. The driving current for the SOA is 119 mA. The
Fig. 5.102 Passive ring resonator with integrated SOA in laser operation
Fig. 5.103 FWM in a ring resonator with integrated SOA
5.7 Wavelength Converters
275
signal wavelength is inserted into the ring resonator from an ECL which is amplified
by an erbium doped fiber amplifier (EDFA) to a total signal power of 3 mW.
Wavelength conversion using integrated ring resonators is a relative novel research
direction as it requires either low loss passive ring resonators or active devices to
achieve comparable conversion efficiencies as if using straight SOAs for example.
This chapter proves again the versatility of ring resonator devices.
In the following chapter, an emerging field will be introduced with several practical
examples: optical signal processing using ring resonators.
5.8 Optical Signal Processing
Optical signal processing (OSP) is one of the research areas which are receiving an
increasing amount of interest from the all-optical network community. In OSP, light
is used to influence, switch and control light. OSP has several advantages compared
to electrical signal processing. One of them is the higher processing speed, which
has been demonstrated to be as high as 100 Gbit s−1 . Elements used for OSP can
be fabricated with current state-of-the-art technologies and are easier to be realized
than compared to similar solutions in electrical signal processing. Several books can
be found dealing with the fundamentals of OSP.
The focus in this chapter is on integrated ring resonators in optical signal
processing. Ring resonators can be used for realizing all-optical switches, multiplexers, and logic gates.
5.8.1 Logic Gates
All-optical logic gates have evolved in the last couple of years and have
received considerable attention. Examples of potential applications in optical signal
processing systems are optical bit-pattern recognition, bit-error rate monitoring,
payload separation and all-optical packet addressing.
One of the most obvious applications of ring resonators in connection with logic
gates is the use as optical delay lines. In optical logic gates, control signals need to be
overlapped in time with incoming data signals. As was shown in an earlier chapter,
ring resonators used as all pass filters can address this application. Optical delay lines
can also serve as an optical buffer to delay signals until the system is ready to process
them. A detailed analysis of all pass filters used as optical delay lines is given in Lenz
et al. (2001). Multiple coupled all pass filters are investigated theoretically in Azaña
and Chen (2002) for optical signal processing applications, especially for real-time
Fourier transformation (RTFT) and pulse repetition rate multiplication (PRRM).
Optical signal processing using fabricated nonlinear integrated ring resonators is
presented in Van et al. (2002a). Applications of the ring resonators to switching, timedivision demultiplexing, pulse routing, and wavelength conversion (see Sect. 5.7)
276
5 Devices
using four wave mixing are demonstrated. The authors also propose architectures for
realizing OR, AND, and XNOR optical logic gates with ring resonators. A schematic
of the proposed logic gates is shown in Fig. 5.104.
The used input signals A, B, and C are tuned to resonances of the ring resonator.
Signal C can be regarded as a constant bias to the gate in the case of asynchronous
operation, or as a clock in the case of synchronous operation. In the case of the OR
and AND gate, the signal wavelength C is not detected at the output D when signals
A and B are not inserted. In the XNOR configuration, the MZI is balanced only when
signal C is present, leading to a signal at output D. In all three configurations, a
bandpass filter (BPF) only allows the wavelength λout to pass through.
In the OR configuration, signal C is brought off-resonance by either signal A or B
which can then be detected at output port D. In the AND configuration, both signals A
and B need to be present for signal C to be off-resonance so that it can be detected at
output port D. In the case of the XNOR gate, signal C will be off-resonance either by
the presence of signal A or B, inducing a π phase shift in the MZI and thus leading to
destructive interference at output port D which means no signal is detected. A signal
at output port D is detected on the other hand if both signals A and B are inserted into
the gate, signal C is off-resonance, the MZI is balanced and signal C can be detected
Fig. 5.104 Optical logic gates using ring resonators. Signals A and B are tuned to resonance
wavelength λin ; signals C and D are at resonance wavelength λout ; BPF: bandpass filter Van et al.
(2002a)
5.8 Optical Signal Processing
277
Fig. 5.105 Signal paths leading to AND/NAND operation in a racetrack shaped ring resonator
filter
at output D. As described in Sect. 5.5, the speed of operation depends on the cavity
ring-down time of the ring resonators.
All optical AND and NAND logic gates are demonstrated experimentally in
Ibrahim et al. (2003b). The nonlinear effect used in the experiment is the change
in refractive index from free carriers generated by two-photon absorption. InP and
GaAs-based racetrack shaped notch filters are used. The InP device has a radius of
10 μm and a 3 μm long straight section. A schematic of the signal paths is shown in
Fig. 5.105. The intensity of the pump beams A and B are alone not strong enough to
induce switching of the probe beam. The probe signal which is initially tuned to one
of the resonance wavelengths of the ring resonator leading to a “0,” is detected at the
receiver when both input signals A and B are fed into the ring resonator corresponding
to a “1.”
When the probe beam is slightly “blue” shifted and out of resonance obtaining a
“1,” NAND gate operation is achieved when both input signals A and B are fed into
the ring resonator leading to a shift of the probe beam into a resonance wavelength
resulting in a “0” at the receiver.
The experiment using the InP device is performed with a mode-locked laser at
5.6 GHz, externally modulated at 140 MHz. The pump pulse has a pulsewidth of
35 ps and energy of 20 pJ. The result of the measurement demonstrating AND logic
gate operation is shown in Fig. 5.106.
The GaAs sample, similar to the InP device, exhibits an FSR of 11 nm. A gainswitched laser diode at 8.4 GHz and externally modulated at 140 MHz, is used for
the data source. The pump pulse energies of 80 pJ per pulse are inserted into the input
port of the device. The measurement of the device showing AND/NAND operation
is given in Fig. 5.107.
An all optical AND logic gate based on the four wave mixing (FWM) effect is
theoretically analyzed in Mikroulis et al. (2005). A GaInAsP ring resonator notch
filter is used for the calculation with a cavity length of 69 μm.
Optical logic gates realized with ring resonator filters are a promising approach
which has room for improvement in the future as smaller devices and material
configurations are fabricated and investigated.
278
5 Devices
Fig. 5.106 Time traces showing an AND logic gate using the InP ring resonator: a “A” and b “B”
are the two input pumps tuned to the resonance at 1550 nm and c “F = A • B” is the output probe
signal tuned to the next higher resonance at 1560 nm Ibrahim et al. (2003b)
5.8.2 Switching
All optical switches rely on the control of light by light (the principle of optical
signal processing) as was shown in the previous section for logic gates. In order to
induce switching, an optical control signal is used to change the optical properties
of a nonlinear medium. The device, in this case the ring resonator, then switches the
data signal, which experiences the changed transmission properties when it passes
through. In all-optical switches MZIs with SOAs have been used so far where the
SOAs provide the nonlinear media. In the case of ring resonators, material systems
providing nonlinearity are required which does not necessarily mean to introduce
electrically contacted gain into the cavity. Ring resonators are ideal for optical
switching as they have a high Q-factor and can be monolithically integrated. A
high field enhancement and finesse in the ring can lower the switching threshold
significantly.
One of the first experimental demonstrations of all optical switching in GaAs ring
resonators is given in Van et al. (2002b). Switching is accomplished by a refractive
index change in the ring resonator due to free carriers generated by two-photon
absorption. This switches the probe wavelength in and out of resonance. The radius
5.8 Optical Signal Processing
279
Fig. 5.107 Time traces showing logic operation using the GaAs resonator: a and b are the inputs
“A” and “B” tuned to the resonance at 1548 nm; c output “F” when the probe was initially in
resonance at 1559 nm; and d output “F” when the probe was initially blue tuned out of resonance
at 1558.6 nm Ibrahim et al. (2003b)
of the used vertically coupled ring resonator notch filter is 10 μm. The parameters of
the device are as follows: FWHM = 0.16 nm, Q-factor = 9, 800, F = 70, calculated
field enhancement factor = 7.3, calculated cavity lifetime = 40 ps. The switching
experiment is carried out using an externally modulated laser diode, producing a
300 ps pump pulse signal with a 20 MHz repetition rate with an average input power
of 10 mW. A 3 mW cw signal is used for the probe wavelength. The pump wavelength
is slightly out of resonance whereas the probe signal is placed on a resonance of the
ring resonator. The result from the experiment is shown in Fig. 5.108. Both pump and
probe beams are inserted at the input port of the ring resonator via a fiber coupler.
After passing through the ring resonator notch filter, the pump and probe beams are
amplified and separated by a bandpass filter. Switching times of the probe beam of
approximately 100 ps is observed.
A similar ring resonator geometry is used in Ibrahim et al. (2002) to demonstrate
all-optical time division demultiplexing and spatial pulse routing. The radius of the
ring resonator add–drop filter is 10 μm. The cavity lifetime of the ring is measured to
be approximately 30 ps. Switching is again accomplished by a refractive index change
280
5 Devices
Fig. 5.108 Measured time
traces of the
pump-and-probe beam
intensities with a probe beam
initially on resonance (low
transmission) and b probe
beam initially off-resonance
(high transmission). The
transmitted probe intensity is
normalized with respect to
the maximum transmittance
at resonance Van et al.
(2002b)
induced by two-photon absorption. A data pulse inserted into the ring resonator is
demultiplexed and collected at the drop–port of the ring resonator filter. An on–off
contrast ratio of 8 dB is achieved.
A detailed theoretical analysis of the nonlinear transfer functions of ring resonators
is given in Blair et al. (2002). Ring resonators are compared to straight nonlinear
sections of different lengths. Ring resonators are demonstrated to have a higher
nonlinear phase shift induced by linear and two-photon absorption when compared
to nonlinear straight devices. Based on the simulated results, a design for an MZI
with integrated ring resonator is presented.
One of the first disk resonators with an electro-absorptive active region is presented
in Djordjev et al. (2002f). The disk uses the quantum confined Stark effect (QCSE) to
loss trim the frequency response of the resonator cavity. The disk vertically coupled
to two bus waveguides has a radius of 10 μm, an FSR of 10.5 nm, a Q-factor of
5700 and an F of 40. The transmission and dropped coefficients can be changed by
introducing additional loss into the cavity at a particular wavelength. One advantage
of using electro-absorptive ring or disk resonators is that the light is not absorbed as
strongly as it would be in an MZI configuration. Switching in ring or disk resonators
is done by changing the resonance characteristics which directs the light to the
drop–port for example.
All-optical switching in a racetrack shaped laterally coupled ring resonator add–
drop filter by carrier injection induced by single photon absorption is demonstrated in
Ibrahim et al. (2003a). Single photon absorption is achieved by optically pumping the
used material above its bandgap energy, generating electron–hole pairs, which in turn
alter the gain–loss coefficient and the refractive index. In comparison to two photon
absorption, the pump beam does not need to be located on a resonance of the ring
resonator, reducing the cavity ring-down time leading to a reduction in the switching
5.8 Optical Signal Processing
281
time. The parameters of the used ring resonator add–drop filter is: FWHM = 1.3 nm,
Q = 1, 200, FSR = 18 nm, and a finesse of 14. In the experiment, the ring resonator
is pumped from the top with a Ti:Sapphire laser with a wavelength of 800 nm. A
switching window of 20 ps is obtained. Two switching schemes are demonstrated.
In the first, the inserted wavelength is located near a resonance causing it to be on
a resonance when the ring resonator is pumped. The signal is then switched to the
drop–port. In the other scheme the signal is tuned to a resonance and by pumping
the ring, the signal is switched to the throughput port. In this way, a modulator is
implemented. A switching contrast of approximately 7 dB is achieved.
A switching time of only 20 ps is demonstrated in Hill et al. (2004) using integrated
ring lasers in GaInAsP/InP having radii of 8 μm. A photograph of the fabricated
device is shown in Fig. 5.109. The width of the waveguides is 2 μm. The lasers
are operated at 281 K in pulsed mode, with current pulses of 80 ns duration every
13.5 ms. The threshold current is approximately 30 mA. The double ring laser device
can have two stable states. In one state, light from ring laser A injection locks ring
laser B, forcing it to lase only in the clockwise direction. In the second state, ring laser
B injection locks ring laser A, forcing it to lase only in the anticlockwise direction.
Pulses of light at the chosen input can set the system in the corresponding state.
Optical signal processing using ring resonators is a useful alternative to for
example MZIs and progress in research on the switching behavior of these devices
will eventually lead to an implementation in all-optical networks.
Fig. 5.109 A memory element formed by two 16 mm diameter microring lasers coupled via
a waveguide on an InP/GaInAsP photonic integrated circuit. Scale bar, 10 mm. The microring
lasers were fabricated in active areas of the integrated circuit containing bulk 1.55 mm bandgap
GaInAsP in the light guiding layer. Separate electrical contacts allowed each laser’s wavelength to
be individually tuned by adjusting the laser current. Passive waveguides connected the microring
lasers to the integrated circuit edges Hill et al. (2004)
282
5 Devices
5.8.3 Telecom Operations
Optical networks consisting of fiber optics are the standard in telecom networks
carrying the highest data rate capacity. Especially now in the digitization and internet
age, optical networking topologies have evolved and more than ever single optical
components are required to handle the vast amount of data traffic in terms of wavelength channels. More information on the topology of different optical networks can
be found in Robertazzi (2017) and Bianco et al. (2012).
Ring resonators as described in several chapters in this book are ideal building
blocks for such all optical networks of the future as they can be used as optical
switching elements (SE) which are the key components of all optical networks.
Another important building block is a ring resonator enabling wavelength conversion
via four wave mixing. This topic has been addressed as well in this book with practical
examples. Four wave mixing or wavelength conversion is necessary in all optical
networks to change the wavelength of a data channel without the need of optical
to electrical conversion. It is beyond the scope of this book to treat the Four wave
mixing, that has been treated in details in other publications (Martini and Politi 2017)
and references therein quoted.
Ring resonators have the advantage of being able to be integrated with other
optical components like detectors, so that optical switches based on ring resonators
can be integrated together with optical detectors on a chip, thus enabling large scale
matrices with detectors for high speed all optical networking.
In addition to optical switches, optical modulators are the other work horses of
all optical networks which have been addressed in another section of this book.
In classical interconnection networks, it is known that input signals suffer power
losses independent of the state of the SEs in interconnection networks. On the
contrary, microring resonator SEs based systems show an intrinsic asymmetric statedependent behavior: as a matter of fact, because optical signals coupled/not coupled to
the ring undergo to different power degradation, depending on the specific microring
design. From a general point of view, as described in details by Garrich and Neri
(2009), the ring resonator has a transfer function identical to that of a Fabry–Perot
cavity. It represents a relatively small free spectral range (FSR) that corresponds to
the wavelength spacing used in dense-WDM (0.8 nm).
Since a microring can be tuned by several methods for example, carrier injection,
electro-optic effect or thermal tuning, it is possible to shift the transfer function. Two
possible states of the 1 × 2 microring based switching element are therefore possible:
untuned and the tuned stated respectively.
In the untuned state, the signal enters the input port and goes out by the throughput
port. In this state, the signal wavelength matches with the maximum signal through
in the transfer function and therefore the signal undergoes negligible losses 0.1 dB
(power through ON). At the same time, a small part of the useful signal is deflected
to the drop port and therefore a power leakage is observed (called power drop OFF)
(Garrich and Neri 2009). In the tuned state, the signal wavelength matches with the
maximum signal of the drop port curve in the transfer function (Garrich and Neri
5.8 Optical Signal Processing
283
Fig. 5.110 Elementary microring-based switching elements (Bianco et al. 2012)
2009). In this case the useful power is obtained at the drop port (called power drop
ON) that is lower than the previously power through ON. Experimental measurements
report that coupling the ring in order to reach the drop port brings a non negligible
attenuation 2.3 dB (Garrich and Neri 2009). At the same time, a higher value of
power leakage is obtained at the through port (called Power through OFF) since the
signal does not couple into the ring (Garrich and Neri 2009).
Starting from this simple description, optical switches based on ring resonators
can have the following configurations (Bianco et al. 2012) depicted in Fig. 5.110.
Different architectures can be built from this exploitation. In a microring resonator
OS (for example, Fig. 5.110a), an incoming optical signal can be either coupled to the
ring or it can continue along its path: the first case is achieved when the input signal
wavelength is matching to the resonance wavelength of the microring, the second if
the input signal wavelength is different from the resonance wavelength respectively.
The classical ring resonator switching configuration where a wavelength channel
is either “dropped” at the drop port from the input port or passed through to the
“throughput” port. This single element can be cascaded to create a switching matrix
consisting of several hundred switches, enabling all optical switches in real time
without any need for optical-electrical conversion and thus no data transmission
speed loss.
This behavior is at the basic one to switch an incoming signal to a different
output port, depending on the ring resonance wavelength. In order to provide the
architecture scalability, it is important to minimize the power degradation through
the interconnection network. To this aim, many efforts have been made to propose
architecture designs and suitable algorithms to control the OS configuration that will
not be treated here since beyond the scope of this book.
The other two configurations depicted in Fig. 5.110b and c are starting configurations for large scale optical switching matrices and the reader is advised to consult
the corresponding publication for further details.
It is however useful to recall that microring-based switching elements 1B-SEs
present an asymmetric power degradation depending on the switching state. As a
consequence, as summarized in Bianco et al. (2012) the design of the microring
resonator is based on a tradeoff between different figures of merit. As a consequence
284
5 Devices
a large coupling coefficient between a microring and adjacent waveguides leads to
low power degradation in signals deflected to the drop port but high degradation to
signals sent towards the through port respectively. On the contrary, a small coupling
coefficient between a microring and adjacent waveguides leads to high degradation in
signals deflected to the drop port but low degradation to signals sent. In the microrings
controlled by laser pumps, input signals sent to the drop port undergo to higher power
losses (around 1.5 dB) than signals routed to the through port (with negligible losses).
As a matter of fact, there is a small coupling coefficient between the microring and
the drop/through waveguides. In this case the loss behavior of the 1B-ES with a
simplified model based on two loss states, assuming either a high-loss state (HLS)
or a low-loss state (LLS).
In general these are the basic architectures for interconnection networks mostly
used: crossbars, Clos networks, and Benes networks respectively. Hybrid configurations are possible, to optimize the final performance in terms of degradation index
and area.
Crossbars Network
Crossbars can be built exploiting the 1B-SE switching element configuration, as
depicted in Fig. 5.111: column waveguides are connected to the input ports and
row waveguides to the outputs (Bianco et al. 2012). The crossbar exhibits the best
Fig. 5.111 4 × 4 microring-based crossbar connecting 1 → 4, 2 → 2, 3 → 1, and 4 → 3 (Bianco
et al. 2012)
5.8 Optical Signal Processing
285
Fig. 5.112 Rearrangeable non-blocking Clos network (Bianco et al. 2012)
scalability in terms of degradation index: although routing is easily achievable, they
exhibit the worst scalability in terms of area.
Clos Network
When a lower number of switching elements (SEs) than the crossbar are used, a
multistage interconnection networks, like the well-known Clos networks is created.
Figure 5.112 reports a symmetric three-stage Clos network as example.
In this case each switching module (SM) of the first stage and of the third stage is
connected with all the SMs of the middle stage (Bianco et al. 2012). As a consequence,
the first design parameter is the number of SMs in the first and the third stage,
respectively, denoted by k. The second design parameter is the number of SMs in
the second stage, influencing the blocking property. In the case that n = N/k SMs
in the middle stage, this is the minimum n value that guarantees a non-blocking
rearrangeable network. As a consequence, the first-stage and third-stage SMs are of
size n × n, and the second-stage SMs are of size k × k.
Benes Network
Benes networks are basically Clos networks recursively constructed with basic SMs
of size 2 × 2. In this way N = 2h for some integer h. They present the best scalability,
being asymptotically optimal. It is worth mentioning that an N × N Benes network
has a number of stages (columns of 2B-SEs) equal to 2log2 N − 1, each stage including
N/2 basic 2B-SEs.
286
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Chapter 6
Sensors
Integrated optical sensors are and have been investigated since a long period of time
and have found their way into many applications. Ring resonator can be used as
sensing elements for example by measuring the resonance frequency shift, which is
induced by a change in the effective refractive index. Integrated waveguide-based
sensors have gained attention since the downturn of the telecommunication industry
left several research groups looking for other fields of application. But this is not the
only cause. The focus of research has turned more and more towards biology where
single molecule and single cell detection are the envisaged goal.
This chapter provides an overview of sensors based on integrated ring resonators in
microfluidics, optofluidics and special focus on biosensors. The following examples
demonstrate the wide range of application of integrated ring resonators which has
grown tremendously in the last 20 years.
In Table 6.1 a comparison among the most used sensor configuration is provided
together with some key sensing parameters such as bulk sensitivity, system detection
limits and intrinsic detection limits depending on the sensor configuration. He values
therein reported should be considered as a order of magnitude of what currently available, destinated to improve in time thanks to the constant optimization of technologies
and the advent of new ones.
Sensors for Measuring Optical Properties of Waveguides
A silicon based integrated ring resonator notch filter with a radius of 3 cm is used
in Adar et al. (1991) to measure the loss in phosphorus-doped silica on silicon
waveguides. The finesse of the resonator is 45. The measuring principle used is the
fact that waveguide loss is related to the width of the resonances (see Chap. 2).
The ring resonator is placed on a temperature controlled surface. An ECL kept at a
constant wavelength, with a linewidth smaller than the width of the resonances of
the ring resonator is used as the input source. The temperature is changed and the
response of the ring resonator is measured, revealing the filter function characteristic
for ring resonator notch filters. As the FSR is known from the parameters of the ring
© Springer Nature Switzerland AG 2020
D. G. Rabus and C. Sada, Integrated Ring Resonators, Springer Series
in Optical Sciences 127, https://doi.org/10.1007/978-3-030-60131-7_6
293
Sensor
configuration
MZI
Ring
Sensor type
Interferometer
Microcavity
TM
TE
TE
TE
TE
TM
TE
TM
TM
TM
TE
TM
Vernier
Vernier
Slot/critical
coupling
Multi-box SWG
SWG
SWG
Slot
Suspended
Thin WG
N/A
Thin WG
1.31 μm Wvl
TE
N/A
TM
TM
N/A
Vernier/suspended
TE
TE
1.31 μm Wvl
TE
Suspended
Slot
TE
Optical mode
Vernier
Strategy
33.5
24
10.1
4.5
12
0.33
9.8
7
2.6
6
20
15
N/A
N/A
N/A
N/A
N/A
N/A
N/A
Q-factor (×103 )
nm
113 nm
133 nm
200 nm
270 nm
290 nm
298 nm
429 nm
490 nm
580 nm
1.3 ×
103
nm
1.3 × 103 nm
2.43 ×
N/A
4.6 × 105 nm
104
N/A
N/A
300 × 2π rad
N/A
N/A
N/A
N/A
N/A
(continued)
1.49 × 10−3
5 × 10−4
7.5 × 10−4
1.2 × 10−3
N/A
1.59 × 10−2
4.2 × 10−5
5.5 × 10−4
1.02 × 10−3
3.71 × 10−4
10−6
N/A
2×
N/A
<10−4
N/A
5.05 × 10−4
N/A
N/A
N/A
4.8 × 10−6
N/A [44]
3.3 × 10−5
460 × 2π rad
N/A
N/A
1.29 ×
4 × 10−5
N/A
1730 × 2π rad
10−5
N/A
Intrinsic detection
limit (RIU)
540 × 2π rad
N/A
N/A
2.15 × 104 nm
740 nm
System detection
limit (RIU)
Bulk sensitivity
(RIU−1 )
Table 6.1 Comparison among the most used sensor configuration is provided together with some key sensing parameters, WG, waveguide; Wvl, wavelength,
1.55 μm where not specified (Luan et al. 2019) and references therin quoted
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6 Sensors
Uniform
Phase-shifted
1D
2D
Disk
Sensor
configuration
TM
TE
1.31 μm Wvl
N/A
TE
TE
Slot
N/A
TE
Multi-box SWG
TE
N/A
TE
Ring-slot
TE
TE
N/A
Slot
TE
TE
N/A
Slot
TM
Suspended
TE
N/A
TM
TE
1.31 μm Wvl
N/A
Optical mode
Strategy
Reprinted under Creative Commons Attribution (CC BY) license
Bragg grating
Photonic crystal
Sensor type
Table 6.1 (continued)
N/A
27.6
76
15
6.2
3
174
11.5
0.4
50
33
0.1
16
15
9.8
Q-factor (×103 )
103
182 nm
59 nm
106 nm
340 nm
610 nm
130 nm
815 nm
160 nm
200 nm
1.5 ×
26 nm
130 nm
142 nm
38 nm
91 nm
nm
Bulk sensitivity
(RIU−1 )
N/A
N/A
N/A
N/A
N/A
7×
N/A
N/A
2×
10−5
10−3
10−6
10−4
7.8 ×
N/A
8×
N/A
N/A
N/A
System detection
limit (RIU)
N/A
9.3 × 10−4
1.6 × 10−4
3 × 10−4
4 × 10−4
4 × 10−3
1 × 10−5
8.75 × 10−5
1.88 × 10−2
2.07 × 10−5
1.8 × 10−3
1.18 × 10−1
6.8 × 10−4
2.7 × 10−3
3.5 × 10−4
Intrinsic detection
limit (RIU)
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296
6 Sensors
Fig. 6.1 Integrated
microring resonator
displacement sensor for
scanning probe microscopies
resonator, the width of the resonances can be taken directly from the transmission
experiment leading to the waveguide loss.
An integrated ring resonator sensor is analyzed theoretically in Kiyat et al.
(2004) to be implemented in a setup to measure the displacement in scanning probe
microscopy. A schematic of the proposed device is shown in Fig. 6.1.
The displacement of the cantilever changes the refractive index of the ring
resonator which changes the transmission spectrum. Several designs including
racetrack-shaped ring resonators are simulated and compared. The highest sensitivity is obtained for a racetrack-shaped ring resonator. Sensitivities as high as 10−4
Å−1 are calculated.
Waveguide birefringence is measured in Carriere et al. (2004) by using an integrated ring resonator with a radius of 14 mm, fabricated by ion exchange in glass.
The waveguide birefringence is defined as the difference between the effective refractive indexes of transverse electric and transverse magnetic modes. The birefringence
nBi ; is calculated using the FSR of a ring resonator as follows (Carriere et al.
2004). Using (2.21) where the group refractive index is used, the shift in wavelength
between the two polarization states seen in the FSRs is given by
FSRBi = FSRTM − FSRTE
1
λ2
1
.
=
−
L n gTM
n gTE
(6.1)
The waveguide birefringence is defined as
n Bi = n eff, TE − n eff, TM .
(6.2)
Using (2.20), the waveguide birefringence in terms of the FSRs is given by
n Bi =
FSRBi
λ2
·
.
L FSR(FSR − FSRBi )
(6.3)
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297
Fig. 6.2 Cross-section and photograph of the polymer ring resonator used for the strain sensor.
Dimensions are in μm Bhola et al. (2005)
Fig. 6.3 Application of controlled strain using a micrometer stage. E is the strain and R the radius
of the bend Bhola et al. (2005)
This equation is straight forward and the birefringence is easily calculated from
the measurement of the FSRs. In order to differentiate the birefringence induced by
the curved sections of a ring resonator, racetrack-shaped and full circle resonators
can be compared in terms of their birefringence. The difference is only due to the
contribution of the straight waveguide sections.
Sensors of Strain
Ring resonators are not only used for measuring birefringence in waveguides, but can
also be applied to determine strain. In Bhola et al. (2005) a polymer ring resonator
strain sensor is demonstrated. A photograph and a cross-section of the fabricated
device are shown in Fig. 6.2. A sketch and a photograph of the strain sensor attached
to a micrometer stage are shown in Fig. 6.3. An advantage of using ring resonators
as strain sensors is that the direction of the strain does not matter due to the ring
geometry. The sensitivity can be increased by using a racetrack shaped ring resonator.
In this case two racetrack-shaped ring resonators perpendicular to one another can
be used to determine the direction of the strain.
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6 Sensors
Fig. 6.4 Layer sequence of
waveguide in a ring
resonator gas sensor
These examples demonstrate a small variety of sensors realized with integrated
ring resonators in different materials. Lately biosensors have attracted a lot of
attention and ring resonators are again focus of research in this new emerging field.
Sensors of Gas
So far solids or liquids are detected with ring resonators. A gas sensor is fabricated
and demonstrated in Ksendzov et al. (2004) which utilizes a polymer sensing layer.
The racetrack-shaped ring resonator add–drop filter has a radius of 1.5 mm. The
straight sections have a length of 0.1 mm with a coupling gap of 2 μm. The layer
sequence of the waveguide used is shown in Fig. 6.4.
The polymer swells in the presence of the analyte and changes its refractive index
due to chemical permeating. The resonance wavelength is monitored with a tunable
laser and the shift is detected in dependence of the concentration of the analyte. The
fabricated ring resonator is brought into a sealed chamber and a controlled mixture
of air, water vapor, and isopropanol is inserted. Sensitivity to isopropanol of 50 ppm
is shown experimentally.
Sensors of Temperature
The optical path length of the ring waveguide changes when thermally-induced
effects act to modify the effective refractive index. Consequently, a shift of the
resonance wavelength occurs that can be probed and monitored by a tunable laser
or spectrometer (Kwon and Steier 2008; Kim et al. 2010; Xu et al. 2014). In these
works, it has been reported that in SOI ring resonators a temperature sensitivity close
to ~80 pm/°C can be achieved. Apart from the sensitivity, the temperature detection
limit (otherwise often addressed as temperature resolution) and the sensing range are
of key importance. Whilst the temperature resolution it is related to the sensor resolution and sensitivity and of the performances of the linewidth tunable laser and/or
spectral analyzer used, the sensing range is determined by the free spectral range
(FSR) of the ring resonator. The last corresponds to the temperature change able to
induce the resonance wavelength shift to a full FSR. In order to increase the sensing
6 Sensors
299
range the easy way is to increasing the FSR, feasible by coherently reducing the
ring size. There are several devices that have been demonstrated: the most known
are a sensing range of 120 °C have been realized by a 9.2 μm-radius ring resonator,
whilst a 280 °C of sensing range by a 4 μm-radius ring resonator respectively. Many
efforts have been devoted to improve the temperature sensing performances of ring
resonators employing different ring resonator configurations. Among those sure it
deserves to cite: cascaded ring resonators (CRR) (Dai 2009; Zamora et al. 2013)
for realizing the Vernier effect and get higher sensitivity-finesse and FSR, vertically
stacked ring resonators for obtaining resonance splitting (Campanella et al. 2014),
and Bragg grating ring resonators for achieving resonance splitting and Fano resonance (De Leonardis et al. 2014) and get enhanced sensor resolution. As reported
in Kim (2016), in a conventional CRR sensor configuration two ring resonators
are exploited in which one acts as reference resonator and the second ad sensor
resonator respectively. They are designed to have slightly different FSRs (FSR1 and
FSR2 , respectively) and to respond differently to a given sensing input: the resonance
wavelength of the sensor resonator shifts whilst the reference resonator provides
unchanged resonance wavelength. In case that the dispersion is neglected, the FSR
of the CRR is therefore given by Claes et al. (2010)
FSRCRR = FSR1 · FSR2 /(FSR1 − FSR2 )
(6.4)
so that the CRR sensitivity is magnified by a factor of FSR · CRR/FSR2 . On the
contrary the sensing range is determined by the FSR of the sensor resonator and does
not benefit of amplification. Although extremely convenient, the CRR configuration
is not trivial to be achieved because it requires that the reference resonator is isolated
from a temperature change. Alternatives have been proposed such as depositing a
cladding layer with negative thermo-optic coefficient such as polymer or TiO2 (Ye
et al. 2008; Guha et al. 2013) on the reference resonator to prevent its temperature
sensitivity. Polymers are not CMOS compatible and therefore present several drawbacks whilst and the selective deposition of a negative thermo-optic cladding layer is
quite expensive requiring several steps made procedures. To solve this problem, Kim
(2016) realized two micro ring resonators with different temperature sensitivities and
different free spectral ranges (FSRs) by tailoring the in-plane geometric parameters
of the two ring resonators respectively. A scheme of the final device is reported in
Fig. 6.5. The CRR temperature sensor was therefore prepared by using a singlemask complementary metal–oxide–semiconductor (CMOS)-compatible process. A
temperature sensitivity of 293.9 pm/°C has been demonstrated and a temperature
sensing range increased by a factor 5.3 times.
A sketch of the CRR temperature sensor operation is shown in Fig. 6.6 where a
cascaded configuration of Rings 1 and 2 is reported together with the Transmission
spectra at the drop ports of the two ring resonators, and at the output of the CRR
respectively.
Finally, the derivative of the effective refractive index neff respect the temperature
as well as the temperature sensitivity of a ring resonator as a function of waveguide
300
6 Sensors
Fig. 6.5 a Optical microscope image of the fabricated CRR temperature sensor. SEM images of
the ring and bus waveguides in the coupling region for b Ring 1 and c Ring 2 (Kim and Yu 2016).
Reprinted under Common Creative License CC BY
Fig. 6.6 Schematic of the CRR temperature sensor operation. a Cascaded configuration of Rings
1 and 2. Transmission spectra b at the drop ports of the two ring resonators, and c at the output of
the CRR. d Power output at the drop port of a single ring resonator as a function of wavelength and
temperature (Kim and Yu 2016)
6 Sensors
301
Fig. 6.7 a ∂neff /∂T, ng , and b temperature sensitivity of a ring resonator as a function of waveguide
width. c FSR and d TP as a function of ring radius with 350 nm and 450 wide waveguides at the
quasi-TM mode. FDTD simulation and analytical calculation were performed at 1550 nm. The
waveguide thickness is 210 nm (Kim and Yu 2016)
width are plotted in Fig. 6.7. FSR and TP as a function of ring radius with 350 and
450 nm wide waveguides at the quasi-TM mode are added for completeness. FDTD
simulation and analytical calculation were performed at 1550 nm, using a waveguide
thickness is 210 nm.
Optical Sensor
This section includes the well received contribution on optical sensors by Patrick
Steglich (Leibniz-Institute for Innovative Microelectronics), which is highly acknowledged with thanks by the authors.
Optical sensors in photonic integrated circuit (PIC) technology have great potential for cost-effective disposable sensors with various applications in environmental
monitoring, food analysis and point-of-care-testing (Steglich et al. 2019a, b). Such
sensors have the potential for the simultaneous analysis of various substances (Wang
et al. 2020) and physical parameters such as temperature (Steglich 2020; Steglich et al.
2020) and stress (Lu and Lee 2009). Further, they provide rapid results within minutes
302
6 Sensors
and the direct translation of the optical into an electrical signal by using a chipintegrated photodiode allows reliable and secure data transfer, employing modern
communication protocols. One main advantage, however, is the miniaturization of the
complete sensor system. This includes the light source, sensor element and electronic
readout, which gives perspectives to mobile and lab-on-a-chip applications.
The working principle of micro-ring resonators as optical sensor is based on a
refractive index change. At this point, we should distinguish between two cases. First,
if the refractive index of the surrounding material changes, we speak about refractive index sensing in bulk material or surface sensing in case of specific detection of
molecules at the surface of the waveguide. Second, if the refractive index of the optical
waveguide is changed, we speak about thermal or stress sensing, depending on either
the refractive index change originates from a temperature change or from the applied
stress inside the silicon waveguide, respectively. Temperature sensing is highly efficient in silicon-based PICs due to its large thermo-optical effect (Weituschat et al.
2020). In all aforementioned cases, the detection principle relies on the change of
the effective refractive index of the optical waveguide which causes a change of the
resonance condition:
λ =
λres
n clad
ng
(6.5)
Here, λres refers to the resonance wavelength, n clad represents the cladding
refractive index change which is similar to the refractive index change of the fluid.
It is useful to distinguish between the waveguide sensitivity and the ring resonator
sensitivity. The former describes the interaction of the guided light with the
surrounding medium. It takes into account that the effective refractive index is altered
if the cladding refractive index is changed. The waveguide sensitivity is given by:
Swg =
n eff
n clad
(6.6)
where n eff represents the effective refractive index change. Such a definition is
useful for waveguide optimization through simulation studies. However, the ring
resonator sensitivity depends not only on the waveguide geometry and, therefore, a
second definition defining the ring resonator sensitivity is given by
Srr =
λ
n eff
(6.7)
Taken both definitions into account, we get the overall photonic device sensitivity
defined by
S = Swg Srr =
n eff λ
λ
=
n clad n eff
n clad
(6.8)
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303
The unit the definition reported in (6.8) is often written as nm/RIU, where RIU
denotes the refractive index unit. The refractive index change n clad can be detected
by tracking the resonance peak position or by measuring the intensity at a fixed
wavelength, as shown in Fig. 6.15.
The peak position is usually tracked by using a broad light source in combination
with an optical spectrum analyser, while the intensity can be measured by employing
a tunable laser with a chip-integrated photodiode.
6.1 Microfluidics
Similar to the technological advances in integrated ring resonator devices, microfluidics developed accordingly and basically started off in the 1990s. Although one
could say that the origin of ring resonators and microfluidics can both be related
back to the advent of MEMS in general.
The aim of this short chapter is to provide you with a brief overview of the
possibilities in such a way, that you can directly start to work on your dedicated
project and run your application so that you can focus on your expertise.
The last years, with growing technological fabrication advanced, have given ring
resonators and microfluidics a huge boost, leading to more and more applications
and products and as such, a variety of specialized technologies exist which will be
described in the following.
The question nowadays is not anymore if microfluidic devices can be realized but
rather what are the requirements for the application and then what follows is merely a
matter of fabrication and system approach and perspective. For example, if you need
to create your microfluidic chip, companies offer a large variety of readily available
configurations and even customized chips are commercially available. 3D printing
has boosted microfluidic applications tremendously. The result is more than visible
in the number of publications in this field, just to mention as an example the recently
published book on 3D Printed Microfluidic Devices by Tasoglu and Folch (2019).
Several available technologies for realizing microfluidics are available for
example in realizing small scale devices in polymeric materials with state of the art
two photons polymerization techniques. Salvatore Puce et al. (2019) demonstrated
what is also known as 4D lithography to combine polymer and metallic structures
for future integration of 3D MEMS multi-material sensing possibilities (Figs. 6.8
and 6.9).
Another possibility to fabricate arbitrary three-dimensional suspended hollow
microstructures in transparent fused silica glass are described in Kotz et al. (2019).
The fabrication of suspended hollow microstructures in fused silica glass steps and
results are reported in Fig. 6.10.
Structures templates produced by direct laser writing and the resulting microfluidic spiral channels in fused silica glass with a channel width of 74 μm are reported
in Fig. 6.11 with the relative characterization in Fig. 6.12.
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6 Sensors
Fig. 6.8 a Schematic representation of a silicon-on-insulator ring resonator. According to the
resonance condition, only selected wavelengths can propagate in the ring and distinct resonance
peaks appear in the output spectrum. b Molecular binding takes place if a sample of the analyte gets
in touch with the adsorbed layer on top of the silicon waveguide leading to a resonance wavelength
shift (Steglich et al. 2019a, b)
Fig. 6.9 Fabrication process flow. (i) Spin coating of bottom resist and drop casting of the top
resist. (ii) 2PP writing process of Sacrificial Stencil Mask and pedestal in one single step. Exclusive
development of the top layer (iii) followed by the metal evaporation step (iv). After the bottom resist
development (v), the structure is fabricated (Puce et al. 2019). Reprinted under Common Creative
license
Printing your own microfluidic device with overlay functionality and integration
of MEMS sensors is also possible today with state-of-the-art equipment.
Microfluidic systems with valves and dosing units or micropumps are possible as
well using commercially available devices.
These are just a few examples to highlight the endless possibilities established in
the last couple of years in the microfluidics field, enabling a steady and fundamental
growth of this exciting field.
The authors believe that future research is geared towards the combination of
disciplines and the system and application aspect is brought into focus resulting in
even further interdisciplinary work- and research groups.
6.1 Microfluidics
305
Fig. 6.10 Double layer resists deposition i. Diffusion of the top resist into the bottom one ii. Floodexposure prevents the diffusion of the two resists (Puce et al. 2019). Reprinted under the permissions
of Elsevier Common Creative license
An example of an integrated ring resonator in a microfluidic setting is presented by
Geidel et al. (2016) where a ring resonator biosensor is embedded into a microfluidic
cartridge (see Fig. 6.13).
The design of the ring resonator is shown in Fig. 6.14 including the integration
into the microfluidic environment (Fig. 6.15).
This is a perfect example of what is already possible today with state-of-the-art
technology thus enabling the further extension of the research boundaries. Having
said this, the authors encourage the scientific community to again focus on the main
interest of their research and using existing readily available technology and scientific interdisciplinary collaborations to proof the system aspect of their research for
enabling a faster demonstration of the application.
6.2 Optofluidic Resonators
A promising strategy for improving the light– matter interaction is to increase as
much as possible the interaction time between the probe and the probed target. For
this reasons ring resonators, and especially integrated microring ones, have attracted
great attention. As defined in Li (2015), optofluidic resonators are optical microcavities that are partially or completely made of liquids: they confine light both spatially
and temporally in some structurally defined resonance modes. Classified into liquidcore, liquid-cladding, and all-liquid resonators, the most common cavity types are
whispering gallery mode (WGM) cavities, photonic crystal or DFB type cavities and
Fabry–Perot type cavities respectively. Among the others, WGM cavities normally
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6 Sensors
Fig. 6.11 Fabrication of suspended hollow microstructures in fused silica glass. a Polymeric filaments are embedded in an amorphous silica nanocomposite. The polymerized nanocomposite is
turned into fused silica glass via thermal debinding and sintering. The polymeric template is removed
during the thermal debinding process and leaves the according hollow cavity. b Microfluidic fused
silica chip fabricated by embedding a nylon thread (scale bar: 9 mm). c Microfluidic meander
fabricated by embedding polymerized PEGDA structured by microlithography (scale bar: 11 mm).
d A mesh structure made from poly(ε-caprolactone) using melt electrowriting (scale bar: 5 mm).
The inset shows the microscopy image of the mesh with a fiber diameter of 25.0 μm (scale bar:
100 μm). e Inverse hollow mesh structure in fused silica glass (scale bar: 4.5 mm). Inset shows the
microcavities with a width of around 18.4 μm (scale bar: 100 μm) (Kotz et al. 2019). Reprinted
under Common Creative License
present ultrahigh quality (Q) factors providing very narrow linewidth cavity resonances favorable for low-threshold lasing and ultrasensitive sensing applications.
Photonic crystal or DFB cavities are instead are more suited for on-chip integration with microfluidics. Microfluidic channels can be combined in the fabrication
process with the optofluidic cavity structure to get on-chip microfluidic tuning and
sample introduction. Fabry–Perot cavity is instead well suited for intracavity sensing
and spectroscopy applications because the ease of access to its intracavity space.
Optofluidic resonators offer tunable optical resonances with extremely large tuning
range (refractive index change can be as high as 0.5 compared with <0.01 in most
solid-state materials) by liquid filling, mixing, or replacement. By placing the target
inside an optical cavity with a high-quality factor Q, in fact, a high gain can be
achieved (Minzioni et al. 2017). Integrated optofluidic resonators in the form of a
6.2 Optofluidic Resonators
307
Fig. 6.12 STR using templates produced by direct laser writing. a Polymeric DNA double-helix
(scale: 500 μm). b Inverse structure in fused silica glass (scale: 400 μm). The smallest channel size
is 20 μm. c Intertwined spirals (scale: 900 μm). d Resulting intertwined microfluidic spiral channels
in fused silica glass with a channel width of 74 μm. The channels were filled with dyes (see inset,
scale: 140 μm). e Polymeric microstructures of an out-of-plane mixer structure (scale: 600 μm).
f Microfluidic mixer structure in fused silica glass with a channel width of 74 μm (scale bar:
280 μm). As can be seen the 3D structures can be replicated with high fidelity and no deformations
(Kotz et al. 2019). Reprinted under Common Creative License
planar ring have been obtained using slot waveguides (SWs), Bragg waveguides
(BWs) or antiresonant reflection optical waveguides (ARROWs). Towards disposable optical sensor chips, the use of a single wavelength light source in combination
with a chip-integrated photodiode is preferable since optical spectrum analyser are
expensive and cannot be miniaturized currently. Such a configuration can be used
for intensity measurements. However, the main drawback of intensity measurement
is the small detection range. Currently, approaches to track the peak position with a
laser and photodiode is realized with a tunable laser, which is expensive and requires
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6 Sensors
Fig. 6.13 Characterization of suspended hollow microstructures in fused silica. a, b SEM of rectangular channel cross-section with an aspect ratio of 0.1 and 10 (scale: 100 μm). c–f SEM of spherical,
triangular, trapezoidal, and rectangular channel cross-sections (scale: 10 μm). All templates were
fabricated using direct laser writing. The flattened side of the “spherical” channel cross-section
is due to the 2-photon polymerization 3D printing process of the template. Structures are printed
on glass slides and a certain contact area is required to prevent the structure from detaching from
the glass. g, h SEM and white light interferometry of the channel structure from a with a mean
roughness of Ra ~ 20 nm (scale: 10 μm) (Kotz et al. 2019)
much space. To avoid this, a tunable optical filter is placed in front of the optical
sensor (Moldenhauer et al. 2017). In this way, a broadband light source such as a
superluminescent diode can be used because only certain wavelengths with sharp
linewidth can pass the optical filter. The transmitted center wavelength can be tuned,
so that the working principle of a tunable laser is achieved. The advantage of a
tunable filter is mainly referred to the fact that it can be realized by integrating an
additional add-drop ring resonator that is thermally tuned using the relatively large
thermo-optical effect in silicon. Metal plates in the back-end of line can be employed
as heaters.
Another bottleneck is related to the light coupling from the external light source
into the chip. Single mode optical fiber having a mode field diameter of 10.4 μm
and a numeric aperture of 0.14 are typically used. Due to these characteristics, the
optical fiber needs to be placed above chip with a distance of about 3 μm, making the
fiber alignment challenging. Therefore, precision 3D translational stages are used.
6.2 Optofluidic Resonators
309
Fig. 6.14 The picture of the newly-designed cartridge shows the reservoirs filled with colored water
except the sample reservoirs. The sample is filled into the corresponding reservoirs using an external
manipulator through tubing’s connected to a port with high performance liquid chromatography
(HPLC)-fitting compatible threadings. The PIC is not shown here presented (Geidel et al. 2016)
However, the alignment procedure is too time consuming and the tolerance against
misalignment is too small. Current research is focused on the development of costeffective fiber-to-chip packaging methods to overcome this issue (Wan et al. 2019;
Nauriyal et al. 2019).
The optical sensor elements can be co-integrated with light-sources and photodetectors. Even a monolithic integration with electronic devices is possible by using
an electronic-photonic-integrated circuit (EPIC) technology. However, PIC technology has a higher potential for disposable sensor applications since the fabrication
is significant cheaper than EPIC. The main bottleneck is still the integration of a
light sources. Therefore, optical fiber coupling using on-chip grating coupler is still
required. In summary the main bottleneck for cost-effective and reliable sensor integration is the co-integration of light-source (optical fiber), electrical signal supply
and micro-fluidic from same interface. From Fig. 6.16 it is apparent that the optical
fiber coupling, the micro-fluidic and the electric contacts obstruct each other mutually. As a consequence, cost-efficient mass-production of optofluidic silicon photonic
biosensors for disposable sensor applications is not yet realized.
A novel integration concept is based on a wafer backside release procedure that
enables a separation of sensing area and, hence, the microfluidic from the optical fiber
and electrical contacts (Steglich 2020; Steglich et al. 2020). In principle, the photonic
sensor is released by a local backside dry-etch followed by a combination of different
chemical wet etch processes. A schematic is shown in Fig. 6.16: a second major
advantage of this approach is the improved compatibility to the baseline CMOSprocess, i.e., the complete back-end of line can be fabricated in a similar way as in
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6 Sensors
Fig. 6.15 Design of the photonic sensor: a microscope image of a part of the photonic sensor
with optical ring resonators (a1), optical waveguides (a2), and optical interfaces on the right (a3);
b drawing of the whole circuit’s layout with an array of optical grating couplers on the left (b1) and
on the right (b3) connected by a waveguide (b2). Optical ring resonators are located in the middle of
the chip (b5). The black frame (b4) is not a part of the chip. It marks the area where the liquids will
be pumped through; c detailed design of an optical ring resonator within the photonic sensor. An
optical waveguide (c1) passes the optical ring resonator (c3) at a small area (c2); and d a schematic
sketch of the fluidic connection of a polymer based cartridge (d8) and a silicon chip d4 using an
elastomer sealing ring (d6). The direction of the pumped liquids is visualized by arrows (Geidel
et al. 2016)
the standard process. Only the passivation layer of the bondpads needs to be adjusted,
as we have reported in Steglich et al. (2019a, b).
The fabrication can be done by utilizing a PIC-technology (Steglich 2020). Such
technology employs 200 mm silicon-on-insulator wafer having a 2 μm buried oxide
and a 220 nm crystalline silicon layer on top. A 248 nm DUV optical lithography
is used to define the waveguide structures. Then, the chip is fabricated, including
all five metal stacks in the back-end of line. As mentioned before, the passivation
module has been adjusted (Steglich et al. 2019a, b). This is required because the
ring resonator is released by a deep silicon etch followed by a chemical wet etch. As
a consequence, the wet etch would underetch the standard passivation and, hence,
destroy the metal pads. The adjusted passivation based on a flattened silicon nitride
layer has been proven to protect the back-end of line (Steglich et al. 2019a, b). A
6.2 Optofluidic Resonators
311
Fig. 6.16 Current status of
optical sensors in a photonic
integrated circuit technology.
The optical light coupling,
connection with
micro-fluidics and
wafer-level packaging are
identified bottlenecks that
hinder a mass-production
detailed description of the fabrication process with focus on the back-side release
process is provided in Steglich (2020) and Steglich et al. (2020).
6.3 Biosensors
The motivation to use integrated ring resonators as biosensors is apparently obvious
by now as we are making use of the resonance wavelength shift which is induced
by changing the effective refractive index the evanescent light field is seeing when
making round trips inside the ring resonator.
In a microcavity resonator structure, the most common configuration starts from
the coupling of the incident light propagating in an input waveguide (or tapered fiber)
the microcavity via the evanescent field. When whispering gallery modes (WGMs) or
circulating waveguide modes with multiple round-trips are created (see also Chap. 7),
optical interference occurs at specific wavelengths of light,
λ=
2πr n eff
m
(6.1)
where λ is the resonant wavelength, r is the radius of the resonator, neff is the resonator
effective refractive index, and m is an integer respectively. The positions of resonant
peaks are related to the refractive index close to the resonator surface whilst the
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6 Sensors
Fig. 6.17 Conceptual illustrations of an optical ring resonator sensor. The resonant light circulates
along the resonator and its evanescent field is present in the surrounding medium outside (a) or
inside (b) the ring resonator, interacting with the analyte on the ring resonator exterior surface (a) or
interior surface (b) and in the surrounding medium (Sun and Fan 2011)
shift is due to the change of neff . It is clear that it can be monitored by scanning the
wavelength or by measuring the intensity at a single wavelength (Luan et al. 2019).
As depicted in Fig. 6.17, it is clear that in order to change the effective refractive
index, the evanescent field is interacting with an analyte which is hooked up to the
ring resonator by bio-chemical binding processes Sun and Fan (2011). The principle
of how a ring resonator biosensor detects the binding of analyte to the surface is
reported in Fig. 6.18. In this case a tunable laser is coupled to the ring resonator: at
the laser resonance with the resonant mode in the resonator, a spectral dip is shown
at the detector to indicate the spectral position.
The quality factor is the one of the most important parameter to have performant
sensors: higher Q-factor corresponds to longer interactions of the light with the
analyte. Moreover, White et al. proved that a high Q-factor reduces the sensor noise
and further improves the Detection Limit (DL) (White and Fan 2008). In general the
DL (or sDL) depends on the measurement system including curve fitting methods
and limitations from light sources or detectors: this is why it is not so common to
clear comparison between sensors. In order to solve this problem, often the so-called
intrinsic detection limit (iDL) is used in for resonant sensors. It depends on intrinsic
characteristics, such as the resonance linewidth, and defined by:
iDL =
λ
QS
(6.1)
where λ, Q, and S are the sensor’s resonant wavelength, quality factor, and sensitivity,
respectively.
Up to now, several types of planar resonant microcavity-based configurations have
been realized for biosensing applications such as microring (MRR), microdisk and
microtoroid shaped resonators. A review on this topic has been also being treated by
Luan et al. (2019): as it is there summarized, although resonator-based biosensors
enable dense on-chip integration and offer a similar DL of 10−5 to 10−7 RIU, their
6.3 Biosensors
313
Fig. 6.18 a Illustration of a
ring resonator biosensor that
detects the binding of analyte
to the surface. A tunable
laser is coupled to the ring
resonator. When the laser is
in resonance with the
resonant mode in the
resonator, a spectral dip is
shown at the detector to
indicate the spectral position.
b The resonant mode shifts
in response to the local RI
change induced by the
molecular binding. c A
sensorgram can be obtained
by monitoring the spectral
shift in real time (Sun and
Fan 2011)
Q-factors (except toroid resonators) are relatively low. As alternatives microspherebased ring resonators and capillary-based opto-fluidic ring resonators (OFRR) have
been recently proposed because characterized by higher Q-factors (>106 ) and DLs
of the order of 10−7 RIU for pesticide, cancer and bacteria. However, due to threedimensional architectures, these devices are not suitable for on-chip fabrication as
well as microfluidics integration.
Fig. 6.19 describes a planar ring resonator for vapor sensing. Its surface is coated
with a layer of vapor-sensitive material such as a polymer. The particular case of a
capillary-based ring resonator for vapor sensing is shown: its inner surface is coated
with a layer of polymer for vapor separation and detection.
A biosensor based on a disk resonator is proposed and analyzed in Boyd and
Heebner (2001). The disk is weakly coupled to a bus waveguide which allows the
field to build up to high values in the disk resonator which is necessary for sensing.
The device designed has the following parameters: a waveguide width of 0.4 μm,
a coupling gap of 0.25 μm and a disk radius of 2.54 μm. The device is operated in
TM polarization. A dielectric constant of the device of 4 is assumed. The achieved
simulated sensitivity is expected to be approximately 100 molecules.
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6 Sensors
Fig. 6.19 a Planar ring resonator for vapor sensing. Its surface is coated with a layer of vaporsensitive material, for example polymer. Upper figure: cross-sectional view. Lower figure: top view.
b Capillary-based ring resonator for vapor sensing. Its inner surface is coated with a layer of polymer
for vapor separation and detection. c Schematic diagram of capillary ring resonator-based vapor
separation and detection. d Sensing signal is generated when each analyte arrives at the detection
position defined in (c) (Sun and Fan 2011). Reprinted with permission from Springer Nature
A sensor using a disk resonator vertically coupled to a bus waveguides is fabricated
and demonstrated in Krioukov et al. (2002). The layer sequence and layout of the
device is shown in Fig. 6.20.
Similar to the previous simulated example, the disk resonator is weakly coupled
to the underlying bus waveguide, allowing modes in resonance with the disk to build
up. The response from the disk is measured using water, ethanol and a mixture of
water and glucose in different concentrations as cladding. A shift in the resonance
wavelength indicates the different solutions.
A glucose concentration sensor is realized in Chao and Guo (2003) using polymer
nanoimprinting. The racetrack shaped ring resonator notch filter includes partially
reflecting junctions in the bus waveguide creating so called Fano resonances (Fan
2002). A schematic of the devices is shown in Fig. 6.21.
Details on the fabrication have been described in Chap. 3 where a similar device
is realized. The measurement is performed by tuning a laser near one of the resonances of the ring and detecting the change in the spectra. The ring resonator is
placed in different glucose concentrations. A minimum detectable concentration
6.3 Biosensors
315
Fig. 6.20 Cross-section and view of an integrated optical MC sensor. Light from a tunable laser
is coupled into the excitation waveguide, and the scattering is measured from the top of the MC
as a function of the wavelength with various solutions in the sensing area. Dotted line, localization
of a high-Q whispering-gallery mode; its propagation direction is shown by an arrow around the
circumference. Device parameters: R = 15 μm, hc = 255 nm, he = 150 mm Krioukov et al. (2002)
Fig. 6.21 Racetrack-shaped ring resonator with partially reflecting waveguide junctions
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6 Sensors
change of glucose solution is estimated to be 0.024%, or 24 mg (dl)−1 . Since the
Q-f actor is proportional to the sensitivity, an increase in the Q-factor of the ring
resonator will also enhance the sensitivity. The shift in the resonance wavelength
is linear with increasing glucose concentration. A detailed analysis of resonantenhanced evanescent-wave fluorescence biosensing in ring and disk resonators is
presented in Blair and Chen (2001). Design layouts are given and the sensitivity and
the enhancement factor are derived.
Another demonstration of a ring resonator used for sensing bio-molecules is given
in Yalcın et al. (2006). The functionality of the device is proven by using avidin–biotin
binding on the surface of a vertically coupled glass ring resonator. The radius of the
ring resonator is 60 μm. The penetration depth of the mode into the medium (deionized water) is calculated to be approximately 360 nm at a wavelength of 1550 nm
assuming an effective refractive index of the waveguide of 1.5. The ring resonator
parameters are as follows: FSR = 4.2 nm, FWHM = 0.126 nm, F = 33, Q = 12,000.
The measurement principle is again the monitoring of the resonance shift due to a
change in the refractive index caused by the binding of biomolecules. The refractive
index sensitivity of the system is 1.8 × 10–5 . Some examples of application and
selection of biomolecules that have been detected by integrated photonic biosensors
based on SOI ring resonators, as reported in Table 6.2 by Steglich et al. (2019a, b).
The comparison between sensor performances results cin the field of silicon
photonic biosensors is presented in Table 6.3 as provided by Luan et al. (2019):
different architectures as well as strategies to improve the S and DL values are summarized. As reported by Luan et al. (2019), bulk sensitivities in the unit of wavelength
(or phase) shift per refractive index change are reported such as light polarization
and wavelength, system and intrinsic detection limits, and Q-factor respectively.
Table 6.2 Examples of application and selection of biomolecules that have been detected by
integrated photonic biosensors based on SOI ring resonators (by Steglich et al. 2019a, b)
Application
Analyte/biomarker
Receptor/target
Detection limit
Acute inflammation
C-reactive protein (CRP)
Anti-CRP
6.5 pM
Acute inflammation
Interleukin 2,4,5
Anti-CRP
6–100 pM
HIV
Human immunoglobulin (Hu-IgG)
Anti-Hu-lgG
1 ng
Hepatitis
Human serum albumin
Anti-albumin
3.4 pg
Meningitis
tmRNA
DNA
0.524 nM
Prostate cancer
Prostate specific antigen (PSA)
Anti-PSA
0.4 nM
Liver cancer
α-fetoprotein (AFP)
Anti-AFP
100 pM
Bowel cancer
Carcinoembrionic antigen (CEA)
Anti-CEA
10 pM
Bladder cancer
Tumor necrosis factor (TNF)
Antibody
100 pM
Model system
Green fluorescent protein (GFP)
Antibody
0.1 mg/mL
Model system
Streptavidin
Biotin
60–150 fM
Food monitoring
Bean pod mottle virus
Antibody
1.43 pM
Reprinted under Common Creative license
Sensor
configuration
MZI
Ring
Sensor type
Interferometer
Microcavity
TE
TE
TE
TE
TM
TE
TM
TM
TM
TE
TM
TE
Slot/critical
coupling
Multi-box SWG
5WG
swc
Slot
Suspended
Thin WG
N/A
Thin WG
1.31 μm Wvl
1.31 μm Wvl
TE
N/A
Vernier
TM
N/A
TM
TE
1.31 μm Wvl
Vernier
TE
Slot
TM
TE
Suspended
Vernier/suspended
TE
Optical made
Vernier
Strategy
9.8
33.5
24
10.1
4.5
12
0.33
9.8
7
2.6
6
20
15
N/A
N/A
N/A
N/A
N/A
N/A
N/A
Q-factor (×103 )
N/A
91 nm
113 nm
133 nm
200 nm
270 nm
290 nm
298 nm
429 nm
490 nm
580 nm
N/A
N/A
N/A
N/A
N/A
N/A
10–5
10–6
4.2 ×
N/A
2×
N/A
N/A
5.05 ×
nm
13 × 103 nm
13 ×
N/A
N/A
2.43 × 104 nm
10–4
N/A
103
N/A
300 × 2π rad
4.6 × 105 nm
(continued)
3.5 × 10–4
1.49 × 10–3
5 × 10–4 [142]
7.5 × 10–4
1.2 × 10–3
N/A
1.59 × 10–2
3.71 × 10–4
5.5 × 10–4
1.02 × 10–3
<10–4
4.8 × 10–6
N/A
N/A
3.3 × 10–5
460 × 2π red
N/A
N/A
N/A
4 × 10–5
N/A
Intrinsic detection
limit (RIU)
540 × 2π rad
1.29 × 10–5
1730 × 2π rad
N/A
N/A
2.15 × 104 nm
740 nm
System detection
limit (RIU)
Bulk sensitivity
(RIU−1 )
Table 6.3 Performance metrics comparison of selected optical biosensors (WG, waveguide; Wvl, wavelength, 1.55 μm where not specified)
6.3 Biosensors
317
Uniform
Phase-shifted
ID
2D
Disk
Sensor
configuration
TM
TE
1.31 μm Wvl
N/A
TE
TE
Slot
N/A
TE
TE
N/A
Multi-box SWG
TE
TE
Ring-slot
Slot
TE
N/A
TE
N/A
TE
TM
Suspended
Slot
TM
TE
N/A
N/A
Optical made
Strategy
Reprinted under CC license from Luan et al. (2019)
Bragg grating
Photonic crystal
Sensor type
Table 6.3 (continued)
N/A
27.6
76
15
6.2
3
174
11.5
0.4
50
33
0.1
16
15
Q-factor (×103 )
182 nm
59 nm
106 nm
340 nm
610 nm
130 nm
815 nm
160 nm
200 nm
N/A
N/A
N/A
N/A
N/A
7×
N/A
N/A
2×
10–5
10–3
7.8 × 10–6
1.5 × 103 nm
10–6
N/A
8×
N/A
N/A
System detection
limit (RIU)
26 nm
130 nm
142 nm
38 nm
Bulk sensitivity
(RIU−1 )
N/A
9.3 × 10–4
1.6 × 10–4
3 × 10–4
4 × 10–4
4 × 10–3
1 × 10–5
8.75 × 10–5
1.88 × 10–2
2.07 × 10–5
1.8 × 10–3
1.18 × 10–1
6.8 × 10–4
2.7 × 10–3
Intrinsic detection
limit (RIU)
318
6 Sensors
6.3 Biosensors
319
An overview of target analytes has been reported by the same authors arranged
in descending molecular weight, with privilege to those that use label-free SOIbased biosensors. As therein reported, SOI-based optical biosensors present a wide
detection range for analytes. It is worth mentioning that larger molecules such as
micrometer-sized cells and bacteria may exceed the evanescent field range limiting
in this case the sensor use. On the other hand, small molecules are difficult to be
detected especially when in low concentrations: the relative low sensitivity and/or
high noise level of SOI-based sensors is in this case a unable to circumvent the
detection problem.
An overview of selected biomolecules that have been detected by optical sensors
using label-free method is instead reported in Table 6.4.
An example of a split ring resonator (SRR) fabricated and integrated with a
microfluidic chamber for biosensing is reported by Jaruwongrungsee et al. (2015).
The authors produced it on a microwave printed circuit board while the microfluidic
chamber has been realized by casting of polydimethylsiloxane (PDMS). In particular
SRR has been immobilized with Anti-Immunoglobulin G (IgG) for IgG detection by
a standard covalent immobilization using Cystamine. Jaruwongrungsee et al. (2015)
aligned the PDMS chamber was aligned on the circuit board so that to monitor the
response of the SRR sensor continuously: they have demonstrated that the reaction
of Immunoglobulin G (IgG) and Anti-IgG results in a shift of resonance frequency,
sensitive to the IgG concentrations. Their SRR integrated device with the PDMS
chamber is reported in Fig. 6.22 whilst the working principle of SRR electrode with
immobilized antibody in microfluidic flow channel before and after binding under
analyte flow ire reported in Fig. 6.23. The Measured real-time frequency response
of a SRR sensor under different loading conditions are presented in Fig. 6.24.
Other sensing applications have been demonstrated in Human-IgG (Human
Immunoglobulin G) and PA (Staphylococcal protein A) respectively (Ren et al. 2013).
The biosensing devices have been achieved by combining the so-called “stamp-andstick” method (Satyanarayana et al. 2005) where a PDMS fluidics channel is mounted
on top of the microring resonator chip, as sketched in Fig. 6.25.
The signals of the PA-coated polymer sensors to specific and nonspecific interactions has been reported: the wavelength shift is due to the interaction with human
IgG (50 and 5 μg/mL) and with BSA (50 μg/mL) respectively (Ren et al. 2013).
A systematic work on the development of optical biosensors built on a novel
polymer platform named PSQ-Ls has been studied by Wang et al. (2012). This
material has ben demonstrated to be very flexible and cheap to get optical devices
with high performances made by UV-based soft imprint lithography technique. Ring
resonators with Q value as high as 5 × 104 and 2.7 × 104 have been achieved
and tested after protein A molecules functionalization by physical immobilization.
Surface binding sensing have been measured with a flow speed of 10 μL/min, deionized water and 0.01 × phosphate buffer solution (PBS), Human-IgG with a concentration of 50 μg/mL and 0.01 × PBS injected into the fluidics channel consecutively.
A wavelength shift of about 230 pm has been induced by the affinity of Human-IgG
for the protein A molecules immobilized on the chip surface as bio-receptors. The
Ring biosensor activity has been tested at different concentrations of Human-IgG
320
6 Sensors
Table 6.4 Overview of selected biomolecules that have been detected by optical sensors using
label-free method (CFU, colony-forming unit; HAU, hemagglutination unit; VP, viral particle)
Biological
material
Target
Weight
Sensor type
Waveguide
material
Detection limit
Cell
E. coli O157:H7
1 pg
MRR
Hydex
105 CFU/mL
MRR
Si
108 CFU/mL
Virus
Protein
Avian influenza
virus
542 MDa
MZI
Si3 N4
5 × 10–4
HAU/mL
Herpes simplex
virus
96 MDa
YI
Si3 N4
850 VP/mL
Bean pod mottle
virus
7 MDa
MRR
Si
1.43 Pm
Human papilloma
virus
5 MDa
PhC
Si
1.4 nM
Immunoglobulin
G
150 kDa
PhC
Si
1 ng/mm2
MZI
Polymer
3.1 nM
Vernier
MRR
Si
47.3 nM
MZI
SiOx Ny
2.14π/nm
PhC
Si
2.5 fg
PhC
Si
344 Pm/nm
Slot MZI
Si3 N4
18 fM
PhC
Si
49 fM
MRR
Si
60 fM
MRR-MZI
Si
20 pM
MRR
SiO2 /Six Ny
0.1 nM
MRR
Si
0.15 nM
(Strept)avidin
55–68 kDa
Human serum
albumins
67 kDa
Prostate specific
antigen
28 kDa
C-reactive protein 25 kDa
Nucleic
acid
RNA
DNA
7–40 kDa
7–12 kDa
Slot disk
SiNx
0.55 nM
YI
Si3 N4
20 fg/mm2
MRR
Si
3.4 pg/mm2
MRR
Si
0.4 Nm
Slot MRR
SiN
1.79 nM
MZI
Six Ny
84 fM
MRR
Si
0.4 nM
MZI
SiN
0.78 nM
MRR
Si
53 fM
MRR
Si
15 fM
Slot MZI
Si3 N4
1 nM
MZI
Si3 N4
300 pM
Slot MZI
Si3 N4
1 nM
(continued)
6.3 Biosensors
321
Table 6.4 (continued)
Biological
material
Small
molecule
Target
Weight
Sensor type
Waveguide
material
Detection limit
MRR
Si
1.95 nM
PhC
Si
19.8 nM
MRR
Hydex
100 nM
Gentamicin
478 Da
PhC
Si
0.1 nM
Biphenyl-4-thiol
186 Da
PhC
Si3 N4
N/A
Reprinted under CC license from Luan et al. (2019)
Fig. 6.22 The photographs of microstrip-coupled SRR integrated with PDMS microchamber
detection (Jaruwongrungsee et al. 2015)
Fig. 6.23 The diagram illustration of SRR electrode with immobilized antibody in microfluidic flow channel a before and b after binding under analyte flow thorugh a channel detection
(Jaruwongrungsee et al. 2015)
322
6 Sensors
Fig. 6.24 Measured real-time frequency response of a SRR sensor under a different loading
conditions and b due to various stages of Anti-IgG immobilization and 100 μg/ml IgG detection
(Jaruwongrungsee et al. 2015)
Fig. 6.25 Sketch of the biosensing process exploiting the PA/IgG affinity couple: a schematic of the
biosensing process using PA/IgG affinity couple; b SEM pictures of the ring resonator fabricated by
UV-based soft imprint lithography technique; c response signals of the PA-coated polymer sensors
to specific and nonspecific interactions. Wavelength shift obtained due to the interaction with human
IgG (50 and 5 μg/mL) and with BSA (50 μg/mL). Every curve corresponds to a different experiment
on a different chip. The time point of the loading of protein samples is shown in the figure (Ren
et al. 2013)
6.3 Biosensors
323
Fig. 6.26 The responsivities
of the PA surface
functionalized photonic
biosensor to specific and
nonspecific interactions.
Resonant wavelength shift
induced by the interaction
with human IgG (50 and
5 μg/mL) and with BSA
(50 μg/mL) (Han et al. 2018)
solutions showing different dynamic responsivities to the antibody concentrations,
with a detected concentration of Human-IgG as low as 5 μg/mL. As reported in Han
et al. (2018), the nonspecific binding is another key factor for a label-free photonic
biosensor. To test the response of polymer-based photonic biosensor toward nontargeted biomolecules, Ren et al. (2013) used Bovine Serum Albumin (BSA) control
protein in a the PA-coated microring surface. In this case the concentration of the
BSA for the test was 50 μg/mL (in 0.01 mol PBS, pH 7.4). In Fig. 6.26 the resonance
shift therefore induced has been measured to be close to 40 pm due to the nonspecific binding of the BSA molecules. A resonant wavelength shift of 90 pm using
the specific binding of the Human-IgG with a concentration of 5 μg/mL was also
observed, validating the recognition ability of the PA-coated microring biosensors.
Ring resonators are ideal for use in sensing biomolecules or even cells, as only a
few molecules are required to induce a change in the resonance wavelength. Going
into the direction of single molecule detection requires so called whispering gallery
mode resonators which will be briefly described in the following chapter.
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Chapter 7
Whispering Gallery Mode Devices
Whispering gallery mode (WGM) resonators and lately photonic crystal resonator
based devices are attractive due to their potential applications in photonics and
recently in biophotonics as is described in the previous chapter. Applications which
have been realized include for example lasers, filters, optical switches and biosensors. This chapter introduces WGM devices, although some examples which have
been given in this book have dimensions of whispering gallery mode resonators. This
chapter serves as a brief introduction into the topic as a significant number of books
and other publications exist on this subject (for example Vahala 2003, 2004).
7.1 Whispering Gallery Modes (WGM)
Whispering gallery modes (WGMs) are named after the whispering gallery at St.
Paul’s Cathedral in London and have been studied by Lord Raleigh in 1910 (Rayleigh
1910, 1912). Whispering gallery modes occur at particular resonant wavelengths
depending on the size of the resonator. At these particular wavelengths, light undergoes total internal reflection at the surface of the resonator creating resonances in the
transmission spectrum of the resonator. Whispering gallery resonators are dielectric
structures in which light waves are confined by continuous total internal reflection.
WGMs can be observed in droplets and glass spheres for example. In this chapter,
examples are limited to planar integrated WGM resonators.
The light in WGM resonators is concentrated near the circumference of the device
and is assigned a mode number and a mode order. The mode number, mn , reveals the
number of wavelengths around the circumference, and the mode order, mo , reveals
the number of maxima in the radial dependence of the electromagnetic field within
the resonator. These modes can have very high Q factors if the losses due to reflection
at the surface of the resonator are low. In addition to high Q values, a high finesse is
also obtained. The high Q factor makes these resonators very attractive to be used as
lasers. In order to couple light in or out of these resonators, the evanescent field of the
© Springer Nature Switzerland AG 2020
D. G. Rabus and C. Sada, Integrated Ring Resonators, Springer Series
in Optical Sciences 127, https://doi.org/10.1007/978-3-030-60131-7_7
327
328
7 Whispering Gallery Mode Devices
whispering gallery modes has to overlap with the evanescent field of a phase-matched
optical bus waveguide. This in and out coupling of WGM resonators is one of the
major technological challenges and was only recently achieved due to the advance
of fabrication technology, as was demonstrated in several examples in this book.
A review of the basic properties of WGM resonators is presented in Matsko and
Ilchenko (2006a, b).
7.2 WGM Filters
Optical filters are one of the first applications when considering optical devices
having wavelength dependent resonances. As in ring resonators, WGM resonators
have a wavelength dependent resonance spectrum. Due to the small size of WGM
resonators, they have large FSRs, high Q factors and high finesse. A review paper
presenting applications of both WGM and ring resonators is given in Matsko and
Ilchenko (2006a, b).
One of the challenging research tasks is to achieve in and output coupling of
these very small (diameter <10 µm) WGM resonators. Several groups have and are
working on this subject. Before being able to couple in and out of a WGM device,
WGM modes must circulate in the device to build up a resonance spectrum. This is
only achieved when the WGM device has sufficiently low internal losses, especially
a low surface roughness. Both of these aspects are theoretically investigated in Little
and Chu (1996). The coupling between a WGM disk resonator and a bus waveguide
is simulated in Dehmubed and Diament (1998).
Design and fabrication of laterally coupled ring and WGM disk resonators in the
material system AlGaAs/GaAs is presented in Hagness et al. (1997) and Rafizadeh
et al. (1998). The layer sequence of the device has been described in Chap. 3.
Photographs of the fabricated ring and WGM disk resonator are shown in Fig. 7.1.
The diameter of the ring and disk resonator is 10.5 µm. A waveguide width of 0.5 µm
is used. The coupling gap between the bus waveguide and the ring and disk is 0.1 µm.
A trench is fabricated around the waveguides with a width of 1 µm.
A detailed description of cylindrical WGM multimode resonators verified by
experimental results realized in silicon oxynitride technology is presented in Klunder
et al. (2002a, b, 2003). The layer sequence of the fabricated cylindrical WGM
resonator is shown in Fig. 7.2.
The intensity distribution inside the WGM resonator is analyzed using photon
scanning tunneling microscope (PSTM) and effects like polarization conversion
and counter propagation is detected. A simulation model is derived for calculating
the finesse, bending losses and FSRs of fundamental quasi guided modes in this
cylindrical WGM resonator.
Another form of WGM resonator is designed and analyzed in detail in
Maolatou et al. (1999) and Hammer (2002). The WGM resonator is in the shape
of a rectangle coupled to bus waveguides. A schematic of the rectangular WGM
resonator is shown in Fig. 7.3. Rectangular shaped resonators are slightly different
7.2 WGM Filters
329
Fig. 7.1 SEM images of a 10.5 µm diameter GaAs/AlGaAs microcavity ring and disk resonator
coupled to 0.5 µm-wide waveguides Hagness et al. (1997)
Fig. 7.2 Layer sequence of
cylindrical WGM resonator
Fig. 7.3 Rectangular WGM
resonator
from ring or disk resonators treated so far in this book with respect to the intensity
distribution at the output ports. As can be seen from Fig. 7.3, some of the input power
is reflected back to the same port and dropped at all the remaining ports. This is in
contrast to ring or disk resonators, where there is a preferred direction of the light
passing the resonator in the on or off resonance state, leading to only one drop and
one throughput port.
Several configurations have been simulated in Hammer (2002) using an operation
wavelength of 1.55 µm. The length L and width W of the rectangular WGM resonator
is varied between 0.81–6.902 µm and 0.81–3.696 µm, respectively. The width of
330
7 Whispering Gallery Mode Devices
Fig. 7.4 Grating assisted
rectangular WGM resonator
the bus waveguides and the coupling gap is varied between 0.035–0.13 µm and
0.32–0.49 µm, respectively. The refractive index of the WGM resonator and the bus
waveguides is assumed to be 3.4, whereas the surrounding refractive index is defined
to be 1.45.
This type of resonator is coupled to gratings on either side of the WGM resonator
which leads to a superior add-drop filter characteristic. The device design is presented
in Hammer et al. (2004). A schematic of the proposed device is shown in Fig. 7.4.
The fabrication of WGM resonators has only been possible recently due to an
advance in nanofabrication technologies. Especially in the case of WGM resonator
filters, in and out coupling is the greatest technological challenge. When these tasks
are overcome, tunability of WGM resonators is the next goal.
Tuning of WGM resonators is addressed in Boriskina et al. (2003). Filter tuning
is proposed by changing the shape of the resonator from circular to elliptic, which
reduces the dependence of the coupling efficiency on the width of the air gap. The
elliptic shape can be compared to a racetrack shaped ring resonator, where the effect
in increasing the coupling length is the same. Two alternative coupling designs are
suggested for monolithic and hybrid integration technologies. The first one is based
on increasing the coupling length. The other makes use of the field concentration at
the increased curvature portion of the deformed WGM resonator.
Another method of tunability (either wavelength or filter shape) in resonators is
be introducing gain into the resonator as described in Chaps. 3 and 5. Active disk
resonators are simulated and designed in Djordjev et al. (2002) for use as modulators,
switches and wavelength routers.
Totally active devices can of course be used as lasers. WGM lasers have been
investigated and demonstrated earlier than WGM resonator filters, which is obvious,
because light only needs to be collected from the WGM resonator and not coupled
into it for detecting the spectrum. In the following chapter, a brief introduction is
given with examples of fabricated WGM lasers.
7.3 WGM Lasers
WGM lasers are expected to be the light sources of future photonic integrated circuits
and optical computer boards due to their extremely small size. Other advantages are
similar to ring and disk resonators and include their compactness and their integration
ability. Further more, no grating or facet is required for optical feedback which is the
7.3 WGM Lasers
331
main advantage when thinking of several WGM lasers on a chip placed at different
locations on the chip. Some examples described in Sect. 5.6.1 can be regarded as
WGM resonator lasers and are therefore not addressed in this chapter.
WGM lasers having diameters of 3, 5 and 10 µm are fabricated in the material
system GaInAsP/InP and demonstrated in McCall et al. (1992). Optically pumped
InGaAs quantum wells are used to achieve lasing at wavelengths of 1.3 and 1.5 µm.
The WGM lasers have the shape of a “mushroom” with an InP pedestal holding the
disk with the quantum well layers. The thickness of the InGaAs quantum wells is
10 nm, the thickness of the GaInAsP barriers is 10 nm as well. The GaInAsP end
caps have a thickness of 20 nm. The mushroom like shape is achieved by selective
chemical etching of the InP below and around the quantum wells, resulting in a disk
on a pedestal.
Even smaller WGM disk lasers are presented in Slusher et al. (1993). Disks with
a diameter of 2.2 and 5 µm in the same material as the previous ones are fabricated.
Six quantum wells with a thickness of 10 nm of the material In0.53 Ga0.47 As are used
together with five 10 nm thick GaInAsP barriers. The bandgap wavelength of the
GaInAsP material is 1.1 eV at room temperature. The disks are optically pumped
with a HeNe laser at a wavelength of 633 nm. A mode spacing of 87 nm is obtained
for the small disk and 37 nm for the larger disk. Q values of 260 and 500 are measured
at pump powers below threshold.
A “submicron” WGM disk laser is presented in Levi (1994) having a radius of
0.8 µm and a thickness of 0.18 µm. The disk consists of six 12 nm thick InGaAs
quantum wells separated by five 12 nm thick GaInAsP barriers. The disk is optically
pumped with a diode laser having a wavelength of 850 nm. Pulses with a length of
8 ns and a repetition period of 100 ns are used for the pumping. A conformal mapping
technique is used in Frateschi and Levi (1995) to determine the radial and azimuthal
eigenvalues and eigenvectors of leaky optical modes of this WGM disk laser.
Quantum cascade (QC) WGM disk lasers with an emission wavelength at 5 µm are
fabricated and demonstrated in Faist et al. (1996). A mushroom like device structure
is again used. A photograph of a fabricated QC disk laser is shown in Fig. 7.5.
The layer sequence of the device is shown in Fig. 7.6.
Disks with diameters of 17, 25, 45, 80, and 125 µm are fabricated. The measurement of the devices is done at a temperature of 15 K. The disks are contacted from
top and are operated using 50 ns pulses. A threshold current of 2.85 mA is measured
for the QC disk with a diameter of 17 µm. QC WGM disk lasers in the material
system InGaAs/AlInAs, emitting at a wavelength of 16 µm, being one of the longest
wavelengths reported for disk lasers, are presented in Tredicucci et al. (2000). The
disk lasers are electrically contacted and operated in pulsed mode. Measurements
are performed at temperatures of 10 K.
Electrically pumped GaInAsP–InP strained quantum well WGM disk injection
lasers with diameter between 2 and 10 µm are presented in Baba (1997) and Baba
et al. (1997). A photograph of WGM disk lasers with diameters of 8, 3 and 2 µm are
shown in Fig. 7.7.
The disks are made of compressive strained multiple quantum wells. Four quantum
well layers with a thickness of 3–4 nm sandwiched between barrier layers with a
332
7 Whispering Gallery Mode Devices
Fig. 7.5 Scanning electron
microscope image of a
25 µm diameter QC disk
laser with total height
15.5 µm Faist et al. (1996)
Fig. 7.6 Layer sequence of
the QC WGM disk laser
Fig. 7.7 WGM disk injection lasers with diameters of 8, 3 and 2 µm (from left to right) Baba
(1997)
bandgap wavelength of 1.2 µm having a thickness of 10 nm. The active layers include
50 nm thick guide layers with a bandgap wavelength of 1.2 and 30 nm thick gradient
index (GRIN) layers with a bandgap wavelength of 1.1 µm. The total thickness of
the active layers is 0.2 µm. A threshold current of 0.2 mA is measured for the disk
7.3 WGM Lasers
333
with a diameter of 2 µm under pulsed operation at a temperature of 286 K. Lasing
is achieved at wavelengths around 1.55 µm.
Optically pumped disk and ring lasers in InGaAs with diameters between 3.5 and
9 µm, fabricated using substrate removal and material transfer to a glass substrate
by liftoff processing are presented in Corbett et al. (1996). This process is used in
Corbett (1998) to fabricate ring and disk lasers with diameters between 6 and 28 µm
having a single compressively strained 3 nm, In0.7 Ga0.3 As quantum well cladded by
a 20 nm GaInAsP layer having a bandgap wavelength of 1.25 µm and a 100 nm
GaInAsP layer with a bandgap wavelength of 1.15 µm, lattice matched to InP with a
total thickness of 245 nm. The devices are optically pumped continuous wave (cw)
with the 514 nm line of an Ar–ion laser at liquid nitrogen temperatures. An optically
pumped threshold of 2 µW is obtained. The lasing wavelength observed is between
1.4 and 1.55 µm. Multimode operation of the lasers is observed at wavelengths
corresponding to whispering gallery modes.
Determining the optical modes in WGM resonators requires a different approach
as the one presented in Chap. 2 for calculating the transmission spectrum of ring
resonator filters. As these WGM resonators can be extremely small as is demonstrated in this chapter, the three dimensional Maxwell equations can not be reduced
to a one dimensional problem. A method for calculating optical modes in WGM
disk resonators giving an eigenvalue equation for optical modes and providing the
distribution of the optical field in exact forms is described in detail in Wang and
Dumitrescu (1998). Based on the results of the optical modes, the emitted optical
modes are determined. Disks with a radius between 0.5 and 1.5 µm having a thickness
of 50, 100 and 150 nm are simulated.
One of the first cw operating, current injection WGM disk lasers in the material
system GaInAsP/InP is presented in Fujita et al. (1999). A schematic of a WGM disk
injection laser is shown in Fig. 7.8. Whispering gallery modes travel round near the
edge of the disk by total internal reflection at the semiconductor/air boundary. The
current is flowed from the top contact. Carriers are injected into the active layer from
the posts.
Fig. 7.8 Schematic of a
WGM disk injection
laser Fujita et al. (1999)
334
7 Whispering Gallery Mode Devices
Fig. 7.9 Laser mode peak
intensity versus current
characteristic and lasing
spectra observed under cw
condition at 298 K for a
3 µm diameter device Fujita
et al. (1999)
A record threshold value of 150 µA is measured for a disk with a diameter of
3 µm at a temperature of 298 K. The measurement curve is shown in Fig. 7.9.
Two resonant modes are seen at a wavelength of 1.63 µm. The lasing mode has
a FWHM of 0.5 nm. The non lasing mode has a FWHM of 0.7 nm. The calculated
Q factors for both of them are 3300 and 2300 respectively.
WGM resonators have not only been realized in GaAs or GaInAsP, but have also
been demonstrated in the material system InGaN/GaN using multiple quantum wells
(MQW). An example of realized WGM ring and disk resonator devices is described in
Zeng et al. (1999). Both realized devices are optically pumped. A schematic diagram
of the InGaN/GaN MQW WGM ring resonators is shown in Fig. 7.10. The response
from a WGM disk resonator is shown in Fig. 7.11.
Different fabrication techniques and material systems have been used to fabricate
WGM disk and ring resonators. A wafer fusion method is described in Song et al.
(2000) to fabricate optically pumped GaInAsP disk lasers on Alx Oy . Continuous wave
room temperature operation is achieved for devices with a diameter of 2.2 µm. The
output power and the spectrum of an optically pumped disk are shown in Fig. 7.12.
Fig. 7.10 Schematic
diagram of representative
InGaN/GaN MQW
microring fabricated by
photolithography patterning
and dry etching Zeng et al.
(1999)
7.3 WGM Lasers
335
Fig. 7.11 Optical emission
spectrum of an InGaN/GaN
MQW microdisk with a
diameter of 9.4 mm. Both the
WG and radial modes are
observed in the
microdisks Zeng et al. (1999)
Fig. 7.12 Output power
against incident pump power
for the 2.2 µm diameter
microdisk laser pumped by
1064 nm Nd:YAG laser. The
spectra are measured by
optical spectrum analyzer
(OSA) with 0.24 nm
resolution Song et al. (2000)
The FSR of adjacent whispering gallery modes is 110 nm. The threshold pump power
is 1.13 mW, as can be seen in the measurement.
So far, WGM disk and ring lasers are measured by placing an optical fiber near the
edge of the disk or ring to collect the emission which is then fed to an optical spectrum
analyzer. In addition to the collection of the output light, cooling of some devices
and measuring in pulsed mode is required. One of the first disk lasers with a radius
of 10 µm vertically coupled to underlying bus waveguides in the material system
GaInAsP/InP is presented in Choi et al. (2002). The device operates cw at room
temperature, has a side mode suppression ratio of 20 dB and emits at a wavelength
around 1.52 µm. The layer sequence and the fabrication of the device are similar to
336
7 Whispering Gallery Mode Devices
the ones described in Chap. 3. A disk laser based on the same fabrication process,
vertically coupled to a single bus waveguide with a radius of 8 µm is demonstrated
in Choi et al. (2003). A photograph of a vertically coupled disk and a schematic of
the cross section are shown in Fig. 7.13.
The width of the bus waveguide is 0.7 µm. The waveguide is anti reflection coated
to avoid Fabry–Perot resonances. A spectrum of the disk laser at an operating current
of 14 mA is shown in Fig. 7.14. The disk laser has a threshold current of 4.5 mA.
The FSR of the disk is 13 nm and the side mode suppression ratio is greater then
30 dB as can be seen in the diagram. Q factors between 5000 and 6000 are measured
for this device. These disk lasers are used in Choi et al. (2004) to fabricate an eight
channel laser array. A photograph of the device is shown in Fig. 7.15.
The radius of the disks varies from 10.6 to 10.95 µm with 0.05 µm difference
leading to spectral spacing of the channels of 1.6 nm. The FSR of the disks is
approximately 9 nm. The bus waveguide is AR coated. The output spectrum of the
laser array is shown in Fig. 7.16.
Fig. 7.13 SEM image (left) and schematic cross-sectional view of the microdisk vertically coupled
to a bus waveguide. Picture was taken after the disk formation. A thin InP membrane remains along
the edges Choi et al. (2003)
Fig. 7.14 Lasing spectrum
for an 8 µm radius microdisk
laser measured at I = 14 mA
Choi et al. (2003)
7.3 WGM Lasers
337
Fig. 7.15 Micrograph
showing the top view of the
fabricated eight-channel
microdisk array vertically
coupled to a single bus
waveguide Choi et al. (2004)
Fig. 7.16 The microdisks
for channels 6–8 are pumped
at I = 13 mA, while the
current injection levels for
the other disks are
maintained at I = 10 mA
Choi et al. (2004)
A FWHM of 0.25 nm and a side mode suppression ratio of 20 dB are obtained.
Different current levels are used to tune the resonance wavelength to realize a channel
spacing of 1.6 nm.
With increasing advance in nanofabrication and modeling, photonic crystal based
devices have made it into real devices. Many applications of ring resonators presented
in this book can be transferred to photonic crystal structures and some have already
been demonstrated and described in several books and journal publications. Therefore
only a few examples of photonic crystal based lasers will be described in the following
paragraph to show the potential and possible future direction.
An optically pumped two dimensional (2D) photonic crystal (PhC) laser in the
material system GaInAsP/InP is fabricated and demonstrated in Painter et al. (1999).
A schematic of the cross section of the 2D PhC laser is shown in Fig. 7.17.
Four 0.85% compressively strained quaternary quantum wells with an emission
wavelength at 1.55 µm are used as the gain source. The membrane has a thickness of
211 nm and a width of approximately 8 µm. The lattice spacing is 500 nm. The holes
338
7 Whispering Gallery Mode Devices
Fig. 7.17 Illustration of a cross-section through the middle of the photonic crystal microcavity.
Photons are localized to the defect region by TIR at the air/slab interface and by Bragg reflection
from the 2-D photonic crystal Painter et al. (1999)
have a radius of 160 nm. A SEM photograph showing a top view of the fabricated
device is shown in Fig. 7.18.
For measuring the properties of the cavity, a semiconductor laser with an emission
wavelength of 830 nm is used. The measurement is performed under pulsed operation
of the pump source. Lasing at a wavelength of 1580 nm is observed. The absorbed
threshold pump power of the PhC laser is estimated to be 500 µW. An upper limit
for the Q factor is derived to be approximately 600.
A similar layout is used in Kim et al. (2002) for fabricating an optically pumped
hexagonal PhC ring laser in GaInAsP/InP emitting around 1.55 µm. A photograph
of the device is shown in Fig. 7.19.
Fig. 7.18 Top view of a
microfabricated 2D
hexagonal array of air holes
with a single central hole
missing. The interhole
spacing, a, is 500 nm, and
the radius of the holes are
approximately
160 nm Painter et al. (1999)
7.3 WGM Lasers
339
Fig. 7.19 The scanning
electron microscope image
of a fabricated laser sample.
The photonic crystal ring
cavity consists of six
waveguides and six 120°
bends. Thus the resonant
mode has similar properties
to the guided mode of
photonic crystal waveguides.
In this picture, lattice
constant a is ~0.57 mm and
the air hole radius r is
~0.36a Kim et al. (2002)
The diameter of the device is 8 µm. The measurement of the device is performed
using a pump laser with a wavelength of 980 nm at room temperature with pulses
having a width of 10 ns. A near field photograph of the standing wave mode in the
PhC ring laser is shown in Fig. 7.20.
The threshold pump power of the laser is measured to be 3 mW. The wavelength
of the lasing mode observed is ~1625 nm. A Q factor of more than 2000 is obtained
for this PhC ring laser.
A detailed analysis of the resonant modes in 2D PhC lasers is presented in Park
et al. (2002). Simulations are compared with two types of fabricated devices, air
based free standing (similar to the one in Fig. 6.17) and SiO2 based epoxy bonded
structures.
Fig. 7.20 Experimentally
measured laser mode using a
CCD. This laser sample has
15 air holes along the ring
diameter. Lattice constant
a of this laser sample is
~0.58 mm and the air hole
radius r is ~0.41a. A
hexagonal ring mode pattern
shows that the laser is
emitted mainly from the ring
region Kim et al. (2002)
340
7 Whispering Gallery Mode Devices
These exemplary examples have demonstrated novel types of devices which have
a great potential for the future in photonic integrated circuits. Compared to the history
of disk or ring resonator structures, active PhC resonator structures are on the way
to being electrically contacted with the ability to connect to the outside fiber world
using integrated PhC bus waveguides.
Laser Spatial and temporal coherences strongly depend on the optical cavity or
resonator characteristics such as the quality factor Q and mode volume V, i.e. the
figure of merit (Q/V ). Since WGM microcavities can support high values of Q/V,
in the recent years the efforts to improve the previously quoted configurations have
been made. Ultralow threshold microlasers have been therefore demonstrated in
microspheres, microdisks, microtoroids and microrings respectively and reviewed
in Jiang et al. (2015). It is worth mentioning that the rotational symmetry of these
WGM cavity structures, however, leads to a laser emission is usually inplane isotropic
as summarized in Fig. 7.21.
In general WGM configurations allow for low collection efficiency in free space
and requires to use, near-field couplers such as high-index prisms, side waveguides or
tapered fibers that need precise alignment of the components, high-resolution lithography to maintain the nanometer-scaled gap between the coupler and the microcavity
Fig. 7.21 (online color at: www.lpr-journal.org) Typical mode distributions of the traditional microcavity (kR # 59, where k is the vacuum wavevector and R is the maximum radius of the micro-cavity)
(a), microcavity with a scatterer on the surface (kR # 59) (b), deformed microcavity (kR # 72) (c),
and a microcavity with a grating structure (kR # 30) (d) (Cai et al. 2012)
7.3 WGM Lasers
341
and phase matching conditions to be fulfilled. In order to overcome these limitations
and to achieve inplane unidirectional laser emission, it has been proposed to break the
inherent rotational symmetry of WGM microcavities either by introducing a “defect”
in the modal region or by using the so-called asymmetric/deformed cavity structures.
Although both solutions provided excellent alternatives, the first one benefits from a
high-Q mode-enhanced scattering and high collimation of the dielectric microcavity
itself: in this way the optical WGM fields can be efficiently scattered and collimated into free space. In the second solution, asymmetrical emission is realized by
adequately shaping the cavity boundary. Finally, vertical emission of a WGM laser
can be promoted by adding a diffraction grating along the WGM microcavity circumference. It is beyond the scope of this book to provide a deep detailed description of
the recent results on this topic. However, for the shake of completeness it is mandatory
to briefly remind some advances obtained in integrated ring resonators, addressing
the reader to the references to gain more information on other geometries. A review
on this topic has been published by (He et al. 2012) where the recent efforts devoted
to optimize the WGM laser performances with a monodirectional emission have
been summarized. As a matter of fact, several WGM microcavities supporting unidirectional laser emission as well as their photonics applications have been presented
mainly based on three different types of WGM cavities: scatterer-induced unidirectional emission, chaos-induced unidirectional emission and grating-induced vertical
emission. Whilst the spatial localization can be described in terms of divergence angle
of the unidirectional emission and the mode volume of the cavity mode, the temporal
localization is strongly depending by the Q factor. The mode volume is influenced by
the cavity size and the wavelength, and therefore the so called kr parameter is the key
feature: higher kr corresponds to higher mode volume. Divergence angle and Q factor
are consequently the most important parameters for unidirectional-emission microcavities. In order to optimize both, theoretical modeling new technology approaches
have been widely performed in the last ten years. In the case of unidirectionalemission cavities the performances have been improved dramatically. In Fig. 7.22 a
Fig. 7.22 Experimentally
demonstrated divergence
angle and Q factor of the
seven types of WGM cavity
with unidirectional laser
emission, including
rounded-isosceles-triangle
cavity, spiral-shaped cavity,
microdisk with diffraction
gratings, notched-elliptical
cavity, microdisk with line
defect, limacon-shaped
cavity, and deformed
microtoroid (Jiang et al.
2015 and references therein
quoted)
342
7 Whispering Gallery Mode Devices
comparison of the recent advances have been reported (Jiang et al. 2015): divergence
angles smaller than 10 degrees can be achieved in the notched-elliptical cavity and
the face-shaped microtoroid. As for the Q factor, most of the cavity shapes possess Q
factors smaller than 104 , except for the limacon-shaped microdisks and face-shaped
microtoroids.
It is worth mentioning that recently, Kim et al. (2014) have reported a microdisk
semiconductor laser with partially directional emission, based on the asymmetric
backscattering from two Rayleigh scatterers. In this case the directionality and
chirality of the laser modes have been tailored by changing some parameters such
as size, shape, and relative positions of scatterers on the microcavity boundary
respectively.
Moreover, deformed silica microtoroids have fabricated on a silicon wafer with
a 2-µm thickness silicon dioxide layer. A deformed silica toroid supported by a
silicon pillar of the top diameter smaller than 10 µm have been therefore realized.
This slim silicon pillar was able to reduce the silica-to-silicon loss since the chaotic
modes can travel everywhere in the cavity (Wang 2015a, b; Jiang et al. 2015). Even
1.5 µm thickness erbium-doped silicon dioxide on a silicon wafer with the Er3+
ions concentration of 2 × 1019 cm−3 was used (Shao et al. 2013) to fabricate the
deformed microtoroids showing unidirectional emission with divergence lower than
10°. In Fig. 7.23 an example of the achieved results is depicted.
Finally, a circular symmetric microcavity, supporting high Q WGMs, can carry
high orbital angular momentum (OAM), which may lead to various photonics applications. Efficient microring devices were fabricated on a silicon-on-insulator chip
with a radius of 3.9 µm, which was designed with Q = 36 and a resonance wavelength in the 1550-nm wavelength band, as shown by Mahler and coworkers (Mahler
et al. 2009).
7.4 WGM Microresonators in LN: Recent Advances
in Dielectric Crystalline Configurations
In the previous sections it has been already evidenced that in whispering-gallerymode (WGM) microresonators have been realized in various kinds of transparent materials such as liquids, polymers, glasses, semiconductors, and dielectric crystals demonstrating physical and/or optical functionalities such as lasing,
filtering, nonlinear wavelength conversion, optomechanics, and cavity electrodynamics. Currently, it is of high interest to push for further on-chip integration of
the WGMs with other photonic micro- and nanostructures. The platforms material that have been addressed as suitable for photonic integration application are
surely semiconductors for their fabrication compatibility with the complementary
metal oxide semiconductor (CMOS) approach. Recently lithium niobate on insulator
(LNOI) has emerged as a valid complementary option thanks to the rapid development of innovative solutions already presented in Chap. 3 and its wide range of
optical transparency.
7.4 WGM Microresonators in LN: Recent Advances …
343
Fig. 7.23 (online color at: www.lpr-journal.org) a Flow diagram of the fabrication process of
ultrahigh-Q deformed microtoroid cavities. Left to right: deformed silica microdisk, first-step undercut etching of the microdisk, CO2 laser reflow and the second-step dry etching of the deformed
microtoroid. b, c Top-view SEM image and its close-up view of a deformed microtoroid with R0
# 49 µm and η # 1.0. The red dashed curve plots the ideal boundary of designed ARC with η =
1.0. The black dashed curve gives the boundary of an ellipse for comparison, and the white dashed
curve shows the boundary of a circle with the same diameter. The inset shows a side-view SEM
image of the deformed toroid. d Experimental Q factors of various microcavities (R # 45 µm) with
different deformation parameters η. e Far-0 field emission distribution for the lasing of CW, CCW
and their sum at 1560.15 nm (Jiang et al. 2012)
Since exterior whispering-gallery modes (WGMs) can be tailored to have mode
energy mainly confined outside the microcavity, high mode overlapping with the
ambient environment can be achieved as well as a strong electric field and gradient
force at the surface. As a consequence highly localized WGMs in the nanoair gap
of a double-layer crystalline microdisk have been obtained (Zheng et al. 2019). The
geometry therein proposed is based on a horizontal slot-waveguide structure of two
vertically stacked crystalline microdisks made of lithium niobate thin films. The slot
WGM therefore presents a quality factor greater than 105 without metallic loss. The
absorption and scattering loss have been reduced by depositing a crystalline nanofilm
at sub-nm rms surface roughness. An example of the achieve structure is shown in
Fig. 7.24.
344
7 Whispering Gallery Mode Devices
Fig. 7.24 a Schematic of
the double-layer LNOI
microdisk evanescently
coupled by a tapered fiber.
b Top-view optical
microscopy image of the
microdisk. The two inner
irregularly shaped circles
indicate inward etching of
the silica buffer layers.
c SEM image of the
microdisk, with enlarged
false-colored images clearly
showing the well-separated
upper and lower LNTF
layers (Zheng et al. 2019)
The experimentally measured transmission spectrum for the double-layer LNOI
microdisks is finally presented in Fig. 7.25.
Moreover, high-Q monocrystalline LN based WGM resonators have been fabricated on a LNOI wafer by using UV-photolithography, Ar+ plasma etching, and HF
etching respectively (Wang 2015a, b). The measured Q factor in 1550 nm band of
LN resonators with a radius of 39.6 µm and a thickness of 500 nm are up to 1.19
× 106 . Electro-optic modulation at 1550 nm has been proved by applying an alternating voltage along the c axis of LN crystal showing a 3.0-GHz/V tuning rate of
the resonance frequency of LN WGM resonators (Wang 2015a, b). A sketch of the
obtained structure and relative result are reported in Figs. 7.26 and 7.27.
Dielectric crystalline WGM resonators have even attracted great attention also as
next generation nonlinear sources of both classical and nonclassical light because of
their high nonlinear optical coefficients, low intrinsic absorption loss, and large transparent windows respectively. Advances on this fields were reported in Lin et al. (2015)
with the fabrication of high-Q lithium niobate whispering-gallery-mode microresonators suspended on silica pedestals by femtosecond laser direct writing followed by
focused ion beam (FIB) milling. In this case the micrometer-scale (diameter ~82 µm)
LN resonator possesses a Q factor of ~2.5 × 105 around 1550 nm wavelength. The
combination of femtosecond laser direct writing with FIB enables high-efficiency,
high-precision nanofabrication of high-Q crystalline microresonators. In Fig. 7.28 a
sketch of the preparation steps is reported.
Some optimizations in the process steps have been made in the last years that
allowed to reach even higher Q factor values (such as 1.46 × 107 at a wavelength of
around 773 nm) (Zhang 2019). With a surface roughness to the order of Ra ~ 0.115,
the major source of optical loss in the microresonator is radiative bending loss, which
7.4 WGM Microresonators in LN: Recent Advances …
345
Fig. 7.25 a Experimentally measured transmission spectrum for the double-layer LNOI microdisk.
The arrows mark the theoretically predicted slot-waveguide WGMs. b Resonance of interior WGM.
c Resonance of slot-waveguide WGM (Zheng et al. 2019)
Fig. 7.26 Sketch of the Cr and silica removal steps (Zhang et al. 2019)
346
7 Whispering Gallery Mode Devices
Fig. 7.27 a Top view scanning electron microscope (SEM) image of a fabricated LN microdisk
resonator. b Close up view SEM image of the area indicated by the red box in (a). c Atomic force
microscope (AFM) image of the microdisk wedge. d Optical microscope image of the microdisk
resonator with different diameters (55, 85, 105, 135, 155, 185, and 205 µm) (Zhang et al. 2019)
Fig. 7.28 Procedures of fabrication of a LN microresonator by water-assisted femtosecond laser
ablation, followed by FIB milling, selective chemical etching, and annealing (Lin et al. 2015)
7.4 WGM Microresonators in LN: Recent Advances …
347
Fig. 7.29 a Measured Q factors of the microdisks of different diameters. b The Lorentz fitting (red
curve) of a splitting mode in the microdisk with a diameter of 105 µm revealed a Q factor of 4.7 ×
107 (Zhang 2019)
can be reduced by increasing the diameters of the microdisks. In Fig. 7.29 an overview
of the Achieved Q factor depending on the microdisk diameter and the transmission
achieved at r = 105 µm.
The wedge angles of the LNOI have been continuously tuned from 9° to 51°
without affecting the Q factor, which is critical for nonlinear optical applications as
the dispersion curve in the microdisks is a function of the wedge angle.
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Chapter 8
Outlook
Ring resonators are ideal candidates for realizing all kinds of devices ranging from
optical filters to lasers for future all optical telecommunication networks to sensors
including biosensors. Current developments are ongoing in the fields of quantum and
neuromorphic computing, demonstrating their high versatility. Ring resonators can
be integrated with other semiconductor-based devices incl. electronics putting them
in the focus of current and future research.
The increasing knowledge of ring resonator devices and the fast improving stateof-the-art in manufacturing technologies is leading and will lead to novel future
devices with greater flexibility and higher level of integration. Miniaturization and
nanofabrication technologies have already led to multiple coupled ring resonator
configurations with and without integrated optical gain.
State-of-the-Art design and manufacturing of ring resonators is open to fab less
companies by way of multiple wafer projects (MWP) which are made available
through for example ePIXfab (https://epixfab.eu/), a not-for-profit open alliance of
academic and industrial organizations with a mission to promote silicon photonics
science, technology and applications. In this way, access to state-of-the-art facilities
is possible for realizing devices on silicon on insulator (SOI) and silicon nitride
(SiN). Another joint community effort is centered around JePPIX (https://www.jep
pix.eu/) which is a joint European platform for photonic integrated components and
circuits, established in 2006. JePPIX provides access to design, training and MWPs
on indium phosphide, silicon nitride and hybrid photonic integration. Both ePIXfab
and JePPIX have their origin in EU funded projects which had the target to create
a straight forward path of optoelectronic semiconductor devices from idea to high
volume production. For example, one of the foundation stones of JePPIX was the
EU funded project PARADIGM (Photonic Advanced Research And Development
for Integrated Generic Manufacturing).
Using these now established manufacturing paths, focus on the enhancement
of device performance is more than ever possible in ring resonators research and
development, thus ring resonators developers can target the applications in a faster
and concrete way.
© Springer Nature Switzerland AG 2020
D. G. Rabus and C. Sada, Integrated Ring Resonators, Springer Series
in Optical Sciences 127, https://doi.org/10.1007/978-3-030-60131-7_8
351
352
8 Outlook
Parallel to semiconductor processing, polymer materials, and polymer manufacturing technologies like embossing or nanoimprinting will play an increasing role also
due to the “bio” component of the current worldwide research direction, integrating
ring resonators with microfluidics and optofluidics.
This merger of technologies is the building block of future ring resonator devices
increasing again their application and thus enhancing the existing portfolio of real
world systems.
Ring resonators will certainly not loose their attractiveness as their versatility will
increase rather than decrease which is also demonstrated by several examples given
in this book and also just by the simple fact that their existence spans already more
than just two decades.
In summary, one could say that ring resonators are ever attracting devices which
never loose their fascination once beginning resonating.
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Index
A
Add-drop filter, 6
Apodization, 38, 40
B
Bandpass, 31
Birefringence, 296
Box like, 19
Buildup factor, 11
Buried heterostructure, 260, 269
Butterworth, 28, 31
C
Cavity ring-down time, 246, 247, 276
Chain matrix, 16, 29
Characteristic matrix, 29, 32
Chebyshev, 28, 31, 32
Chebyshev type I, 28
Chebyshev type II, 28
Conformal transformation, 188
Coupling
asymmetrical coupling, 58
critical coupling, 6
cut-back, 118, 119
symmetric coupling, 8
D
Delay lines, 276
Differential group delay, 242
Dispersion, 238
chromatic dispersion, 238, 239
dispersion compensation, 199
intermodal dispersion, 239
material dispersion, 238
modal dispersion, 239
negative dispersion, 238, 240
polarization mode dispersion, 239
positive dispersion, 238, 240
quadratic dispersion, 239
structural dispersion, 239
waveguide dispersion, 238
E
Etching, 55
anisotropic, 55, 56
isotropic, 55
F
Fabry–Perot method, 119
Filters, 200
Finesse F, 10
Four wave mixing, 270
Free carrier plasma effect, 269
Free Spectral Range (FSR), 9
Frequency beating, 257
Full-width at Half-Maximum (FWHM), 9
G
Grating, 25
Group velocity, 13
Group-velocity dispersion, 42
Group-velocity reduction, 42
I
Intensity enhancement factor, 11
Ion beam milling, 139, 154, 344
Ion implanted waveguide, 129, 131, 132, 135
© Springer Nature Switzerland AG 2020
D. G. Rabus and C. Sada, Integrated Ring Resonators, Springer Series
in Optical Sciences 127, https://doi.org/10.1007/978-3-030-60131-7
359
360
L
Label-free optical biosensor, 319, 320, 323
Lateral coupling, 47
Lithium niobate, 44, 51, 127–133, 135, 136,
138–142, 144, 146, 147, 154, 156,
161, 162, 165, 167, 230, 342, 343,
344
Lithium Niobate on Insulator (LNOI), 133,
134, 136, 146, 149–151, 154–156,
159, 160, 163, 165, 192, 342, 344,
345, 347
Lorentzian function, 206
N
Notch filter, 3
P
Polarization, 114, 115
Proton exchange, 128, 130, 131, 141, 142,
146
Q
Quality factor Q, 10
Quantum cascade laser, 331
Quantum confined Stark effect, 281
R
Racetrack, 17
Ridge waveguides, 69, 83, 84, 132, 133, 135,
138, 139, 142, 144, 184, 257, 258,
261
S
Saturable absorber, 260
Scattering matrix, 16
Shape factor, 214
Silicon on Insulator (SOI), 51, 56, 57, 59, 60,
116, 136, 155, 192, 193, 195, 196,
Index
229, 236, 248, 251, 298, 304, 310,
316, 319, 342, 351
Single photon absorption, 281
Smart cut, 132, 135–138, 150
T
Taylor series expansion, 15
Ti-indiffusion, 129, 131, 132, 146
Time dependent relations, 12
decay time-constant, 13
Total internal reflection, 90, 222, 327
Transfer matrix, 16, 29
Tuning
carrier injection, 224, 231
electro-optic tuning, 224, 229
free carrier injection, 224, 269
photobleaching technique, 236
thermo-optic tuning, 224
Tuning enhancement factor, 266
Two-photon absorption, 276, 280
V
Vernier effect, 213, 257, 266, 269
Vertical coupling, 47
W
Wafer bonding, 51
adhesion bonding, 51
anodic bonding, 53
electrostatic bonding, 53
eutectic bonding, 52
fusion bonding, 52
hydrophobic bonding, 52
Wavelength reflective filter, 25
reflector, 35, 268
Z
Z-transformation, 14