Silicon-on-Insulator, Free-Spectral-Range-Free Devices
for Wavelength-Division Multiplexing Applications
by
Ajay Mistry
B.A.Sc., The University of British Columbia, 2017
A THESIS SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
Master of Applied Science
in
THE FACULTY OF GRADUATE AND POSTDOCTORAL
STUDIES
(Electrical and Computer Engineering)
The University of British Columbia
(Vancouver)
March 2020
c Ajay Mistry, 2020
The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:
Silicon-on-Insulator, Free-Spectral-Range-Free Devices for WavelengthDivision Multiplexing Applications
submitted by Ajay Mistry in partial fulfillment of the requirements for the degree
of Master of Applied Science in Electrical and Computer Engineering.
Examining Committee:
Dr. Nicolas A. F. Jaeger, The Department of Electrical and Computer Engineering
Supervisor
Dr. Lukas Chrostowski, The Department of Electrical and Computer Engineering
Supervisory Committee Member
Dr. Shahriah Mirabassi, The Department of Electrical and Computer Engineering
Additional Examiner
ii
Abstract
Silicon-on-insulator (SOI) microring resonator (MRR)-based modulators and filters have been researched extensively for use in wavelength-division multiplexing
(WDM) systems due to their attractive spectral characteristics and small device
footprints. However, an inherent drawback of using MRRs in WDM systems is
their free-spectral-ranges (FSR). The FSR limits the aggregate data rate of the system, as it limits the number of channels that can be selectively modulated in a
WDM transmitter, or simultaneously de-multiplexed in a WDM receiver. The goal
of this thesis is to present and demonstrate SOI, MRR-based modulators and filters
with FSR-free responses.
We first experimentally demonstrate an SOI, FSR-free, MRR-based filter with
a reconfigurable bandwidth. The device uses a grating-assisted coupler integrated
into the MRR cavity to achieve an FSR-free response. Here, we demonstrate a nonadjacent channel isolation, for 400-GHz WDM, greater than 26.7 dB. A thermally
tunable coupling scheme is utilized to compensate for fabrication variations and to
demonstrate the reconfigurable filter bandwidth. We then demonstrate how lithography effects affect the performance of SOI devices, which include grating-based
components. Using lithography models developed for deep ultraviolet lithography processes, we analyze the effects of lithography on the performance of an
MRR with an integrated, grating-assisted coupler. We show that, if the effects of
lithography are not taken in account during device design flow, large discrepancies result between the predicted “as-fabricated” and “as-designed” device performance. We also demonstrate how to use the lithography models to compensate for
lithographic-effects in future device designs. Lastly, we experimentally demonstrate an FSR-free, MRR-based, coupling modulator. We demonstrate open eye
iii
diagrams at 2.5 Gbps and discuss how the effects of DUV lithography limited the
electro-optic bandwidth of the fabricated modulator to 2.6 GHz. We also discuss
the effects of lithography on the modulation crosstalk of the device and how to
significantly improve the electro-optic bandwidth and how to minimize crosstalk
in future implementations of the device.
iv
Lay Summary
Wavelength-division multiplexing (WDM) technology has become one of the most
widely used technologies to meet current demands for data transmission in optical communication networks. Due to their attractive spectral characteristics and
small device footprints, silicon-on-insulator (SOI) microring resonator (MRR)based modulators and filters have been researched extensively for use in WDM
systems. However, the aggregate data rate of MRR-based, WDM systems is inherently limited by the spacing between the MRR resonances, also known as the
MRR’s free-spectral-range (FSR). The goal of this thesis is to present and experimentally demonstrate SOI, MRR-based modulators and filters that overcome the
current limitations. In particular, we focus on the integration of grating-assisted
couplers into MRR cavities in order to achieve FSR-free responses and also analyze the effects of deep ultra violet lithography on device performance.
v
Preface
The content of this thesis is based on three publications, listed below, in which I am
the principal author. Most of Chapter 2 is based on the following publication [1]:
1. A. Mistry, M. Hammood, H. Shoman, L. Chrostowski, and N. A. F. Jaeger,
“Bandwidth-tunable, FSR-free, microring-based, SOI filter with integrated
contra-directional couplers,” Optics Letters, 2018. c 2018 The Optical Society of America. Material including text and figures used with permission.
N. A. F. Jaeger conceived the idea. I designed and modelled the device. The
mask layout was created by myself and M. Hammood. I performed the measurements of the fabricated device, with assistance from M. Hammood and H. Shoman.
L. Chrostowski obtained access to the fabrication technology used for this project. I
wrote the first draft of the manuscript, and N. A. F. Jaeger and M. Hammood helped
determine the final content and to edit the manuscript. H. Shoman and L. Chrostowski provided feedback during the design process and on the manuscript.
Chapter 3 is based on the following publication [2]:
2. A. Mistry, M. Hammood, S. Lin, L. Chrostowski, and N. A. F. Jaeger, “Effect of lithography on SOI, grating-based devices for sensor and telecommunications applications,” in 2019 IEEE 10th Annual Information Technology, Electronics and Mobile Communication Conference (IEMCON), 2019.
c 2019 IEEE. Material including text and figures used with permission.
I, together with Lukas Chrostowski and M. Hammood, conceived the idea for the
paper. I performed the device simulations and analysis. The mask layout for the
vi
fabricated test structures was created by M. Hammood and S. Lin. The lithography
model used for the analysis and modelling was developed by S. Lin. M. Hammood
and I performed the measurements of the fabricated test structures. L. Chrostowski
obtained access to the fabrication technology used for this project. M. Hammood
and I wrote the first draft of the manuscript, and N. A. F. Jaeger and S. Lin helped
determine the final content and to edit the manuscript. L. Chrostowski also gave
feedback on the manuscript.
Chapter 4 is based on the following publication (which has been accepted) [3]:
3. A. Mistry, M. Hammood, H. Shoman, S. Lin, L. Chrostowski, and N. A. F.
Jaeger, “Free-spectral-range-free microring-based coupling modulator with
integrated contra-directional couplers,” presented at SPIE Photonics West,
2020. c 2020 SPIE. Material including text and figures used with permission.
I, together with N. A. F. Jaeger and M. Hammood, conceived the idea for the
project. I designed the device and performed the device simulations. The mask
layout was created by myself and M. Hammood. I performed the measurements
of the fabricated device, with assistance from M. Hammood and H. Shoman. L.
Chrostowski and N. A. F. Jaeger obtained access to the fabrication technology used
for this project. The lithography model used for analysis was developed by S. Lin.
I wrote the first draft of the manuscript, and N. A. F. Jaeger and M. Hammood
helped determine the final content and to edit the manuscript. H. Shoman provided
insights during the design process and gave feedback on the manuscript.
vii
Table of Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iii
Lay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
viii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
xix
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1
Silicon Photonics . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
WDM Optical Communication Systems . . . . . . . . . . . . . .
2
1.3
OADMs in WDM Links . . . . . . . . . . . . . . . . . . . . . .
4
1.4
Modulators in WDM Links . . . . . . . . . . . . . . . . . . . . .
6
1.5
Thesis Objective . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.6
Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . .
10
Bandwidth-Tunable, FSR-free, Microring-Based, SOI Filter with Integrated Contra-Directional Couplers . . . . . . . . . . . . . . . . .
viii
11
2.1
Contra-Directional Couplers . . . . . . . . . . . . . . . . . . . .
12
2.1.1
Overview and Theory . . . . . . . . . . . . . . . . . . . .
12
2.1.2
Calculation of the Distributed Coupling Coefficient . . . .
15
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
2.2.1
Bent Contra-DCs . . . . . . . . . . . . . . . . . . . . . .
22
2.2.2
MZI-Based Couplers . . . . . . . . . . . . . . . . . . . .
23
2.3
Device Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.4
Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.5
Experimental Results . . . . . . . . . . . . . . . . . . . . . . . .
31
2.6
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
2.2
3
4
Effect of Lithography on SOI, Grating-Based Devices for Sensor and
Telecommunications Applications . . . . . . . . . . . . . . . . . . .
39
3.1
Device Behaviour and Modelling . . . . . . . . . . . . . . . . . .
40
3.2
Effect of Lithography on Filter Performance . . . . . . . . . . . .
44
3.3
Compensating for Lithographic-Effects . . . . . . . . . . . . . .
49
3.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
Free-Spectral-Range-Free, Microring-Based Coupling Modulator with
Integrated Contra-Directional Couplers . . . . . . . . . . . . . . . .
52
4.1
Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
4.2
DUV Lithography . . . . . . . . . . . . . . . . . . . . . . . . . .
56
4.3
Device Simulation . . . . . . . . . . . . . . . . . . . . . . . . . .
57
4.4
Experimental Results . . . . . . . . . . . . . . . . . . . . . . . .
58
4.4.1
DC Device Characterization . . . . . . . . . . . . . . . .
59
4.4.2
High-Speed Characterization and Testing . . . . . . . . .
63
4.4.3
Adjacent and Non-Adjacent Resonance Suppression . . .
66
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
Summary, Conclusions, and Suggestions for Future Work . . . . . .
71
5.1
Summary and Conclusions . . . . . . . . . . . . . . . . . . . . .
71
5.2
Suggestions for Future Work . . . . . . . . . . . . . . . . . . . .
72
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
4.5
5
ix
List of Tables
Table 2.1
κ0 values of various bent contra-DC designs. . . . . . . . . . .
28
Table 2.2
Design parameters for the bent contra-DC in the filter. . . . . .
28
x
List of Figures
Figure 1.1
A block diagram of a WDM link. . . . . . . . . . . . . . . .
Figure 1.2
Schematic of a) a conventional Mach-Zehnder modulator and
b) a conventional microring resonator-based modulator. . . . .
Figure 1.3
8
a) Diagram of a straight contra-DC. b) Zoom-in of the structure
illustrating device design parameters. . . . . . . . . . . . . .
Figure 2.2
7
A block diagram of a 4-channel, single-bus, MRR-based WDM
transmitter architecture. . . . . . . . . . . . . . . . . . . . .
Figure 2.1
2
12
Graphical solution for the phase match conditions of a contraDC with WB = 450 nm, WR = 550 nm, and Λ = 318 nm. The
solid arrow shows the wavelength at which contra-directional
coupling occurs and the dashed arrows show the wavelengths
at which intra-Bragg reflections can occur. . . . . . . . . . . .
Figure 2.3
Theoretical through-port (|tc
|2 )
and drop-port (|kc
|2 )
amplitude
responses of a contra-DC. . . . . . . . . . . . . . . . . . . .
Figure 2.4
14
15
Band diagram of a contra-DC. The spacing between the arrows is the bandgap (∆λbg ) of the contra-DC and represents the
wavelengths at which light is reflected and, hence, the wavelengths at which contra-directional coupling occurs. . . . . . .
Figure 2.5
Band diagram of a contra-DC with WB = 450 nm, WR = 550 nm,
∆WB = 50 nm, ∆WR = 60 nm, Λ = 318 nm, and g = 280 nm. . .
Figure 2.6
16
18
Comparison between contra-DC k0 values determined via bandstructure calculations and k0 values extracted from measured
test structures fabricated at UW and ANT. . . . . . . . . . . .
xi
19
Figure 2.7
Spectral responses (arbitrary linear scales) of a) the contraDC drop-port response, b) the MRR response, and c) the MZI
cross-state response when ∆λnull = 2FSRring = FSRMZI . The
BW of the filter is tuned as the MZI response is redshifted
(green arrow). Reprinted with permission from [1] c The Optical Society of America. . . . . . . . . . . . . . . . . . . . .
Figure 2.8
A schematic of our tunable filter. Inset shows the design parameters of the bent contra-DC. Reprinted with permission
from [1] c The Optical Society of America. . . . . . . . . .
Figure 2.9
21
22
Diagram of filter illustrating the coupling coefficients of the
bent contra-DC and MZI-coupler. The coupling coefficients,
te f f and ke f f (not shown in figure), of the MZI-coupler can be
readily controlled by tuning φarm . . . . . . . . . . . . . . . .
25
Figure 2.10 Graphical solution to Equation 2.12, for select κ0 values, to
determine Lc required to satisfy 2FSRring = ∆λnull . . . . . . .
27
Figure 2.11 a) Simulated through- and drop-port responses of the filter,
with the nulls of the MZI-coupler cross-port response aligned
with the contra-DC nulls. b) Zoom-in around the operating
wavelength. Dotted lines represent the wavelengths of suppressed resonant modes. . . . . . . . . . . . . . . . . . . . .
29
Figure 2.12 a) Filter drop-port response (blue) with the MZI-coupler crossport response (grey-dotted) shifted by a quarter cycle (φarm =
−π/2), and b) by a half cycle (φarm = ± π). The contra-DC
response (red-dotted) is static and does not shift as a function
of φarm . Adapted with permission from [1] c The Optical
Society of America. . . . . . . . . . . . . . . . . . . . . . . .
Figure 2.13 Filter a) 3-dB BW and |te f f
|2
versus φarm and b) SMSR and IL
versus φarm . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xii
30
30
Figure 2.14 The through- (blue) and drop-port (red) responses of the filter;
a) before alignment-tuning, b) aligned to the operating wavelength (1548.2 nm) and tuned to the maximum BW (60 GHz),
and c) aligned to the operating wavelength (1548.2 nm) and
tuned to the minimum BW (25 GHz). Dotted lines show possible channel locations on a 400-GHz grid. The simulated dropport responses, based on extracted fit parameters, are overlayed
onto the measured drop-port response. Reprinted with permission from [1] c The Optical Society of America. . . . . . . .
32
Figure 2.15 Spectral responses of the fabricated, point-coupled reference
devices with a) complete suppression of the adjacent MRR side
modes and b) one adjacent side mode not fully suppressed due
to 2FSRring > ∆λnull , due to fabrication variations. Reprinted
with permission from [1] c The Optical Society of America.
35
Figure 2.16 a) Drop-port BW and extracted effective MZI-coupler power
coupling coefficient as a function of control-arm heater current. b) Ai and nAi of the filter for a 400-GHz grid WDM, and
SMSR as a function of control-arm heater current. Reprinted
with permission from [1] c The Optical Society of America.
36
Figure 2.17 Group delay at the through-port of the filter (when operated
in the overcoupled region) and of a grating coupler test structure (zero set arbitrarily). A single spike in the filter’s group
Figure 3.1
Figure 3.2
delay is observed at the resonant wavelength. Reprinted with
permission from [1] c The Optical Society of America. . . .
37
Schematic of an MRR with an integrated contra-directional
coupler. c 2019 IEEE. . . . . . . . . . . . . . . . . . . . . .
41
Graphical solutions for the phase match condition of a contraDC with Λ = 318 nm and 1) WB = 450 nm and WR = 550 nm
(blue line) and 2) WB = 429 nm and WR = 528 nm (red line). .
xiii
42
Figure 3.3
Simulated spectral response of our MRR drop-port (blue). Dotted grey lines show the locations of the suppressed MRR sides
modes (adjacent to the operating wavelength), due to nullcoupling to the cavity via the contra-DC (red). c 2019 IEEE. .
Figure 3.4
43
(a) Mask layout of a section of our as-designed contra-DC. (b)
The predicted outcome of our lithography model. Smoothing
and proximity effects can be clearly seen on the corrugations.
(c) A scanning electron microscope image of our as-fabricated
contra-DC. c 2019 IEEE. . . . . . . . . . . . . . . . . . . .
Figure 3.5
45
Drop-port response of an as-fabricated contra-DC test structure
(red), simulated prediction-model (black) and simulated asdesigned (blue) contra-DC test structures (detuned to the central wavelength of the drop-port response of the as-fabricated
test structure, 1534 nm). Lithographic-effects reduce the coupling strength, κ0 , from the simulated/expected value of 9,350 m-1
to approximately 1,900 m-1 . c 2019 IEEE. . . . . . . . . . . 47
Figure 3.6
a) Simulated spectral drop-port response after applying the lithography model to the contra-DC test structure (solid). Simulated
as-designed response detuned to the central wavelength of the
post-lithography response (dashed), shown for reference. The
MRR side mode adjacent to the right of the operating wavelength is not fully suppressed due to a reduced κ0 and the
change in the cavity resonance condition. The insertion loss
of the MRR increases and the 3-dB bandwidth of the MRR
decreases. b) Zoom-in of the un-suppressed adjacent MRR
mode. The adjacent channel SMSR is reduced to 26 dB since
∆λnull < 2FSRring . c 2019 IEEE. . . . . . . . . . . . . . . .
Figure 3.7
48
a) Mask layout of a section of our re-designed contra-DC. (b)
The predicted outcome of our lithography model. The κ0 of
the prediction-model of the re-designed device matches that of
the as-designed contra-DC (see Figure 3.4a). c 2019 IEEE. .
xiv
49
Figure 3.8
Simulated drop-port spectra of the as-design contra-DC (red)
and lithography prediction-model of the re-designed device
(blue). c 2019 IEEE. . . . . . . . . . . . . . . . . . . . . . .
Figure 4.1
Schematic of the modulator. Inset shows the design parameters
of the bent contra-DC. . . . . . . . . . . . . . . . . . . . . .
Figure 4.2
54
Cross-section of the p-n junction segment integrated in the
modulation-arm (not shown to scale). . . . . . . . . . . . . .
Figure 4.3
50
55
a) Theoretical through-port response of the modulator with
the static phase of the modulation-arm set to 0. An FSRfree response is observed across the C-band with a single resonance mode located near 1550 nm. The contra-DC dropport response (dotted-red) and locations of the suppressed resonant wavelengths are shown for reference (dotted-black). b)
Through-port response of the modulator for various reverse
bias voltages applied to the modulation-arm p-n junction with
the static phase shift set to 4.25 radians. . . . . . . . . . . . .
Figure 4.4
58
Micrograph of the fabricated modulator showing DC (left-side)
and RF (right-side) signal pads. The contra-DC test structure
is also shown, located close to the modulator. . . . . . . . . .
Figure 4.5
59
a) Measured through-port spectral response, with the modulationarm tuned close to critical coupling, overlayed with the theoretical response generated using device parameters obtained
by curve-fitting the measured response to analytical equations.
b) Zoom-in on the operating resonance mode. c) Analytical
cavity linewidth and Q-factor of an add-drop ring resonator at
critical coupling, as a function of κ0 , assuming a contra-DC
through-port coupler. The calculated loaded Q-factor factor
(63,000) and cavity linewidth (3.11 GHz) closely match the
measured values. . . . . . . . . . . . . . . . . . . . . . . . .
xv
61
Figure 4.6
a) ER of the modulator as functions of voltage applied to the
modulation-arm heater. b) Measured through-port spectra for
various reverse-bias voltages applied to a p-n junction segment
in the modulation-arm. c) Static modulation depth as functions
of wavelength for a bias voltage of -2 V and Vpp swings of 2 V
and 4 V. Dotted line shows the operating wavelength (1529.56
nm) where the static modulation depths are 3.75 dB and 6 dB
for 2 Vpp and 4 Vpp , respectively. . . . . . . . . . . . . . . .
Figure 4.7
Block diagrams of the experimental setups used a) to measure
the modulator EOBW and b) to generate eye-diagrams.
Figure 4.8
62
. . .
64
a) Measured EOBW of the modulator. The EOBW for a 1.0 GHz
detuning from resonance was 2.6 GHz. b) Optical eye diagram
at the modulator through-port for a 2.488 Gbps, 2 Vpp drive
signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figure 4.9
Contra-DC response for our κ0
design value of 6,900 m-1
65
(solid-
red) and ring response of the cavity (dotted-black). The intersection of the two curves (blue circles) is the amount of
coupling to the cavity when the contra-DC nulls are optimally
aligned to the resonance modes. The coupling to the cavity
saturates at wavelengths far from the operating mode (less than
-38 dB, shown by the shaded blue area). . . . . . . . . . . . .
67
Figure 4.10 a) Measured through-port spectra at the left adjacent resonance
mode for various reverse-bias voltages (with the right adjacent
mode suppressed). b) Static modulation depth as functions of
wavelength for a bias voltage of -2 V and a Vpp swing of 2 V.
69
Figure 4.11 Measured response of an as-fabricated contra-DC test structure and predicted response of the as-designed contra-DC after
applying lithography models. The responses are detuned to the
central wavelength of the as-fabricated test structure response
(1530 nm). . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figure 5.1
70
Schematic of the proposed filter; an FSR-free MRR filter cascaded with a two-stage, series-cascaded contra-DC.
xvi
. . . . .
73
List of Acronyms
AWG
Arrayed waveguide grating
BER
Bit error rate
BPF
Bandpass optical tunable filter
BW
3-dB bandwidth
CMOS Complementary metal-oxide-semiconductor
CW
Continuous wave
CWDM Coarse wavelength-division multiplexing
DCA
Digital communications analyzer
DEMUX De-multiplexer
DUV
Deep-ultra-violet
DWDM Dense wavelength-division multiplexing
EDFA
Erbium-doped fiber amplifiers
EOBW Electro-optic bandwidth
FDTD
Finite-difference time-domain
FSR
Free-spectral-range
FWHM Full width at half maximum
xvii
GC
Grating coupler
IL
Insertion loss
LIDAR Light detection and ranging
MRR
Microring resonator
MUX
Multiplexer
MZI
Mach-Zehnder interferometer
OADM Optical add-drop multiplexer
OBRR
Out-of-band rejection ratio
OOK
On-off-keying
PAM
Pulse-amplitude modulation
PIC
Photonic-integrated circuit
PPG
Pulse pattern generator
PRBS
Pseudo-random binary sequence
QSFP
Quad small form-factor pluggable
SEM
Scanning electron microscope
SLSR
Side lobe suppression ratio
SMSR
Side mode suppression ratio
SOI
Silicon-on-insulator
WDM
Wavelength-division multiplexing
VNA
Vector network analyzer
xviii
Acknowledgments
I would like to first express my gratitude to my supervisor, Dr. Nicolas A. F. Jaeger,
for providing me guidance and mentorship over the past years. I want to especially
thank him for being so passionate and supporting when it came to our work, and for
his outright commitment to his students and willingness to be patient with them.
I would also like to thank Dr. Lukas Chrostowski for all the opportunities that he
provided during my time at UBC, as well as the time he took to discuss and provide
feedback on my research.
I would also like to thank all my colleagues who I got to work with and become
friends with at UBC. I especially want to thank Mustafa Hammood and Hossam
Shoman, for supporting and collaborating on projects with me, as well as Han Yun,
Stephen Lin, Jaspreet Jhoja, Enxiao Luan, Rui Cheng, Minglei Ma, and Abdelrahman Afifi. I would also like to thank all the collaborators from other institutions
that I was able to work with over the past years, as well as Elenion Technologies,
for providing me with the opportunity to continue my studies while working as a
photonics engineer.
I also acknowledge the Natural Sciences and Engineering Research Council of
Canada (NSERC) and the SiEPIC program and for financial support. Additionally,
I acknowledge CMC Microsystems, The University of Washington Nanofabrication Facility, and Applied Nanotools Inc. for their assistance in fabricating devices,
and Lumerical Inc. for providing simulation software and technical support.
Lastly, I would like to thank my family for teaching me importance of working
hard and prioritizing my education and for always providing me with unconditional
support in all my endeavours. I am also grateful for my friends for their friendship,
encouragement, and for always motivating me to strive for success.
xix
Chapter 1
Introduction
1.1
Silicon Photonics
Silicon photonic (SiPh) platforms, such as silicon-on-insulator (SOI), have shown
enormous potential to meet demands in fields such as telecommunications and data
communications, quantum computing, light detection and ranging (LIDAR), and
optical sensing technologies. The SOI platform is particularly attractive as it leverages the already mature and reliable complementary metal-oxide-semiconductor
(CMOS) technology, enabling eventual monolithic integration of photonic devices
and CMOS electronics [4–7]. On the SOI platform, due to the high index contrast
between the silicon (core) layer and the oxide cladding layers, light is primarily
confined to the core allowing for the realization of compact nanowires with tight
bend radii and components with small feature sizes. As a result, densely integrated
photonic integrated circuits (PICs) with small footprints can be made [8–11]. Various components for use in PICs on the SOI platform have been demonstrated in
the literature, including lasers [12–15], photodetectors [16–19], splitters [20–24],
polarization rotators [25–29], and variable optical attenuators [30–32].
Silicon photonics has demonstrated the capability to meet the increasing demand for higher data transmission capacity in optical communication systems,
such as short-reach optical interconnects and long-haul telecommunications systems [33–35]. Due to the current availability and cost effectiveness of 100 Gbps
and 400 Gbps devices, the global optical transceiver market is projected to be worth
1
at least 20 billion dollars by 2023 [36], with the total market for SiPh PIC-based
transceivers expected to grow to around 4 billion dollars in 2024 [37]. Major players in the SiPh-based transceiver market include companies such as Luxtera/Cisco,
Intel, Acacia Communications, InPhi, Ciena, and Elenion Technologies [38], with
hyperscale networking companies like Alibaba Cloud, Amazon, Apple, Facebook,
Google, and Microsoft motivating the future development and deployment of SiPhbased technologies and transceivers. Intel, for example, has developed a 100 Gbps
quad small form-factor pluggable 28 (QSFP-28) transceiver, with four channels,
each capable of supporting data rates up to 28 Gbps [39]. Alibaba Group also
recently launched a 400 Gbps optical transceiver through joint technology development with Elenion Technologies [40].
1.2
WDM Optical Communication Systems
Data In 1
λ1
Rx Out 1
Detector
Data In 2
Modulator
CW Laser
N-Channel MUX
λ2
Optical Fiber
λ1, λ2, ... , λN
N-Channel DEMUX
CW Laser
λ1
Modulator
λ2
Rx Out 2
Detector
Data In N
λN
λN
Modulator
Rx Out N
Detector
CW Laser
Transmitter (Tx)
Receiver (Rx)
Figure 1.1: A block diagram of a WDM link.
One of the most widely used technologies for high-capacity optical communication systems is wavelength-division multiplexing (WDM) [41–46]. Figure 1.1
shows a schematic of a typical WDM transceiver. In a WDM transceiver, at the
transmitter side, several electro-optic modulators are used to encode optical carriers with data. Here, we show external modulators in which light from several
continuous-wave (CW) laser sources is modulated. The encoded data is then com2
bined onto a single communications link using a multiplexer (MUX). This is an
advantage of a WDM system, in which separate data streams can be encoded onto
optical carriers operating at different wavelengths, in parallel, and then combined
and transmitted simultaneously down a single communication medium. Transmitting multiple frequencies over the single link results in a higher aggregate data
rate for the link; i.e., for a system with N channels, each transmitting at a data
rate R, the aggregate data rate becomes NR. While On-Off-Keying (OOK), or
pulse-amplitude modulation (PAM)-2, is the simplest encoding scheme and one of
the most common modulation formats employed in short reach optical interconnects [47, 48], different encoding schemes may be used in order to further increase
the data rate of the link. In OOK, the digital data (0s and 1s) are represented in
the form of absence or presence of light. By employing higher-order modulation
formats, i.e., PAM-4 and PAM-8, where four and eight levels of optical amplitude
are used to represent data, respectively, the bits per symbol (bits/sym) increases
from 1 bit/sym for PAM-2, to 2 bits/sym and 3 bits/sym for PAM-4 and PAM8, respectively. The communications medium used is typically an optical fiber
(shown in Figure 1.1), but in short-reach or on-chip integrated photonics applications, the medium may be a waveguide. On the receiver side of the transceiver, a
de-multiplexer (DEMUX) is used to separate the signals encoded on each optical
carrier. The optical signals are then converted to electrical signals using photodetectors, and the data can then be further processed.
WDM systems typically fall into two categories; dense-WDM (DWDM) and
coarse-WDM (CWDM). DWDM systems have higher aggregate data rates, as
channels are closely spaced (in wavelength) and a large number of channels per
fiber are transmitted. For example, in the C- and L-bands, with 100-GHz frequency
spacing (≈ 0.8 nm), a total of 115 wavelength channels can be transmitted in one
fiber. DWDM systems are predominantly used in long-haul communications due
to the optical fiber amplifiers required to compensate for optical fiber losses [45,
49]. DWDM is advantageous because a large number of tightly spaced channels
can utilize the limited gain bandwidths of typical erbium-doped fiber amplifiers
(EDFAs). CWDM is typically used for short-range communications and uses a
wider-range of frequencies with the operating wavelengths spaced further apart
(typically around 20 nm). This standardized channel spacing allows for levels of
3
laser wavelength drift during operation which would not be acceptable in DWDM
[50]. As a result, CWDM can be used as a cost-effective solution when spectral
efficiency can be sacrificed (i.e., in short-reach applications), as expensive stable
laser source and EDFAs are not required [50, 51].
1.3
OADMs in WDM Links
Optical add-drop multiplexers (OADM) are important components on both the
transmitter and receiver side of a WDM link. On the transmitter side, an OADM
is used to multiplex the individual wavelength channels, while on the receiver side
an OADM is used to de-multiplex or filter the channels. The performance of an
optical filter can be defined by several figures-of-merit (FOMs), including, insertion loss (IL), 3-dB bandwidth (BW), group delay and out-of-band rejection ratios
(OBRRs). The required performance metrics vary based on the application of the
OADM. For example, filters in CWDM de-multiplexers require wide bandwidths
and flat-top responses, in order to compensate for laser wavelength drift, while filters in DWDM de-multiplexer would require a narrow bandwidth due to the dense
channel spacing, as described in the previous section. One of the most important
OADM FOMs is the free-spectral-range (FSR) of the device. Devices with wider
FSRs enable WDM receivers in which a larger number channels can be selectively
multiplexed or de-multiplexed within a particular communication band. In this section, we present an overview of some OADMs on the SOI platform demonstrated
in the literature, including lattice filters [52–54], echelle gratings [55–57], arrayed
waveguide gratings (AWGs) [58–61], grating-assisted couplers [62–65], and microring resonator (MRR)-based filters [66–69].
Lattice filters consist of multiple cascaded stages of unbalanced Mach-Zehnder
interferometers (MZIs). Each MZI-stage introduces a constant phase delay in one
arm, resulting in either constructive (or destructive) interference at certain wavelengths at the output of each stage. By controlling the number of stages, the coupling coefficient of the directional couplers, and the phase delays in each stage, the
spectral response of the lattice filter can be designed to achieve low-loss and flat-top
pass bands. However, the shape of the lattice filter spectral response is susceptible
to fabrication variations, as fabrication-induced deviations from the “as-designed”
4
optical phase delays and coupling coefficients will deteriorate the filter response.
As a result, precise control of the waveguide phase delays and the coupling coefficients are required to produce filters that meet the required design targets. While
thermal tuners can be used to actively tune the phase delays of each lattice stage,
this significantly increases the overall power consumption of the filter. Also, due
to the periodic nature of the MZI response, the device cannot be FSR-free.
Echelle gratings and AWGs have similar operating principles and are based on
multi-path interference [70]. In an echelle grating, the input signal, consisting of
multiple wavelength channels, enters a free-propagation region, where the light diverges and impinges upon a grating reflector, creating interference patterns in the
reflection. Based on the angle of the grating reflector and the phase delays introduced in the propagation region, light of a particular wavelength will be focused
onto/coupled into its corresponding output waveguide. Similarly, in an AWG, the
incoming (multi-wavelength channel) signal is split into multiple paths which then
propagate through a waveguide array. Here, the incoming beam is split using an
input star coupler. Based on the optical phase delays introduced in each path, interference between the light from each path leads to light of a particular wavelength
being refocused onto a particular output in an output star-coupler. As a result,
in both echelle gratings and AWGs, the wavelength channel coupled into each of
the output waveguides will be de-multiplexed from the other wavelength channels.
While both echelle gratings and AWGs have been demonstrated to have flat-top responses [71] with large FSRs, both typically have large footprints, relatively large
insertion losses, and are also susceptible to fabrication variations.
Grating-assisted couplers, such as contra-directional couplers (contra-DCs),
have also been demonstrated in the literature as OADMs [72–74]. The contra-DC
consists of two parallel Bragg grating waveguides. Each Bragg grating waveguide
is a structure with a periodic modulation of the effective refractive index in the
propagation direction. In a single Bragg grating, the modulation of the effective
index causes multiple distributed reflections, resulting in constructive interference
around a narrow wavelength band in which light is strongly reflected [75]. In the
contra-DC, contra-directional coupling occurs when the two grating waveguides
are bought close to together and the forward propagating mode of one waveguide
is in phase with the backward propagating mode of the second waveguide. As a
5
result, light from the input waveguide is coupled backwards into the second output
waveguide, instead of the same input waveguide like in a standalone Bragg grating. Contra-DC based filters are particularly attractive for CWDM applications,
as devices with wide bandwidths, flat-top responses, large OBRRs, and low insertion losses have been demonstrated in the literature [65, 76]. While the spectral
response of contra-DCs can easily be tailored by modulating the grating coupling
coefficient along the length of the device, a major drawback of grating-assisted
filters is their small device features which are sensitive to fabrication variations,
namely lithographic-effects including smoothing and proximity effects [77].
SOI-based MRR filters for OADMs have been researched extensively, namely
for DWDM applications due to their relatively narrow linewidths. Moreover, different methods, such as two-point coupling [78], can be used to make the device
reconfigurable (in terms of bandwidth, extinction ratio, etc.) [79–81]. While MRR
filters have demonstrated good performance as regards narrow and reconfigurable
bandwidths, large OBRRs, and low insertion losses, the device performance is often sensitive to fabrication and temperature variations [82]. Moreover, single-ring
MRRs have limited FSRs, reducing the number of channels that can be selectively
filtered in an OADM. For example, if the spacing between two adjacent MRR
modes (the FSR) is smaller than the communication band, two or more signals corresponding to separate wavelength channels would be de-multiplexed by a single
filter, leading to interchannel crosstalk [83]. In order to extend the FSR or eliminate the FSR in MRR filters (and enable increased channel capacities for WDM
systems), multiple methods have been demonstrated in the literature. These methods include higher-order MRRs and the Vernier effect [69], MZI-based coupling
[84, 85], and grating-assisted coupling [86–88]. The work in [86], [87], and [88]
demonstrated that by integrating contra-DCs within the coupling regions of singleor higher-order MRRs, suppression of all but one MRR mode could be achieved,
resulting in effectively FSR-free responses.
1.4
Modulators in WDM Links
The optical modulator is an essential component of the WDM link, setting important link metrics such as the data rate [89]. Typically, modulators on the SOI
6
platform integrate a p-n junction into a waveguide section and use the free-carrier
plasma dispersion effect to change the refractive index of silicon [89, 90]. When
a voltage is applied across the junction, free carriers are either depleted or injected
into the junction, changing the effective index of the waveguide. The effective index change results in a phase shift, which translates to optical signal modulation
in interferometric or resonant modulators. In this section, we discuss the two most
prominent modulator types researched and developed; the Mach-Zehnder modulator (MZM) [91–94] and the MRR modulator [95–100]. Schematics of a conventional MZM and MRR modulator are shown in Figure 1.2a and Figure 1.2b,
respectively.
b)
a)
V
V1
Input
Output
Input
V2
k
Output
Figure 1.2: Schematic of a) a conventional Mach-Zehnder modulator and b)
a conventional microring resonator-based modulator.
In an MZM, a phase shift is applied to either one (single-ended drive) or both
(push-pull drive) of the MZM arms, changing the interference conditions and the
amount of light that exits at the output of the modulator. Typically, MZMs require multi-millimeter long p-n junction segments due to the small refractive index
changes that result when carrier-depletion mode phase shifters are used. As a result, travelling-wave electrodes are required in order to minimize the RF signal and
optical velocity mismatch which enables high electro-optic bandwidths (EOBWs).
While travelling-wave MZMs with large bandwidths have been demonstrated in
the literature [101–103], these devices typically have higher energy consumption,
greater design complexity and occupy a larger footprint as compared to their MRR
modulator counterparts.
Two types of MRR modulation schemes have been demonstrated; intracavity
7
modulation and coupling modulation. Typically, intracavity modulation has been
dominant, where applying a phase shift to the microring cavity results in a shift in
the resonant wavelength of the cavity and, hence, a change in the output power.
In coupling modulation, the resonant wavelength remains constant, while the coupling coefficients (t and k) of the resonator are modulated, changing the extinction ratio of the modulator and, hence, power at the output port (see Figure 1.2b).
MRR intracavity modulators presented in the literature have demonstrated large
EOBWs while occupying very small footprints and achieving very high power per
bit efficiencies [104–106]. Coupling modulators that have been demonstrated have
shown the ability to achieve data rates that exceed the cavity linewidth limit that
typically restricts the maximum data rate of intracavity-modulated MRRs [107–
109]. It should be noted that MRR modulators (like, MRR filters) are also sensitive to temperature variations and fabrication imperfections and also require the
use of resonance wavelength tuning and/or stabilization schemes, which increases
the overall power consumption of the modulator.
λ1
DATA1
λ2
λ4
λ3
DATA2
DATA3
DATA4
Figure 1.3: A block diagram of a 4-channel, single-bus, MRR-based WDM
transmitter architecture.
MRR-based modulators are particularly appealing in WDM transmitter applications in which a series of ring modulators are coupled to a common bus waveguide and each modulator only modulates at a single wavelength [110, 111]. A simplified 4-channel example of this single-bus architecture is shown in Figure 1.3.
This type of transmitter configuration simplifies the WDM architecture, as all of
the channels can be combined onto a single output without the need for an additional wavelength multiplexer (i.e., which would be needed if MZMs were used).
8
However, as previously mentioned, an inherent drawback of using MRRs is their
FSRs. In this particular application, the FSRs would limit the aggregate data rate of
the system, as it restricts the number of channels that can be selectively modulated
within a particular communication band [1, 110, 112, 113].
1.5
Thesis Objective
The research presented in this thesis focuses on SOI, FSR-free, MRR-based filters and modulators for WDM transceiver applications. Specifically, we focus
on the use of contra-DCs integrated into MRR cavities in order to achieve FSRfree responses. Our first objective is to demonstrate a truly FSR-free, microringbased filter, with integrated contra-DCs, in which the adjacent MRR side modes
are completely suppressed. While there have been previous demonstrations of
FSR-free, single-ring MRR-based filters with integrated contra-DCs in the literature ([86, 88]), these designs did not achieve full suppression of the adjacent MRR
side modes. Moreover, these designs were not robust to fabrication variations.
Here, in this work, we demonstrate a filter with improved MRR side mode suppression ratios (SMSRs), and with an integrated, thermally-tunable, two-point coupling
scheme to compensate for fabrication variations and to provide post-fabrication
control of the filter performance (such as a reconfigurable filter bandwidth).
While we show that contra-DCs have many advantages when used as wavelength selective couplers in SOI devices, due to their small feature sizes, contraDCs fabricated using deep-ultra-violet (DUV) lithography are susceptible to smoothing and proximity effects. As a result, if lithography effects are not compensated
for when designing devices that use contra-DCs, large discrepancies arise between
the “as-designed” and “as-fabricated” device performance. In this work, using
lithography models developed for DUV processes, we simulate and analyze the effects of lithography on the performance of an MRR with an integrated contra-DC.
We establish that it is possible to use the lithography models to compensate for
lithographic effects during device design flow and layout. Using this approach, we
then design a contra-DC in which the as-fabricated spectral response matches the
target/expected as-designed spectral response.
Finally, our last objective is to demonstrate a proof-of-concept, MRR-based
9
modulator with an FSR-free response at its through-port for single-bus, WDM
transmitter architectures. While an extended FSR MRR modulator was recently
demonstrated in the literature ([113]), it would be difficult to design an MRR modulator based on this design with an FSR greater than the C-band. Here, in this
work, by integrating a contra-DC into an MRR cavity, we demonstrate a modulator with an FSR-free response. We demonstrate open eyes at a data rate of
2.5 Gbps. We discuss how the effects of DUV lithography on the contra-DC introduced non-fully-suppressed resonance modes in the modulator response and also
how the effects limited the EOBW of the fabricated modulator to 2.6 GHz. We
also provide suggestions on how to significantly improve the EOBW and minimize
channel crosstalk in future designs of the modulator.
1.6
Thesis Organization
This thesis is divided into five chapters. In this chapter, first we presented an introduction to silicon photonics and WDM communication systems. Then we provided
an overview of SOI OADMs and optical modulators that have been demonstrated
in the literature and, finally, the thesis objectives were outlined. In Chapter 2,
first we present an overview of contra-directional couplers and the related theory.
Then we present an FSR-free, MRR-based filter with a reconfigurable bandwidth
and large SMSRs. In Chapter 3, we discuss the effects of lithography on SOI devices that integrate contra-DCs and demonstrate methods to compensate for these
effects during device design flow. In Chapter 4, we experimentally demonstrate
a proof-of-concept, FSR-free, MRR-based coupling modulator for use in singlebus WDM transmitter applications and discuss methods to improve the modulator
performance in future designs. Finally, in Chapter 5, a summary of this work,
conclusions drawn, and suggestions for future work are provided.
10
Chapter 2
Bandwidth-Tunable, FSR-free,
Microring-Based, SOI Filter with
Integrated Contra-Directional
Couplers
In this chapter, we experimentally demonstrate a bandwidth tunable, FSR-free
MRR filter with integrated bent contra-DCs. A thermally tunable MZI-coupler is
used to compensate for fabrication variations, allowing the fabricated filter to have
a reconfigurable bandwidth, as compared to non-tunable filters which have fixed
bandwidths and which lack post-fabrication control of their performance. For example, we show that one can achieve a desired operating point by easily tuning the
filter (regardless of system losses) while maintaining a large non-adjacent channel
isolation for a 400-GHz grid WDM system. Our device also has larger SMSRs
than similar designs previously reported in [86] and [88]. We also show that the
amplitude and phase responses at the through-port of our filter are truly FSR-free
by presenting the measured group delay response of our filter. In this chapter, we
first present an overview of contra-DC theory and design. We then discuss the motivation behind our filter design and provide device theory and design parameters.
Lastly, we present and discuss the measurement results of the fabricated filter.
11
2.1
2.1.1
Contra-Directional Couplers
Overview and Theory
𝒕𝒄
a)
Input
Through
Waveguide B
𝒌𝒄
Drop
Waveguide R
b)
𝚲
𝑾𝑩
𝚫𝑾𝑩
𝒈
𝚫𝑾𝑹
𝑾𝑹
Figure 2.1: a) Diagram of a straight contra-DC. b) Zoom-in of the structure
illustrating device design parameters.
A contra-DC, like a Bragg grating, is a grating-assisted waveguide structure
in which a periodic modulation of the effective refractive index along the structure creates a Bragg reflector. In a contra-DC, the forward propagating mode in a
waveguide couples to the backward propagating mode in a second, parallel waveguide [62, 63]. This is in contrast to a waveguide Bragg grating, in which the forward
propagating mode of a waveguide couples to the backward propagating mode in the
same waveguide [114]. A schematic of a contra-DC is shown in Figure 2.1. The
contra-DC consists of two parallel waveguides (waveguide B and waveguide R)
with average waveguide widths, WB and WR , separated by an average gap distance,
g. Typically, in a contra-DC, the two waveguides have dissimilar widths in order
to reduce forward cross-coupling [72]. In the contra-DC, the periodic modulation
of the effective refractive index is achieved by creating corrugation profiles along
the side-walls of waveguide B and waveguide R, with corrugations depths ∆WB
and ∆WR , respectively. While the corrugations shown in Figure 2.1 are rectangular,
other corrugation profiles, such as sinusoidal and trapezoidal profiles, can also be
12
used. Contra-directional coupling will occur when the forward propagating mode
of waveguide B is in phase with the backward propagating mode of waveguide R.
The phase match condition is given by,
βB Λ + βR Λ = 2π
(2.1)
where Λ is the grating period and βB and βR are the propagation constants for
waveguide B and waveguide R, respectively. The propagation constants are given
by,
βB =
2πne f f ,B (λ0 )
λ0
(2.2)
βR =
2πne f f ,R (λ0 )
λ0
(2.3)
and,
where λ0 is the free space wavelength and ne f f ,B and ne f f ,R are the wavelengthdependent effective indices of waveguide B and waveguide R, respectively. Solving
for the wavelength at which contra-directional coupling occurs, the phase match
condition of the contra-DC becomes:
λ0 = Λ[ne f f ,B (λ0 ) + ne f f ,R (λ0 )]
(2.4)
Within each waveguide, intra-waveguide Bragg reflections can also occur. The
phase match conditions for the Bragg reflections are βB Λ = 2π for waveguide B
and βR Λ = 2π for waveguide R. These intra-waveguide Bragg reflections can be
suppressed by using an “anti-reflection” grating, where the outer corrugations of
each waveguide are out-of-phase with the inner corrugations [73]. This misalignment is shown in Figure 2.1. Figure 2.2 shows a graphical solution to the three
phase match conditions of the contra-DC. In this plot, 220 nm thick strip waveguides (surrounded by a silicon dioxide cladding) are assumed, with WB = 450 nm,
WR = 550 nm, and Λ = 318 nm. The waveguide effective indices were simulated in
MODE Solutions, by Lumerical Inc.
The transfer functions for the through-port and drop-port of the contra-DC can
be derived using coupled-mode theory [115]. The through-port and drop-port trans13
𝜆
2Λ
neff,R
navg
neff,B
Figure 2.2: Graphical solution for the phase match conditions of a contraDC with WB = 450 nm, WR = 550 nm, and Λ = 318 nm. The solid arrow
shows the wavelength at which contra-directional coupling occurs and
the dashed arrows show the wavelengths at which intra-Bragg reflections can occur.
fer functions, tc and kc , respectively, are given by [116],
tc =
Ethrough
− jκ0 sinh(sLc )
=
Einput
s cosh(sLc ) + j ∆β
2 sinh(sLc )
(2.5)
and
∆β
Edrop
se j 2 Lc
kc =
=
Einput
s cosh(sLc ) + j ∆β
2 sinh(sLc )
where s =
(2.6)
q
2
κ02 − ∆β4 , ∆β = βR + βB − 2π
Λ , and Lc is the length of contra-DC (Lc
is given by NΛ, where N is the number of corrugations used). κ0 is the distributed
field coupling coefficient per unit length of the contra-DC and is effectively a measure of coupling strength between the forward coupling mode in one waveguide
14
and the backward coupling mode in the other waveguide. In Figure 2.3, we plot the
through-port and drop-port amplitude responses for a contra-DC with WB = 450 nm,
WR = 550 nm, Λ = 318 nm, N = 470, and κ0 = 12,000 m-1 .
0
10log 10|tc| 2
10log 10|k c| 2
Transmission (dB)
-5
-10
-15
-20
-25
-30
1530
1535
1540
1545
1550
1555
1560
1565
1570
Wavelength (nm)
Figure 2.3: Theoretical through-port (|tc |2 ) and drop-port (|kc |2 ) amplitude
responses of a contra-DC.
2.1.2
Calculation of the Distributed Coupling Coefficient
κ0 is commonly defined analytically via the following equation [62, 72, 117, 118]:
ω
κ0 =
4
ZZ
E1∗ (x, y) · ∆ε1 (x, y)E2 (x, y) dx dy
(2.7)
where ω is the angular frequency, E1 and E2 are the normalized transverse modes
of the unperturbed waveguides (waveguides without side-wall corrugations), and
∆ε1 (x, y) is the first-order Fourier-expansion coefficient of the dielectric perturbation (due to the side-wall corrugation profile). Intuitively, Equation 2.7 shows that
stronger coupling (a larger κ0 ) is achieved when there is a large mode overlap between the two waveguides and/or when the dielectric perturbation is large. This
15
Δλbg
λ0
Figure 2.4: Band diagram of a contra-DC. The spacing between the arrows
is the bandgap (∆λbg ) of the contra-DC and represents the wavelengths
at which light is reflected and, hence, the wavelengths at which contradirectional coupling occurs.
translates to a contra-DC with a smaller average gap between the two waveguides
(g) and/or large corrugation depths (∆WB and ∆WR ).
When designing contra-DCs, there are various methods that have been demonstrated in the literature to determine κ0 . One method is to solve for κ0 using
Equation 2.7, by simulating the mode distributions of the two-waveguide system
via eigenmode simulations, either treating each waveguide as an isolated, unperturbed waveguide, or by using a super-mode analysis [62, 63, 72, 117, 118]. Another method, which was originally proposed to obtain the coupling coefficient of
Bragg gratings, involves determining the photonic band structure of a contra-DC
unit-cell via three-dimensional (3-D) finite-difference-time-domain (FDTD) simulations and extracting κ0 from the band diagram [119]. Recently, this method was
also used to calculate the band structure of a sub-wavelength contra-DC [120]. We
adopted this approach in our contra-DC design flow, and present it here.
16
The photonic band diagram, or ω-k dispersion relation, is a plot of the propagating solutions to the wave equation in a dielectric medium at angular frequencies,
ω, for various values of the wavevector, kz , as shown in Figure 2.4. Similar to onedimensional (1-D) photonic crystals, Bragg gratings and contra-DCs can be effectively described as structures with periodic perturbations of the dielectric medium
in the direction of the propagating optical mode. These periodic perturbations give
rise to photonics bandgaps (∆λbg ); ranges of wavelengths or frequencies in which
there are no propagating solutions to Maxwell’s equations for any wavevector, kz
(see Figure 2.4) [121]. Within this range of wavelengths, light will be reflected.
The band diagram of a contra-DC can be used to extract its ∆λbg and central wavelength, λ0 [119, 120, 122]. The ∆λbg of the contra-DC band diagram, in fact,
corresponds to ∆λnull of an infinitely long contra-DC, in which ∆λnull is the spacing between the first nulls of the contra-DC drop-port response (see Figure 2.3)
[120]. ∆λnull for an infinitely long contra-DC is given by [116],
∆λnull (Lc → ∞) =
2λ02 κ0
π[ng,R (λ0 ) + ng,B (λ0 )]
(2.8)
where ng,B and ng,R are the wavelength-dependent group indices of waveguide B
and waveguide R, respectively. Thus, κ0 for a contra-DC can be determined via
Equation 2.8. To plot the ω-k dispersion relation of a contra-DC, we perform
FDTD bandstructure calculations using FDTD Solutions, by Lumerical Inc. In the
simulations, we consider an infinitely long contra-DC as a single contra-DC unitcell (single grating period) with Bloch boundary conditions. By sweeping kz , and
performing a Fourier transform on the time-domain signals in the simulation, ωn
for the nth propagating Bloch mode in a given frequency range, can be determined
[119, 120, 122]. The ω-k dispersion diagram can then be constructed and ∆λbg and
λ0 can be extracted to determine κ0 of the contra-DC.
Figure 2.5 shows the calculated band diagram for a contra-DC with the parameters WB = 450 nm, WR = 550 nm, ∆WB = 50 nm, ∆WR = 60 nm, Λ = 318 nm, and
g = 280 nm. In the plot, ω was converted to wavelength and kz was normalized by a
factor of Λ/2π. In the band diagram, the blue and red dotted lines represent the individual dispersion relations for waveguide B and waveguide R, respectively. The
band diagram shows that at wavelengths far from the bandgap, optical modes prop17
λBragg,R
Δλbg
λBragg,B
Figure 2.5: Band diagram of a contra-DC with WB = 450 nm, WR = 550 nm,
∆WB = 50 nm, ∆WR = 60 nm, Λ = 318 nm, and g = 280 nm.
agate through the perturbed waveguides as if the waveguides were unperturbed.
However, at wavelengths near the band gap, where there is an effective crossing
between the waveguide modes, light is reflected, and contra-directional coupling
occurs. The spacing between the arrows in Figure 2.5 denotes the bandgap of this
particular contra-DC. The bandgap is 2.2 nm, centered around 1550 nm, corresponding to a κ0 value of 12,000 m-1 . (This is the same κ0 value that was used
to simulate the contra-DC through- and drop-port responses in Figure 2.1). The
band diagram can also be used to determine the strength of the intra-waveguide
Bragg reflections from each waveguide, which occur at a normalized kz value of
0.5 (corresponding to the edge of the first Brillouin zone) [119]. Here, because
anti-reflection grating waveguides were simulated, no bandgap is visible at kz =
0.5, and the effect of the intra-Bragg reflections can be considered negligible.
Similar to [119] and [123], we demonstrate how κ0 values extracted from bandstructure calculations compare with experimental results of fabricated contra-DCs.
Here, we present measurement results of fabricated contra-DC test structures from
18
6
104
5
(m -1)
4
Rect. Simulated
Sinu. Simulated
Rect. UW
Sinu. UW
Rect. ANT
Sinu. ANT
0
3
2
1
0
10/20
30/40
50/60
70/80
90/100
110/120
130/140
WB / WR (nm)
Figure 2.6: Comparison between contra-DC k0 values determined via bandstructure calculations and k0 values extracted from measured test structures fabricated at UW and ANT.
two different fabrication facilities: The University of Washington Microfabrication/Nanotechnology User Facility (UW) and Applied Nanotools, Inc. (ANT).
Both sets of test structures were fabricated using electron-beam (e-beam) lithography. The devices had a 220 nm silicon thickness with a target 3 µm silicon dioxide
cladding layer deposited over top. The test structure parameters were WB = 450 nm,
WR = 550 nm, Λ = 318 nm, and g = 280 nm. The contra-DCs were 159 µm long
(N = 500). ∆WR was varied from 20 nm to 140 nm in 20 nm steps and ∆WB for
each structure was 10 nm less than ∆WR . Test structures with rectangular and sinusoidal corrugation profiles were simulated and fabricated. The κ0 values of the
fabricated test structures from both UW and ANT were extracted from the measured drop-port spectra using the full width at half maximum (FWHM) method
presented in [123]. The κ0 values of the simulated and fabricated test structures
are plotted in Figure 2.6. The κ0 values extracted from our bandstructure calculations (which have been fitted to a 4th order polynomial) show good agreement with
19
the measured test structures for both rectangular and sinusoidal contra-DCs from
both fabrication runs. Having plots like Figure 2.6 is advantageous during device
design flow, as they can be used as look-up tables to determine which values of the
contra-DC parameters are required to achieve a desired κ0 value.
2.2
Motivation
Grating-assisted filters have typically been demonstrated as coarse-WDM filters.
This is due to such filters having wide-bandwidths and FSR-free responses with
high side lobe suppression ratios (SLSRs) [72]. Used solely as couplers, as compared to conventional broadband directional couplers used in MRR filters, contraDCs effectively filter selected wavelengths at the drop-port of the device. This
type of coupler can be used in MRR devices to prevent certain wavelengths from
coupling to, and resonating in, the cavity, as compared to conventional directional
couplers in which light at all wavelengths couples to the cavity. As a result, if
wavelengths that are not filtered to the drop-port coincide with the resonant wavelengths of the MRR cavity, light will not enter the cavity and, thus, the selective
suppression of those MRR resonant modes occur [88]. An FSR-free response is
achieved when the contra-DC suppresses all MRR modes except the one at or near
the contra-DC central wavelength (λ0 ). Maximum suppression of the amplitude responses at all other undesired resonant wavelengths (side modes) will be achieved
provided that the spacing between the first nulls of the contra-DC, ∆λnull , is equal to
twice the FSR of the MRR (2FSRring = ∆λnull ), as shown in Figures 2.7a and 2.7b.
A schematic of the proposed filter is given in Figure 2.8. The filter consists
of an add-drop (AD) MRR with a bent contra-DC integrated into the through-port
coupling region and an MZI-coupler as the drop-port coupler. The design differs
from that presented in [88], as we only integrate a contra-DC into the through-port
coupling region rather than both the through- and drop-port coupling regions. As
demonstrated in [88], in order to meet the maximum suppression condition, each
contra-DC should cover approximately 50% of the cavity. Bent contra-DCs are,
thus, used to achieve this condition, as compared to cavities with straight contraDCs [86] in racetrack resonator configurations in which the maximum suppression
condition cannot be met. However, devices that use two bent contra-DCs, that
20
Δλnull = 2FSRring
(a)
Contra-DC
FSRring
(b)
Ring
FSRMZI
(c)
MZI
Figure 2.7: Spectral responses (arbitrary linear scales) of a) the contra-DC
drop-port response, b) the MRR response, and c) the MZI cross-state
response when ∆λnull = 2FSRring = FSRMZI . The BW of the filter is
tuned as the MZI response is redshifted (green arrow). Reprinted with
permission from [1] c The Optical Society of America.
combined cover approximately 100% of the cavity, are susceptible to fabrication
variations and are not practical as they do not allow adequate space to connect bus
waveguides to route the filter to external components (optical input/output, other
devices, etc.) [88]. As the suppression of the MRR side modes is primarily dependent on the through-port coupler, we have replaced the drop-port contra-DC in
[88] with a tunable MZI-coupler, such that the through-port contra-DC can cover
approximately 50% of the cavity to enable larger side mode suppression ratios
(SMSRs) as compared to filters presented in [86] and [88]. Moreover, the tunable
coupler itself allows for the post-fabrication control of the drop-port couplers coupling coefficient (this is shown as the MZI response in Figure 2.7c) and enables the
bandwidth reconfigurability of the device.
21
WB
ΔWB Λ
ΔWR
g
R
WR
Input
Through
L1
L2
Drop
TiN Heater
Figure 2.8: A schematic of our tunable filter. Inset shows the design parameters of the bent contra-DC. Reprinted with permission from [1] c The
Optical Society of America.
2.2.1
Bent Contra-DCs
As shown in Figure 2.8, the bent contra-DC is integrated into the through-port
coupling region of the MRR cavity. In a bent contra-DC, the outer waveguide is
wrapped around the inner waveguide, which as a radius of curvature, R. Here, we
denote the upper waveguide of the bent contra-DC as the bus (grating) waveguide
(WB ) and the inner waveguide as the ring (grating) waveguide (WR ), where the ring
waveguide also forms part of the MRR cavity. The bent contra-DC shares the same
design parameters as a straight contra-DC, however, Λ of the bent contra-DC is
measured in the center of the coupler’s gap. By defining Λ this way, the phase
match condition of a bent contra-DC becomes [116],
λ0 = Λ
ne f f ,B (λ0 )[R + W2B + g + W2R ] + ne f f ,R (λ0 )R
R + g + W2B
(2.9)
For large R, Equation 2.4 and Equation 2.9 yield approximately the same solution. The equations for tc (Equation 2.5) and kc (Equation 2.6) of a straight contra22
DC also hold for a bent contra-DC. ∆λnull of a contra-DC with a finite length, Lc is
given by [116],
∆λnull
2λ02
=
π[ng,R (λ0 ) + ng,B (λ0 )]
r
π
κ02 + ( )2
Lc
(2.10)
where ng,B and ng,R are the group indices of the bus and ring waveguides, respectively. The FSR of the MRR is given by,
FSRring =
λ02
2πRng,R (λ0 ).
(2.11)
Hence, to achieve the 2FSRring = ∆λnull , the length of the contra-DC integrated
into the MRR cavity, Lc , should satisfy the following relation, which can be determined from Equation 2.10 and Equation 2.11:
2π
Lc = q
ng,R (λ0 )+ng,B (λ0 ) 2
( ng,R (λ0 )R ) − 4κ02
2.2.2
(2.12)
MZI-Based Couplers
MZI-based coupling schemes have been used to double the FSR of single- [78]
and double-ring AD MRR filters [84, 85]. Here, in this paper, we use an MZIcoupling scheme in the drop-coupler of our MRR (see Figure 2.8) for two purposes. Firstly, we show that, if the nulls of the MZI-coupler cross state align with
the contra-DC nulls, then the directly adjacent side mode of the MRR response can
be further suppressed at the drop-port regardless of any fabrication induced misalignment between the contra-DC and ring responses. This requires that the FSR
of the MZI matches ∆λnull of the contra-DC (Figures 2.7a and 2.7c). Secondly, the
MZI-coupler can provide independent control of the drop-port coupler coupling
coefficients by introducing a phase shift (φarm ) in the lower (control)-arm of the
coupler (see Figure 2.8). A phase shift induces a redshift of the MZI response and
a change in the effective coupling coefficients of the drop-port coupler at the operating wavelength, resulting in an adjustable drop-port BW. (The phase shift can
be induced via the thermo-optic effect by placing resistive metal heaters over the
waveguide, or via the plasma-dispersion effect by integrating p-n junctions into the
23
control-arm waveguide.) This effect can be understood by analyzing the equation
for the BW of an AD MRR. The BW is given by [124],
BW3dB =
(1 − t1t2 a)λ02
√
πng,R Lrt t1t2 a
(2.13)
where t1 is the self-coupling coefficient of the through-port coupler, t2 is the selfcoupling coefficient of the drop-port coupler, a is the attenuation factor of the
MRR, and Lrt is the roundtrip length of the cavity. Clearly, if all other resonator
parameters are static, the MRR BW can be adjusted dynamically by varying t2 .
In our device, by using an MZI-coupler, t2 becomes of function of φarm and thus,
the BW becomes a function of φarm . The BW tunability allows one to compensate
for fabrication variations (i.e., variations in the directional coupler coupling coefficients, variations in the roundtrip cavity losses, etc.), enabling post-fabrication
control of the device to achieve the “as-designed” or desired device performance.
2.3
Device Theory
The through-port and drop-port transfer functions of our device are determined
following the Mason’s rule [125] based approach presented in [116] and [126].
The equations of our device differ from those presented in [88] and [116], as in
our device, the drop-port coupler is an MZI-coupler. The MZI-coupler consists of
two directional couplers, K1 and K2 , with the top arm of the coupler (of length L1 )
sharing part of the microring cavity (see Figure 2.9). The transfer matrix of the
MZI-coupler, H, is given by,
"
H=
t2
− jk2
− jk2
t2
#"
X1
0
#"
0
X2
t1
− jk1
− jk1
t1
#
(2.14)
where,
X1 = e− jβR L1 e−
αR
2 L1
X2 = e− jβR L2 − jφarm e−
,
αR
2 L2
(2.15)
,
(2.16)
q
ki is the field cross-coupling coefficient of Ki , ti = 1 − ki2 (and assuming lossless
24
𝒕𝒄 ,B
𝒕𝒄,𝑹
𝒌𝒄
𝒌𝒄
L1
K1
K2
𝒕𝒆𝒇𝒇 (𝝋𝒂𝒓𝒎 )
L2 + φarm
Figure 2.9: Diagram of filter illustrating the coupling coefficients of the bent
contra-DC and MZI-coupler. The coupling coefficients, te f f and ke f f
(not shown in figure), of the MZI-coupler can be readily controlled by
tuning φarm .
couplers), L1 is the length of the MZI-coupler arm that is shared with the microring
cavity, L2 is the length of the control-arm, and αR is the field loss coefficient of the
waveguides (which have the same width as the ring waveguide). If we assume that
the directional couplers are the same (K1 = K2 ), then the effective through-port
(te f f ) and cross-port (ke f f ) coupling coefficients of the MZI-coupler are given by
Equation 2.17 and Equation 2.18, respectively. As can be seen from their respective
equations, te f f and ke f f are both functions of φarm .
te f f = H11 = t12 e−
αR
2 L1
ke f f = H12 = − jk1t1 [e−
e− jβR L1 − k12 e−
αR
2 L1
e− jβR L1 + e−
αR
2 L2
αR
2 L2
e− j(βR L2 +φarm )
(2.17)
e− j(βR L2 +φarm ) ]
(2.18)
Following a similar derivation for the device presented in [116], the resulting
25
through-port and drop-port transfer functions of our device are given by,
Ethru =
te f f kc2 X + tc,B [1 − te f f tc,R X]
1 − te f f tc,R X
√
ke f f kc X
Edrop =
1 − te f f tc,R X
(2.19)
(2.20)
where,
tc,B = tc e− jβB Lc e−
αB
2 Lc
,
(2.21)
tc,R = tc e− jβR Lc e−
αR
2 Lc
,
(2.22)
X = e− jβR LR e−
αR
2 LR
,
(2.23)
LR is the residual cavity path length that is not shared with the contra-DC ring
waveguide or the top arm of the MZI-coupler (LR = 2πR − Lc − L1 ) and αB is the
field loss coefficient of the bus waveguide. The equations for tc,B and tc,R differ
from Equation 2.5 in order to account for the difference in phase accumulation in
the contra-DC bus and ring waveguides (see Figure 2.9).
2.4
Device Design
The devices were designed assuming a 220 nm silicon thickness and a top oxide
cladding layer. WB and WR of the bent contra-DC were chosen to be 450 nm and
550 nm, respectively, and Λ was set to 318 nm to place the filter operating wavelength close to 1550 nm. The large asymmetry between the waveguide widths reduced forward cross-coupling. To determine the length of the contra-DC required
to achieve 2FSR = ∆λnull , we plotted Lc as a function of R for various κ0 values
based on Equation 2.12. (The group indices used to solve for Lc for unperturbed
waveguides, waveguide B and waveguide R, were 4.11 and 4.33, respectively, determined using MODE Solutions). To compare our design to that presented in
[88], we chose R to be also be equal to 34 µm. From Figure 2.10, we see that the
maximum suppression condition for a 34 µm ring is met when κ0 = 4,700 m-1 and
Lc = 105.3 µm. This length corresponds to N = 330 and thus, the contra-DC cover-
26
age of the ring was 48.44%. The corresponding contra-DC design parameters for
the κ0 values plotted in Figure 2.10, are listed in Table 2.1. These values were determined from the bandstructure simulation results which we plotted in Figure 2.6.
Because the radius of curvature of the ring was relatively large, we assumed that
the κ0 values of the bent contra-DCs were approximately equal for straight contraDCs with similar design parameters. This assumption was verified by simulating
the full bent contra-DC structures in FDTD and comparing the extracted κ0 from
those simulations to the bandstructure results. From Table 2.1, a contra-DC with
κ0 = 4,700 m-1 is achieved by setting ∆WB equal to 20 nm, ∆WR equal to 30 nm,
and g equal to 280 nm. A summary of the chosen design parameters for the bent
contra-DC used in the filter is presented in Table 2.2.
125
L c (µm)
2900 m -1
120
4700 m -1
6900 m -1
115
9350 m -1
110
105
100
95
90
30
31
32
33
34
35
36
37
38
R (µm)
Figure 2.10: Graphical solution to Equation 2.12, for select κ0 values, to determine Lc required to satisfy 2FSRring = ∆λnull .
To set the FSR of the MZI-coupler to be equal to ∆λnull , the length of the MZIcoupler control-arm, L2 , was chosen such that L2 = L1 + πR (L1 was 50 µm long)
and the width of the coupler arm waveguide was also 550 nm. The gap width for
27
Table 2.1: κ0 values of various bent contra-DC designs.
κ0
2,900 m-1
4,700 m-1
6,900 m-1
9,350 m-1
g
∆WB
∆WR
280 nm
280 nm
280 nm
280 nm
10 nm
20 nm
30 nm
40 nm
20 nm
30 nm
40 nm
50 nm
Table 2.2: Design parameters for the bent contra-DC in the filter.
Design Parameters
Value
WB
∆WB
WR
∆WR
Λ
g
N
R
450 nm
20 nm
550 nm
30 nm
318 nm
280 nm
330
34 µm
each directional coupler used in the MZI-coupler was set to 60 nm to maximize
|ke f f |2 of the MZI-coupler (60 nm was the minimum resolvable gap width guaranteed by the fabrication process). The coupling coefficient of the directional coupler
at 1550 nm was 15% based on FDTD simulations. A 160 µm long TiN heater
was placed above the MZI-coupler control arm in order to thermally induce the
phase shift used to tune the coupling coefficients of the drop-port coupler (via the
thermo-optic effect). A second 105 µm long TiN heater was also placed above the
contra-DC to allow us to align the contra-DC and ring responses. A third 80 µm
long TiN heater was placed across the section of the ring not covered by the contraDC or MZI-coupler to allow us to tune the operating wavelength of the filter. The
TiN heaters were 3 µm wide, 200 nm in thickness and had a target bulk resistivity
of 0.8 µΩ-m. We also designed a reference device with a conventional directional
coupler in the drop-port coupling region in order to compare the effect of fabrication variations on the contra-DC and filter SMSR. The device was also designed to
achieve a wide target BW of 46 GHz (0.375 nm). The coupler had a gap of 60 nm
28
SMSR
SMSR
Δλnull
Figure 2.11: a) Simulated through- and drop-port responses of the filter, with
the nulls of the MZI-coupler cross-port response aligned with the
contra-DC nulls. b) Zoom-in around the operating wavelength. Dotted
lines represent the wavelengths of suppressed resonant modes.
and a power coupling coefficient of 25% at 1550 nm.
The through-port and drop-port responses of our designed filter are shown
in Figure 2.11a. The responses are simulated in MATLAB R , based on the device transfer functions (Equation 2.19 and Equation 2.20). In our simulations, we
assume the waveguide propagation loss for all waveguides to be 3 dB/cm. Figure 2.11a shows the response of the filter when the nulls of the MZI-coupler crossstate align with the contra-DC nulls. Across the 80 nm wavelength range shown
in Figure 2.11a, the resonant modes of the MRR are suppressed at all wavelengths
other than the operating wavelength (1547.8 nm). The insertion loss is 1.3 dB
and the 3-dB BW is approximately 60 GHz. Figure 2.11b shows a zoom-in of
the responses near the operating wavelength, where the dotted lines represent the
(wavelength) locations of the first two left adjacent and first two right adjacent
suppressed MRR side modes. The directly adjacent side modes are suppressed
due to both the MZI-coupler and the contra-DC, while the second adjacent side
modes are suppressed solely by the contra-DC. Interstitial peaks are also visible
in the drop-port transmission spectra. While these peaks at not located directly
at suppressed resonant wavelengths, the peaks can potentially lead to interchannel
crosstalk. Here, we define the SMSR of the filter to be the minimum difference
29
between the drop-port transmission at the operating wavelength and the maximum
drop-port transmission of the largest interstitial peak on either side of the drop-port
operating wavelength (within the C-band). The SMSR of the simulated device is
26.5 dB.
Figure 2.12: a) Filter drop-port response (blue) with the MZI-coupler crossport response (grey-dotted) shifted by a quarter cycle (φarm = −π/2),
and b) by a half cycle (φarm = ± π). The contra-DC response (reddotted) is static and does not shift as a function of φarm . Adapted with
permission from [1] c The Optical Society of America.
Figure 2.13: Filter a) 3-dB BW and |te f f |2 versus φarm and b) SMSR and IL
versus φarm .
30
Figure 2.12 shows how the drop-port spectrum changes when a phase shift
is applied to the MZI-coupler control-arm. In Figure 2.12a, φarm = −π/2, and
the MZI-coupler cross-state is shifted by a quarter cycle. The phase shift alters
the coupling conditions around the operating wavelength and, hence, results in a
change in the 3-dB BW of the filter (as per Equation 2.13). The BW is reduced to
26 GHz. The simulated filter BW as a function of φarm is plotted in Figure 2.13a.
The MZI-coupler through-port power coupling coefficient (|te f f |2 ) is also plotted
as a function of φarm in Figure 2.13a. When a phase shift is applied to the controlarm, because the contra-DC response remains static, the MRR side modes are still
suppressed. However, the interstitial peaks become larger due to the change in
|ke f f |2 at wavelengths near a suppressed mode. This effect decreases the SMSR of
the filter, as demonstrated in Figure 2.12a. In Figure 2.13b, we plot the SMSR of
the filter as a function φarm . Over the π/2 phase shift range, the SMSR remains
greater than 22.5 dB. The insertion loss of the filter is also a function of φarm .
As the phase shift approaches π, destructive interference occurs at the cross-port
of the MZI-coupler and no light will be transmitted to the drop-port of the filter,
as demonstrated in Figure 2.12b. For phase shifts ranging from −π/2 to 0, the
insertion loss of the filter is less than 1.4 dB, as shown in Figure 2.13b.
2.5
Experimental Results
Our devices were fabricated by Applied Nanotools, Inc., using their electron-beam
lithography process. Sub-wavelength fiber grating couplers (GCs) were used for
the optical input and output. The devices were measured using an Agilent 81600B
tunable laser source and two Agilent 81635A optical power sensors. First, one of
the cavity heaters was used to align the contra-DC nulls with the cavity resonant
modes. The MZI-coupler was then tuned to achieve a desired operating BW. Lastly,
a common signal was applied to both the cavity heaters to obtain the target operating wavelength of the filter (1548.2 nm). The operating wavelength was set last in
order to compensate for the parasitic wavelength shift that accompanies the tuning
of the control-arm [127]. Figures 2.14a and 2.14b show the measured throughand drop-port responses of a fabricated filter before and after this alignment-tuning
process, respectively. The responses were normalized to remove the spectral re-
31
3.2 nm
a)
b)
Ai
SMSR
nAi
c)
Ai
SMSR
nAi
Figure 2.14: The through- (blue) and drop-port (red) responses of the filter; a) before alignment-tuning, b) aligned to the operating wavelength
(1548.2 nm) and tuned to the maximum BW (60 GHz), and c) aligned
to the operating wavelength (1548.2 nm) and tuned to the minimum
BW (25 GHz). Dotted lines show possible channel locations on a
400-GHz grid. The simulated drop-port responses, based on extracted
fit parameters, are overlayed onto the measured drop-port response.
Reprinted with permission from [1] c The Optical Society of America.
32
sponses from the input and output (through/drop-port) GCs. Due to high losses
of the fabricated GCs, it should be noted that our measurements of the drop-port
spectrum was limited by the noise floor of the power sensors.
A single resonant mode is observed within the C-band. The drop-port response
shows a large 3-dB BW of approximately 60 GHz (0.48 nm) and an insertion loss
of less than 3 dB. As seen in Figure 2.14b, the MRR side modes adjacent to the
operating wavelength are completely suppressed. Moreover, all suppressed modes
at the through-port notches have magnitudes of less than 0.75 dB. The measured
SMSR was 20.8 dB, which is larger than the values reported in both [86] and [88].
Figure 2.14c (to be discussed in further detail below) shows the same filter when
the MZI-coupler was tuned to achieve a BW of 25 GHz.
Here, we also characterize the filters adjacent channel isolation, Ai , and nonadjacent channel isolation, nAi , as defined in [87], for a channel spacing of 400 GHz
(3.2 nm). Ai is defined as the minimum difference (in dB) between the transmission of the filter at the operating wavelength and its transmission at the location
of the directly adjacent channels. nAi is the minimum difference (in dB) between
the transmission of the filter at the operating wavelength and its transmission at
all non-adjacent channels within the C-band (1528.77 nm to 1563.86 nm [69]). In
other words, here we only considered the 11 possible channels in the C-band (6 to
the left and 4 to the right of the operating wavelength) when calculating Ai and nAi .
Ideally, one would like the nAi to be greater than the Ai to minimize interchannel
crosstalk in a WDM system [83, 85]. Adjusting the control-arm phase of our filter
to have a 60 GHz BW, the Ai of our filter was 35.5 dB and the nAi was 26.7 dB.
In order to extract the filter parameters of the “as-fabricated” device, we fit the
measured drop-port response to the device transfer function (Equation 2.20). The
design parameters of interest were the waveguide loss, power coupling coefficient
of the MZI-coupler directional couplers (|k1 |2 ) and κ0 of the contra-DC. These parameters were most likely to vary from the as-designed values. In our fitting, we assumed that the waveguide dimensions of the fabricated device did not deviate from
the as-designed dimensions, and, hence, the waveguide effective index models used
for fitting were the same as those used in the device simulations. From the fitting,
it was determined that κ0 of the fabricated filter was 4,100 m-1 , the waveguide loss
was 18 dB/cm and |k1 |2 was 14.1%. The simulated drop-port responses based on
33
the extract fit parameters show good agreement with the measured drop-port responses in Figures 2.14b and 2.14c. We also extracted κ0 from the measurement
results of an on-chip, bent contra-DC test structure that was located close to the
filter (using the method presented in [123]). The κ0 value extracted from the test
structure agreed well with the value determined from the fitting. The waveguide
loss determined from the fitting was also close to the value that we extracted from
on-chip waveguide loop-back calibration structures, validating our extracted fit parameters. Due to the small feature sizes of the contra-DC, κ0 is very sensitive to
fabrication variations. Hence, the reduction in κ0 from the design value was likely
due to fabrication variations which reduced the corrugation depths and/or increased
the average gap between the grating waveguides. FSRring of the fabricated device
was also extracted by measuring the spacing between the major through-port notch
and the suppressed through-port notch left adjacent to the major notch. The measured FSR was 2.74 nm. Based this value, the group index of the ring waveguide
was solved for using Equation 2.11. The measured group index near 1550 nm was
4.1, which closely matched the simulated value of 4.11. Based on the extracted
parameters, clearly ∆λnull of the fabricated device was less than 2FSRring and the
maximum suppression condition was not met. However, for the filter state where
the first contra-DC nulls align with the MZI-coupler cross-state nulls, the adjacent
MRR side modes were still completely suppressed due to the MZI-coupler.
We also compared the suppression of the adjacent MRR side modes for the
reference devices with drop-port point couplers (instead of an MZI-coupler). Figure 2.15 shows the measured drop-port spectra (after alignment) of the two devices, which were spaced 460 µm apart on the chip. Compared to the tunable filter,
both reference devices had smaller SMSRs (approximately 17 dB). While the adjacent side modes of the first reference device appear to be completely suppressed
(Figure 2.15a), the right adjacent side mode of the second device is not fully suppressed (Figure 2.15b). For the second device 2FSRring was greater than ∆λnull
and, hence, the contra-DC nulls could not be aligned to the ring resonant wavelengths. Moreover, this misalignment resulted in minor notches in the throughport response. This result illustrates the versatility of using an MZI-coupler, in
which large suppressions of the adjacent MRR side modes can still be achieved,
regardless of variations between the as-designed and as-fabricated κ0 values (due
34
SMSR
SMSR
Figure 2.15: Spectral responses of the fabricated, point-coupled reference
devices with a) complete suppression of the adjacent MRR side
modes and b) one adjacent side mode not fully suppressed due to
2FSRring > ∆λnull , due to fabrication variations. Reprinted with permission from [1] c The Optical Society of America.
to fabrication variations, wafer thickness variations, etc.).
Besides having contra-DC and ring responses that could not be aligned, the
measured drop-port BWs of the reference devices (33.8 GHz and 31.3 GHz) were
also lower than their target design value of 46 GHz. While these devices could not
achieve their target BWs, with our tunable device, we demonstrate that independent
control of the filter’s drop-port coupling coefficient allows us to achieve a range of
BWs from a maximum of approximately 60 GHz to a minimum of 25 GHz. Figure 2.16a demonstrates how the device BW changes when a current is applied to
the MZI-coupler control-arm heater. We also plot |ke f f |2 as a function of heater
current, which was determined using the extracted fit parameters. At a heater current of approximately 20 mA, the maximum BW of the filter was achieved when
the effective cross-coupling coefficient of the drop-port coupler was at a maximum
and the MZI coupler cross-state nulls and the contra-DC nulls were aligned (as
show in Figure 2.14a). For these coupling conditions, the MRR was undercoupled,
as the light that was effectively lost to the MRR (due to waveguide loss and light
coupled to the drop-port) was greater than that which was coupled to the MRR
[124]. As the heater current was reduced, the |ke f f |2 decreased, the MRR became
35
less undercoupled and the BW decreased. Figure 2.14c shows the through- and
drop-port responses of the filter, where the BW was reduced to 25 GHz for a heater
current of 15 mA. Smaller bandwidths were achievable at the expense of higher
insertion losses. Over the demonstrated tuning range, the device maintained an
SMSR greater than 15.25 dB, an Ai greater than 23.5 dB, and an nAi greater than
26.7 dB, as shown in Figure 2.16b. When tuning the MZI-coupler, this reduction
in Ai was due to the redshift of the MZI-nulls and the increase of the effective
coupling coefficients at wavelengths near resonant wavelengths, as demonstrated
in device simulations. The Ai was at its minimum across the tuning range when
the filter was tuned to the 25 GHz BW operating point (Figure 2.14c).
Figure 2.16: a) Drop-port BW and extracted effective MZI-coupler power
coupling coefficient as a function of control-arm heater current. b) Ai
and nAi of the filter for a 400-GHz grid WDM, and SMSR as a function of control-arm heater current. Reprinted with permission from [1]
c The Optical Society of America.
Here, we also show that resonance-induced through-port phase responses at
suppressed resonant modes are virtually non-existent, as compared to Vernier effect filter designs. This because the contra-DC effectively prevents light from coupling to the ring at these all wavelengths other than at the operating wavelength,
as compared to conventional broadband directional couplers used in Vernier devices. As a result, low dispersions and group delays occur when the contra-DC and
ring responses are aligned, reducing signal distortion in the passband and the need
36
for dispersion compensation [128]. To illustrate this, we show the group delay of
our filter when the control-arm is tuned to operate the filter in the over-coupled
regime close to critical coupling, where the largest MRR group delays occur [124]
(it should be noted that we actually operated our filter in the under-coupled regime
where the group delays near resonance are typically much smaller). As shown in
Figure 2.17, a large group delay at through-port is observed at the operating wavelength, while minimal group delay is observed across the C-band. The group delay
response for the filter includes the response of the input and output GCs. Here,
we believe the measurement resolution was limited by the high losses and noise
introduced by the input and output GCs (the group delay of a GC test structure is
also shown in Figure 2.17).
Group Delay (ps)
400
GC Response
Filter Through Response
300
200
100
0
1530
1535
1540
1545
1550
1555
1560
Wavelength (nm)
Figure 2.17: Group delay at the through-port of the filter (when operated in
the overcoupled region) and of a grating coupler test structure (zero
set arbitrarily). A single spike in the filter’s group delay is observed at
the resonant wavelength. Reprinted with permission from [1] c The
Optical Society of America.
2.6
Summary
In this chapter, we have demonstrated a BW-tunable, MRR-based filter with FSRfree through- and drop-port responses for WDM applications. The device is truly
FSR-free at the through-port as resonance-induced amplitude and phase responses
are virtually non-existent at the suppressed resonant modes of the MRR. The fil37
ter is capable of achieving drop-port BWs as high as 60 GHz and as low as 25
GHz. Our filter is capable of achieving an nAi greater than 26.7 dB for a 400-GHz
WDM grid, while also maintaining the true FSR-free response with minimum SMSRs greater than 15.25 dB. The device can be used to compensate for fabrication
variations, allowing one to control the filter to achieve the as-designed device performance.
While the devices presented in this chapter where fabricated using an e-beam
lithography process, DUV lithography could also be used. However, the performance of grating-based devices fabricated using DUV lithography typically suffers more drastically from lithographic distortions. In the following chapter, we
demonstrate how lithography smoothing and proximity effects from the DUV process affect the performance of SOI devices that include grating-based components,
like contra-DCs, and present a method to compensate for such lithography effects
during device design flow.
38
Chapter 3
Effect of Lithography on SOI,
Grating-Based Devices for Sensor
and Telecommunications
Applications
Grating-based devices on the SOI platform, such as Bragg gratings [114, 129], subwavelength structures [130, 131], and contra-DCs [72], have attracted considerable
interest for use in sensors [132–134] and in telecommunications systems [73, 135].
Due to their small feature sizes, grating-based devices such as Bragg gratings
and contra-DCs have typically been fabricated using e-beam lithography processes
which can consistently resolve such feature sizes. However, the low throughput
of the e-beam process makes it unsuitable for large-scale production of photonic
devices. For high volume production, CMOS-compatible processes, such as DUV
lithography, have been proven suitable [136]. However, the performance of devices
with feature sizes that are smaller than the resolution limit is affected by lithography effects such as smoothing [137] and proximity effects [74]. For example, for
Bragg gratings designed with rectangular-shaped, side-wall gratings, the smoothing of the gratings mainly affects the central wavelength and coupling strength,
κ0 , of fabricated devices [137, 138]. Therefore, to truly enable the high-volume
39
production of photonic systems that integrate such grating-based devices, it is important to account for the effect of DUV lithography during the device and system
design flow.
In this chapter, using a computational lithography smoothing prediction model
[77], we demonstrate how smoothing and proximity effects affect the performance
of devices that include gratings. In particular, we use the example of an MRR with
integrated contra-DC couplers. The MRR with integrated contra-DCs was chosen to investigate the effects of lithography, as it contains both a ring-based cavity
and grating-assisted couplers. These components have been demonstrated in both
sensor and telecommunication applications, and, stand-alone, would exhibit discrepancies between as-designed and as-fabricated performance due to lithographiceffects. Using analytical models, we demonstrate the effect of lithography on important MRR characteristics such as BW, IL, and adjacent SMSR and discuss a
method to account for lithography effects in future device designs. We also present
the lithography prediction model for contra-DCs fabricated using 193 nm DUV
lithography. We show that the prediction model achieves good agreement with
fabricated test structures. We also validate that, like Bragg gratings, the central
wavelengths and coupling strengths of the fabricated contra-DCs are affected by
the lithography.
3.1
Device Behaviour and Modelling
FSR-free, MRR filters with integrated contra-DCs have been experimentally demonstrated using e-beam lithography [1, 88]. By integrating contra-DCs into the coupling regions of a ring resonator, FSR-free drop-port responses, large SMSRs, and
large adjacent channel isolations have been achieved. Other wide-FSR, microring
ring devices have been demonstrated in the literature [69, 84, 85], however, these
devices are not compact, as they consist of multiple rings, each of which requires
tuning to align their resonant wavelengths.
Figure 3.1 shows a schematic of the MRR under investigation. The device consists of an add-drop MRR with a bent contra-DC integrated into the through-port
coupling region, and a conventional directional coupler in the drop-port coupling
region. The design parameters of the device presented in this paper are similar
40
WB
ΔWB Λ
ΔWR
g
WR
R
Through
Input
Drop
Figure 3.1: Schematic of an MRR with an integrated contra-directional coupler. c 2019 IEEE.
to those described in [1] and [88]. To achieve an FSR-free response, the contraDC should suppress all MRR modes except for the one at, or near, the contra-DC
central wavelength. This requires that the spacing between the first nulls of the
contra-DC drop-port response, ∆λnull , where no light is coupled to the resonator,
is equal to twice the FSR of the MRR (2FSRring = ∆λnull ). Full suppression of
the amplitude responses at all other undesired resonant wavelengths occurs if this
condition is met.
In our bent contra-DC design and modelling, we make an approximation and
assume straight waveguides since the radius of curvature of the waveguides in our
MRR is relatively large. Assuming 220 nm thick strip waveguides (surrounded
by silicon dioxide), based on the phase match condition given by Equation 2.1,
to set λ0 of the contra-DC close to 1550 nm, the bus grating waveguide, WB , and
ring grating waveguide, WR , were 450 nm and 550 nm, respectively, and the grating
period, Λ, was 318 nm. A graphical solution to the phase match condition is shown
in Figure 3.2. Based on Equation 2.12, by setting R to 34 µm, and choosing a
κ0 value of 6900 m-1 , 2FSRring = ∆λnull is achieved for N = 335. As will be
discussed in the following sections of this paper, the desired coupling strength of
the contra-DC is achieved by controlling the corrugation depths of the bus and ring
41
waveguides (∆WB and ∆WR , respectively) and the gap width (g) between the two
grating waveguides. The total device response is modeled analytically based on the
transfer functions presented in Section 2.3 (where, here, the drop-port MZI-coupler
is replaced with a simple directional coupler). The power coupling coefficients
and waveguide effective indices were simulated in FDTD Solutions and MODE
Solutions, both by Lumerical Inc. In our simulations, we assumed a waveguide
propagation loss of 3 dB/cm and that the power coupling coefficient of the dropport coupler was 29%. The simulated drop-port response of the MRR is shown in
Figure 3.3.
𝜆
2Λ
𝒏𝒆𝒇𝒇,𝟒𝟓𝟎 + 𝒏𝒆𝒇𝒇,𝟓𝟓𝟎
𝟐
𝒏𝒆𝒇𝒇,𝟒𝟐𝟗 + 𝒏𝒆𝒇𝒇,𝟓𝟐𝟖
𝟐
Figure 3.2: Graphical solutions for the phase match condition of a contra-DC
with Λ = 318 nm and 1) WB = 450 nm and WR = 550 nm (blue line) and
2) WB = 429 nm and WR = 528 nm (red line).
As can be seen in Figure 3.3, the MRR side modes directly adjacent to the
operating wavelength are completely suppressed. The first contra-DC nulls align
with the adjacent MRR side modes and no light is coupled to the resonator cavity
at the corresponding wavelengths (“null-coupling”), demonstrating an effectively
infinite, adjacent SMSR. Here, we define the adjacent SMSR as the minimum dif42
0
-5
Transmission (dB)
-10
-15
-20
-25
-30
-35
-40
-45
-50
1530
1535
1540
1545
1550
1555
1560
1565
Wavelength (nm)
Figure 3.3: Simulated spectral response of our MRR drop-port (blue). Dotted
grey lines show the locations of the suppressed MRR sides modes (adjacent to the operating wavelength), due to null-coupling to the cavity
via the contra-DC (red). c 2019 IEEE.
ference (in dB) between the transmission of the MRR at the operating wavelength
and its transmission at the locations of either of the directly adjacent MRR modes.
The device has a predicted insertion loss of 0.4 dB and an operating 3-dB BW
of 46 GHz. Due to dispersion, at wavelengths further from λ0 , at non-adjacent
side modes, the contra-DC nulls and MRR side modes are not perfectly aligned,
resulting in minor peaks in the drop-port response. Nevertheless, the sinc-functionlike response of the contra-DC ensures that there is still significant suppression of
these non-adjacent side modes, as the amount of light coupled to the cavity at the
non-adjacent side mode wavelengths is small as compared to that at the central
wavelength.
43
3.2
Effect of Lithography on Filter Performance
As previously discussed, the suppression of the MRR side modes is heavily dependent on the κ0 of the contra-DC. By varying the corrugation depths and the gap
between the waveguides, κ0 can be controlled. Figure 3.4a shows a GDS image of
our contra-DC. The device has rectangular corrugations with ∆WB equal to 30 nm,
∆WR equal to 40 nm, and an average gap equal to 280 nm, which yields a κ0 value
close to our design target of 6,900 m-1 . The full length of the contra-DC was simulated in FDTD Solutions, and the κ0 was determined using equation 2.10. Due
to the small feature sizes and proximity of the grating waveguides, the contra-DC
is particularly prone to fabrication variations, including lithographic-effects [77],
[122]. Lithography affects the κ0 and central wavelength of the contra-DC, leading
to discrepancies between as-designed and as-fabricated MRR performance, mainly
regarding the operating wavelength, adjacent SMSRs and the 3-dB bandwidth.
We applied a computational lithography smoothing prediction model, developed for 193 nm DUV lithography [77], to demonstrate the influence on MRR
performance when lithography effects are not considered during the device design flow and layout. While fabricated devices are often sensitive to other fabrication imperfections such as wafer thickness and waveguide width variability [122],
[139], here, we focus solely on lithographic-effects. Figure 3.4b shows the result
of the lithography prediction model on the contra-DC in our MRR. Figure 3.4c, we
present a scanning electron microscope (SEM) image of a fabricated, bent contraDC test structure. Comparing the prediction-model and SEM, we can see that
the model accurately predicts the change in corrugation profile from a rectangular to a sinusoidal-like shape and that the inner corrugations are smoothed to a
greater extent than the outer corrugations. The change in corrugation shape is due
to smoothing, while the discrepancies between the smoothing of the inner and outer
corrugations is due to proximity effects [77]. As a result, the average widths of the
bus and ring waveguides are also reduced from 450 nm to 429 nm and from 550 nm
to 528 nm, respectively, as per Figure 3.4b.
In Figure 3.5, we present the measured drop-port spectrum of a contra-DC test
structure fabricated using 193-nm DUV lithography. This test structure shares the
same device parameters as our design, as mentioned above, however, the corruga-
44
ΔW = 30 nm
W2 = 450 nm
ΔW = 40 nm
Gap = 280 nm
W1 = 550 nm
(a)
W2 = 429 nm
ΔW = 18 nm
Gap = 325 nm
ΔW = 26 nm
W1 = 528 nm
(b)
200 nm
(c)
Figure 3.4: (a) Mask layout of a section of our as-designed contra-DC. (b)
The predicted outcome of our lithography model. Smoothing and
proximity effects can be clearly seen on the corrugations. (c) A
scanning electron microscope image of our as-fabricated contra-DC.
c 2019 IEEE.
45
tion widths were slightly larger (∆WB equaled 40 nm and ∆WR equaled 50 nm). The
lithography has two main effects on fabricated contra-DC performance. Firstly, the
smoothing reduces the average waveguide widths of the contra-DC waveguides.
This results in a change in the phase-match condition and, hence, a shift in the
contra-DC central wavelength from the as-designed value. As seen in Figure 3.5,
the central wavelength of the as-fabricated contra-DC is 1534 nm, as compared
to our as-designed value of 1548 nm. Assuming that the fabricated waveguides
were 220 nm thick, this result is consistent with the phase-match conditions for
a contra-DC with WB = 429 nm and WR = 528 nm, as plotted in Figure 3.2. It
should also be noted that the central wavelength deviation is typically also affected
by wafer thickness variations [114], [140]. Here, based on the phase-match condition for the prediction-model device, we present a test structure from a die that
we believe is closest to having a 220 nm silicon thickness. Secondly, lithographiceffects reduce the coupling strength, κ0 , of as-fabricated contra-DCs (as compared
to the as-designed values). The smoothing and proximity effects reduce the corrugation depths and alters the profiles of the gratings and increases the average gap
between the two waveguides, resulting in a decrease in coupling between the forward and backward propagating modes of the two-waveguide system [72, 115]. To
demonstrate this effect on the as-fabricated κ0 , we simulate the as-designed and
prediction-model contra-DC test structures in FDTD and compare their drop port
responses to the response of the measured device. The drop-port spectrum results
are shown Figure 3.5, with the simulated responses detuned to the central wavelength of the fabricated test structure. After detuning, the simulated response of
the prediction-model device shows good agreement with the measured test structure (1534 nm). We determine κ0 from the simulated responses, and observe that
the expected κ0 value, based on the ideal structure of 9,350 m-1 , is reduced to approximately 1,900 m-1 after applying the prediction-model. If lithographic-effects
were not taken into account during design flow, the reduced κ0 of the contra-DC
would have detrimental effects on the overall performance of the fabricated MRR
with integrated contra-DCs.
For our MRR design, after applying the lithography model, the κ0 of the contraDC is reduced to approximately 1,600 m-1 as compared to the design value of
6,900 m-1 . The average widths of the bus and ring waveguides are also reduced
46
0
-5
Transmission (dB)
-10
-15
-20
-25
-30
-35
-40
Test structure (measured)
Litho-model (FDTD)
"As-designed" (FDTD)
-45
-50
-55
1531
1532
1533
1534
1535
1536
1537
Wavelength (nm)
Figure 3.5: Drop-port response of an as-fabricated contra-DC test structure
(red), simulated prediction-model (black) and simulated as-designed
(blue) contra-DC test structures (detuned to the central wavelength
of the drop-port response of the as-fabricated test structure, 1534
nm). Lithographic-effects reduce the coupling strength, κ0 , from the
simulated/expected value of 9,350 m-1 to approximately 1,900 m-1 .
c 2019 IEEE.
from 450 nm to 429 nm and from 550 nm to 528 nm, respectively. In Figure 3.6a,
we plot the simulated MRR drop-port response with the adjusted κ0 value and
effective and group indices of the waveguides. The operating wavelength of the
MRR is now 1534 nm due to the new phase-match condition for the contra-DC,
and the maximum suppression condition is no longer met due to the change in κ0
and group index of the ring waveguide. In our simulation, we suppress the adjacent
MRR side mode to the left of the operating wavelength by aligning to the first
contra-DC null to the left of the central wavelength. This results in the adjacent side
mode to the right of the operating wavelength not being fully suppressed as ∆λnull
is less than 2FSRring . With a change in the group index of the ring waveguide,
the wavelengths of the MRR resonant modes are also different. However, we still
define the adjacent SMSR for a channel spacing to be equal to the FSR of our target
47
design. As seen in Figure 3.6b, as compared to our target design, the adjacent
SMSR is now 26 dB due to the reduced κ0 and the change in the cavity resonance
condition.
Figure 3.6: a) Simulated spectral drop-port response after applying the
lithography model to the contra-DC test structure (solid). Simulated
as-designed response detuned to the central wavelength of the postlithography response (dashed), shown for reference. The MRR side
mode adjacent to the right of the operating wavelength is not fully suppressed due to a reduced κ0 and the change in the cavity resonance condition. The insertion loss of the MRR increases and the 3-dB bandwidth of the MRR decreases. b) Zoom-in of the un-suppressed adjacent
MRR mode. The adjacent channel SMSR is reduced to 26 dB since
∆λnull < 2FSRring . c 2019 IEEE.
The operating bandwidth also decreases, from 41 GHz to 21 GHz. This is
because the reduction in κ0 reduces the effective power coupling coefficient of the
coupler and the amount of light coupled into and out of the ring. The insertion loss
of the device also increased by 5.5 dB. Clearly, the effects of lithography result
in large discrepancies between as-fabricated and as-designed performance MRR
performance. While the operating wavelength of the MRR can be adjusted using
separate thermal tuners placed over the contra-DC and the ring waveguide, the κ0
and ∆λnull of the contra-DC cannot be adjusted post-fabrication. In the following
section, we demonstrate how our lithography model can be used to compensate for
lithographic-effects during device design flow.
48
3.3
Compensating for Lithographic-Effects
As part of the design flow, we compensate for the effects of DUV lithography by
utilizing a lithography model [77] that predicts the shapes of specific, as-fabricated
device features. The lithography model is built using a set of known parameters for
the intended foundry process and using calibration measurements obtained from a
test pattern [77]. The test pattern was fabricated using the intended DUV process.
Figure 3.4a shows the model’s predicted, as-fabricated outcome of our as-designed
device (Figure 3.4b), as compared to the actual fabricated outcome, as seen in the
SEM image (Figure 3.4c). We see good agreement between the predicted device
shapes generated by our model and the fabricated device.
ΔW = 50 nm
W2 = 450 nm
ΔW = 60 nm
Gap = 228 nm
W1 = 550 nm
(a)
ΔW = 30 nm
W2 = 429 nm
Gap = 245 nm
ΔW = 40 nm
W1 = 528 nm
(b)
Figure 3.7: a) Mask layout of a section of our re-designed contra-DC. (b) The
predicted outcome of our lithography model. The κ0 of the predictionmodel of the re-designed device matches that of the as-designed contraDC (see Figure 3.4a). c 2019 IEEE.
49
Figure 3.8: Simulated drop-port spectra of the as-design contra-DC (red)
and lithography prediction-model of the re-designed device (blue).
c 2019 IEEE.
To compensate for the lithographic-effects that reduce the κ0 of our contraDCs, we propose a design approach using the prediction model, similar to that
presented in [77]. In our approach we aim to produce a re-designed contra-DC
in which the κ0 of the prediction-model device matches that of our as-designed
contra-DC. This is done by re-designing the contra-DC with a narrower gap and
larger corrugations depths than intended (to compensate for smoothing and proximity effects), then by applying the lithography model, and, finally, by running FDTD
simulations of the entire contra-DC to confirm that the prediction-model performance of the re-designed contra-DC matches the target contra-DC performance.
This approach was applied to our as-designed contra-DC (see Figure 3.4a). The
re-designed contra-DC with adjusted design parameters is shown in Figure 3.7a,
with the lithography prediction-model of this re-designed device shown in Figure 3.7b. This set of new design parameters was obtained by iteratively simulating variations of post-lithography devices until we converged on a design that
yielded our target κ0 value. The κ0 of the prediction-model of the re-designed
contra-DC (7,250 m-1 ) is close to our intended design value (6,900 m-1 ). The sim50
ulated drop-port spectra of the as-designed contra-DC and the prediction model
of the re-designed contra-DC show good agreement, as shown in Figure 3.8. The
simulated drop-port spectrum of the as-designed device is detuned to the central
wavelength of the prediction-model device (1534 nm). Our re-design methodology
currently does not compensate for the central wavelength variations between the
as-designed and as-fabricated device, which can be compensated for using thermal
tuners. Here, we only compensate for the reduction in κ0 by varying the contra-DC
gap and corrugation depths. Future iterations of the re-design approach will need
to compensate for the variations in average waveguide widths after lithography so
that the as-fabricated, re-designed contra-DC shares the same central wavelength
and κ0 of the as-designed device.
3.4
Summary
In this chapter, we demonstrated how DUV lithography affects the performance of
grating-based SOI devices. Smoothing and proximity effects, due to lithography,
result in differences between the shapes of features on the mask layout and on the
fabricated structures. As a result, if these effects are not taken into account during
design flow and layout, discrepancies arise between the “as-designed” and “asfabricated” device performance. Here, we focused on an MRR with an integrated
contra-DC. Using a computational lithography model, we predicted and simulated
the device performance and showed how lithographic-effects adversely affect the
performance of the MRR as regards the device BW, IL, and adjacent SMSR. We
also verified the computational lithography model used in our simulations by using
SEM images and fabricated test structures and we have concluded that it is possible to effectively account for lithographic-effects in the device design flow using
the lithography model. By doing so, one can significantly improve the agreement
between the performance of as-designed and as-fabricated devices during future
device and system design flow.
In the following chapter, we experimentally demonstrate how lithography smoothing and proximity effects affected the performance of a fabricated MRR-based
modulator with an integrated contra-DC, where lithography effects were not compensated for during device design flow and layout.
51
Chapter 4
Free-Spectral-Range-Free,
Microring-Based Coupling
Modulator with Integrated
Contra-Directional Couplers
MRR-based modulators have been demonstrated as integral components for nextgeneration optical interconnects and WDM applications. However, an inherent
drawback of using MRR modulators in WDM systems is their FSR. The FSR
limits the aggregate data rate of the system, as it restrains the number of channels that can be selectively modulated within a particular band. In this chapter,
we experimentally demonstrate an FSR-free, MRR-based, coupling modulator that
integrates a bent, grating-based contra-DC into a microring cavity to achieve an
FSR-free response at its through-port. Our modulator suppresses the amplitude response at all but one resonant, operating mode (hence, has an FSR-free response).
In our modulator, coupling modulation is used and is achieved by modulating a
relatively short, 210 µm long, p-n junction phase-shifter in a two-point coupler
(which forms the drop-port coupler of the MRR). We demonstrate open eyes at 2.5
Gbps and discuss how the effects of DUV lithography on the contra-DC limited the
electro-optic bandwidth of the fabricated modulator to 2.6 GHz. In this chapter,
52
we also cover details of the device design and theory and the small and large signal
characterization of the device, including an analysis of the effects of lithography
on the “as-fabricated” device performance. We also discuss how to significantly
improve the electro-optic bandwidth in future implementations by accounting for
these lithographic effects in the device design flow and layout.
4.1
Device Design
The modulator consists of an MZI-assisted MRR, with a bent contra-DC integrated
in the through-port coupling region of the cavity, in order to achieve the FSR-free
through-port response, and a two-point, or MZI-coupler, integrated into the dropport coupling region to enable optical amplitude modulation via coupling modulation. A schematic of the modulator is shown in Figure 4.1. To achieve the FSR-free
through-port response, the spacing between the nulls of the contra-DC drop-port
response, ∆λnull (see Equation 4.1) should be equal to twice the FSR of the microring cavity (i.e., 2FSRring = ∆λnull ). When the “null coupling” wavelengths of
the contra-DC drop-port response are aligned with the resonant wavelengths of the
cavity, no light is coupled to the cavity. Hence, the resonance modes of the cavity
at such wavelengths will be suppressed and the device will have a single operating mode at, or near, the contra-DC central wavelength, where sufficient light is
coupled to the cavity.
The bent contra-DC was designed for strip waveguides with a silicon thickness
of 220 nm and an oxide cladding. The cavity and contra-DC parameters used here
were the same as those used in [88]. The average widths of the bus grating waveguide, WB , and ring grating waveguide, WR , were 450 nm and 550 nm, respectively.
We set the radius of curvature of the ring grating waveguide, R, to 34 µm and the
grating period of the contra-DC, Λ, to 318 nm to place the operating wavelength
of the modulator close to 1550 nm. In order to satisfy 2FSRring = ∆λnull , the overall length of the contra-DC and κ0 , the distributed field coupling coefficient per
unit length of the contra-DC, were then determined. With the total length of the
microring cavity equal to 213.62 µm (2πR), a contra-DC with κ0 = 6,900 m-1 and
N = 335 corrugations satisfied 2FSRring = ∆λnull . κ0 of the contra-DC is controlled
by varying the corrugation depths of the bus and ring waveguides (∆WB and ∆WR ,
53
Heater
pn-junction
Figure 4.1: Schematic of the modulator. Inset shows the design parameters
of the bent contra-DC.
respectively) and the average gap width, g, between the two waveguides. In our
design, ∆WB and ∆WR , were 30 nm and 40 nm, respectively, and g was 280 nm. A
TiN thermal heater was placed above the contra-DC (not shown in the schematic)
to align the contra-DC and ring responses, and another heater was placed across the
section of the ring not covered by the contra-DC to tune the operating wavelength
of the device.
The optical signal modulation in our modulator was achieved via coupling
modulation. In our design, we use an MZI-coupler in the drop-port coupling region of the MRR (see Figure 4.1), where, by applying a phase shift to the lower
MZI-coupler arm, or “modulation-arm,” results in both a shift in the resonance
wavelength of the MRR and a change in the through-port transmission amplitude
[127, 141]. It should be noted that using a single-end electrical drive signal in the
modulation-arm results in both a shift in the resonant wavelength of the MRR and
a change in the through-port transmission amplitude [127, 141]. This is in contrast
to ring-based coupling modulators demonstrated in the literature that use push-pull
54
drive signals. When using a push-pull drive configuration, there is no shift in the
resonant wavelength of the MRR. As a result, MRR modulators have been demonstrated with optical modulation rates that exceed the conventional cavity linewidth
limitation as the bandwidth of the modulator is not limited by the cavity photon
lifetime [108, 109].
The modulation-arm shown has two p-n junction segments embedded in 500 nm
wide rib waveguides, for optical modulation, each with lengths equal to 210 µm.
Four 5 µm long linear tapers are used to transition to and from 550 nm strip waveguides segments to the 500 nm rib waveguide segments (see Figure 4.1a). The total
length of the modulation-arm is 460 µm. To form the junctions in the rib waveguides, lightly doped p and n levels with implant densities of 5 x 1017 cm-3 and
3 x 1017 cm-3 , respectively, are used. To reduce the series resistance of the junction, intermediate p+ and n+ doped levels, with densities of 2 x 1018 cm-3 and
3 x 1018 cm-3 , respectively, are used and to create ohmic contacts, highly doped
p++ and n++ levels, with densities of 1 x 1020 cm-3 , are used. A cross section of a
pn diode segment, with dimensions for each doping layer, is shown in Figure 4.2.
For the directional couplers in the MZI-coupler, the coupling length and the gap
for each are 10 µm and 200 nm, respectively. A 400 µm long, 2 µm wide TiN
heater is also placed over the modulation-arm in order to induce the static phase
shift required to optimize the extinction ratio and to set the operating point of the
modulator.
0.5 μm
P
P++
N
P+
0.80 μm
N+
0.40 μm
0.40 μm
N++
0.80 μm
Figure 4.2: Cross-section of the p-n junction segment integrated in the
modulation-arm (not shown to scale).
55
4.2
DUV Lithography
The modulator was designed to be fabricated using a 193-nm DUV lithography
process. However, photonic structures, like gratings, fabricated using DUV lithography processes are particularly sensitive to lithographic-effects such as smoothing and proximity effects [77, 114, 122, 138]. As a result, the κ0 s and central
wavelengths of fabricated devices deviate from the “as-designed” values. These
deviations would negatively impact the performances of the fabricated modulators, affecting the fabricated ∆λnull s and changing the amount of power coupled to
the cavity via the contra-DC (|kc |2 ). These effects are realized by considering the
equations for ∆λnull and |kc |2 , given by [88, 116],
∆λnull
2λ02
=
π[ng,R (λ0 ) + ng,B (λ0 )]
r
π
κ02 + ( )2
Lc
(4.1)
and
|kc |2 = |
− jκ0 sinh(sLc )
s cosh(sLc ) +
j ∆β
2
sinh(sLc )
|2 ,
(4.2)
q
2
respectively, where λ0 is the contra-DC central wavelength, s = κ02 − ∆β4 , and
∆β = βR +βB − 2π
Λ . Here, βB and ng,B and βR and ng,R are the propagation constants
and group indices of the bus and ring waveguides, respectively. From Equation 4.1
and 2FSRring = ∆λnull , changing κ0 from its optimal value reduces the suppression of the adjacent and non-adjacent MRR side modes, while from Equation 4.2,
changing κ0 alters the amount of coupling to the cavity at the through-port, which
changes the cavity linewidth of the modulator. Ideally, lithography models, calibrated to their specific process, would be provided by the foundry to enable the
designer to account for lithography effects during device design flow and layout,
but access to such models were not available at the time of our design. However,
from SEM images of other grating-based devices demonstrated in the literature, the
most evident effect of DUV lithography tends to be smoothing, where the rectangular corrugation profiles of the devices turn into sinusoidal-like profiles, reducing
the effective amplitudes of the corrugations. Based on this observation, and in the
absence of such lithography models, at the time of our design we made the assump-
56
tion that the dominant effect of the lithography on the fabricated device would be
smoothing of the corrugation profile, and, hence, could estimate the reduction in κ0
due to smoothing based on coupled-mode theory [115]. From coupled-mode theory, for a sinusoidal effective index variation, the coupling coefficient is reduced by
a factor of π/4 (as compared to a rectangular variation with the same corrugation
depths) [142]. To compensate for the lithography smoothing, in our design, we
adjusted the corrugation depths of our contra-DC to increase the κ0 value by close
to a factor of 4/π. By increasing the corrugation depths of the rectangular grating profile to ∆WB equals 40 nm and ∆WR equals 50 nm, the simulated κ0 of the
contra-DC was 9,350 m-1 . Based on our coupled-mode theory approximation to
account for smoothing, we determined that, with these new ∆WB and ∆WR values,
the “as-fabricated”, lithography-smoothed κ0 should be close to the design value
of 6,900 m-1 (9,350 m-1 x π/4 = 7,340 m-1 ).
4.3
Device Simulation
The device was modelled based on the through-port transfer function of the MRR
given by Equation 2.19 in Section 2.3, where, here, φarm = φ pn + φheater to account
for the phase shifts induced by the modulation-arm p-n junction phase shifter (φ pn )
and thermal heater (φheater ). The waveguide effective indices were simulated in
MODE Solutions by Lumerical, Inc. The power coupling coefficient of the directional couplers of the modulator was 10%, based on FDTD simulations. In our
modelling, we also assume a waveguide propagation loss of 3 dB/cm for un-doped
waveguides and 7 dB/cm for doped waveguides. In these simulations, we assumed
a κ0 value of 5,420 m-1 (which is the original design value reduced by a factor
of 4/π). Figure 4.3a shows the through-port response of the modulator with the
initial static phase shift in the modulation-arm set to 0. An FSR-free response can
be seen across the C-band with a single resonance near 1550 nm. Based on the
simulated values, the calculated ∆λnull and FSRring of the device were approximately 5.44 nm and 2.72 nm, which come close to satisfying 2FSRring = ∆λnull .
Even though the κ0 used in the simulation was less than the design value, significant suppression of the adjacent MRR side modes is still observed. The alignment
of the ring response with the contra-DC response is shown in Figure 4.3a for ref-
57
erence. We then set the static phase shift to 4.25 radians, to operate the modulator
close to its linear operating regime. To demonstrate the static modulation depth of
the design, for Figure 4.3b, we simulate the through-port spectral responses at this
operating point with a range of reverse-bias voltages applied to the two p-n junction segments of the modulation-arm. In this simulation, we assumed a linearized
p-n junction model with a Vπ Lπ of 2.0 V-cm. As seen in Figure 4.3b, both the
resonant wavelength and extinction ratio increases with (reverse-bias) voltage. A
static modulation depth of 5 dB close to 1547.9 nm is achieved for a peak-to-peak
voltage swing (Vpp ) of 5 V. The cavity linewidth at the operating static phase shift
is approximately 20 GHz, sufficient for data rates of at least 20 Gbps.
a)
b)
Figure 4.3: a) Theoretical through-port response of the modulator with the
static phase of the modulation-arm set to 0. An FSR-free response is
observed across the C-band with a single resonance mode located near
1550 nm. The contra-DC drop-port response (dotted-red) and locations
of the suppressed resonant wavelengths are shown for reference (dottedblack). b) Through-port response of the modulator for various reverse
bias voltages applied to the modulation-arm p-n junction with the static
phase shift set to 4.25 radians.
4.4
Experimental Results
In this section, we present experimental results for the fabricated device. The device was fabricated via a Multi-Project Wafer (MPW) shuttle run using 193-nm
58
DUV lithography. Figure 4.4 shows a micrograph of the fabricated modulator. The
pads on the left were used for DC tuning the modulator and the pads on the right
were used for applying the RF signal to the modulation-arm. Not shown in the
figure are the fiber grating couplers (GCs) used for the optical input and output.
We first present the DC characterization of the device, followed by the small and
large signal characterization of the modulator. As will be demonstrated, the effect
of lithography smoothing and proximity effects were underestimated during device design flow, resulting in the fabricated modulator having a small EOBW and
non-fully-suppressed resonance modes in through-port response.
Modulator
G
GND
S
Tunercontra
Tunerring
Contra-DC test
structure
TunerMZI
150 μm
Figure 4.4: Micrograph of the fabricated modulator showing DC (left-side)
and RF (right-side) signal pads. The contra-DC test structure is also
shown, located close to the modulator.
4.4.1
DC Device Characterization
To perform the DC characterization of the modulator, first the contra-DC thermal
heater was used to align the contra-DC response to that of the ring. The ring heater
was then used to set the operating wavelength of the modulator, while an additional
voltage was applied to the contra-DC heater to track the resulting wavelength shift.
Once the operating wavelength was set, the modulation-arm heater was used to
tune the drop-port coupling coefficient and to set the operating point of the modula59
tor. Lastly, the cavity heaters were adjusted again to compensate for the additional
wavelength shift that accompanied the tuning of the modulation-arm. Figure 4.5a
shows the through-port response of the modulator with the modulation-arm tuned
close to critical coupling (here, VMZI = 9.10V). An FSR-free through-port response
is observed across the 60 nm wavelength range, with a single major resonance
mode visible near 1530 nm. The spectral responses shown were calibrated to remove the effects of the input and output GCs. While small in magnitude, the minor
notches seen in the spectrum are non-fully-suppressed resonance modes and are
a consequence of lithography effects on the fabricated device, as will be further
discussed in Section 4.4.3. Here, the contra-DC and ring responses were aligned
so that the right adjacent resonance mode was completely suppressed.
The measured cavity linewidth of the modulator near critical coupling was
3.11 GHz, which was significantly less than the simulated value. The reduced
cavity linewidth was also a consequence of the effects of DUV lithography on the
fabricated contra-DC’s κ0 value. To determine the fabricated κ0 value, we fit the
measured through-port response to the analytic equation for the modulator. From
the fit, the κ0 obtained was 1,700 m-1 , which was considerably less than the design value of 6,900 m-1 . The κ0 obtained from the fit agreed well with the value
extracted from the on-chip bent contra-DC test structure that was measured. The
test structure was located close to the modulator (see Figure 4.4) and the κ0 value
was extracted using the method presented in [123]. From the fit, we also obtained
the waveguide loss (2 dB/cm) and power coupling coefficient of the directional
couplers, |k1 |2 , (5.8 %), and used these parameters to simulate the through-port
response of the fabricated device. The simulated response, shown in Figure 4.5a,
shows good agreement with the measured response. A zoom-in of the measured
through-port response, and simulated fit, near the operating wavelength is shown
in Figure 4.5b. The reduced cavity linewidth (and, in turn, the increased loaded
Q-factor of the device), as compared to the theoretical design, can be explained
by the reduction in the power that was coupled the to the cavity via the fabricated
contra-DC. With κ0 equal to 1,700 m-1 , the maximum power coupling coefficient
of the contra-DC (at the resonant wavelength) was reduced as compared to the design/expected value. Here, we calculate the cavity linewidth and loaded Q-factor
of a critically-coupled, add-drop, ring resonator (using the equations presented in
60
a)
b)
3.11 GHz
c)
Figure 4.5: a) Measured through-port spectral response, with the modulationarm tuned close to critical coupling, overlayed with the theoretical response generated using device parameters obtained by curve-fitting the
measured response to analytical equations. b) Zoom-in on the operating
resonance mode. c) Analytical cavity linewidth and Q-factor of an adddrop ring resonator at critical coupling, as a function of κ0 , assuming a
contra-DC through-port coupler. The calculated loaded Q-factor factor
(63,000) and cavity linewidth (3.11 GHz) closely match the measured
values.
[124]) as functions of κ0 , using the parameters obtained from the fit and by assuming the through-port power coupling coefficient was given by the maximum
of |kc |2 . As shown in Figure 4.5c, the calculated values for a contra-DC with κ0
equal to 1,700 m-1 , closely match the measured cavity linewidth (3.11 GHz) and
61
Q-factor (63,000). The increase in Q-factor limited the maximum achievable data
rate of the fabricated modulator, due to the cavity photon lifetime limit [143]. This
is demonstrated in the high-speed characterization of the device.
a)
b)
c)
Figure 4.6: a) ER of the modulator as functions of voltage applied to the
modulation-arm heater. b) Measured through-port spectra for various reverse-bias voltages applied to a p-n junction segment in the
modulation-arm. c) Static modulation depth as functions of wavelength
for a bias voltage of -2 V and Vpp swings of 2 V and 4 V. Dotted line
shows the operating wavelength (1529.56 nm) where the static modulation depths are 3.75 dB and 6 dB for 2 Vpp and 4 Vpp , respectively.
Figure 4.6a shows the extinction ratio (ER) of the modulator as a function of
voltage applied to the modulation-arm heater, with critical coupling being achieved
at around 9.40 V. Figure 4.6b shows the through-port response of the modulator at
62
the operating wavelength for various reverse bias voltages applied to one of the p-n
junction segments of the modulation-arm. The static ER of the modulator was set
to 25 dB, using the modulation-arm thermal tuner, before applying a voltage to the
p-n junction. The Vπ Lπ of the junction was measured to be 2.64 V-cm using the
on-chip test structures. In Figure 4.6c, we plot the static modulation depth of the
modulator as functions of wavelength for a bias voltage of -2 V and Vpp swings
of 2 V and 4 V. We show that large extinction ratios are still achievable for small
phase shifts induced by the p-n junction. This is because in high-Q resonators,
like ours, the intracavity power is large compared to the input signal. Thus, very
small changes in the coupling coefficient allows for a large change in the modulated optical signal coupled out of the cavity [144], while the rest of the power
is recirculated. Larger modulation depths are achievable, closer to resonance due
to the large change in slope of the through-port transmission, however, at the expense of higher insertion losses and slower data rates due to reduced modulation
bandwidths.
4.4.2
High-Speed Characterization and Testing
To characterize the high-speed performance, we performed small-signal measurements of the modulators EOBW. A block diagram of the experimental setup up
used for the characterization is shown in Figure 4.7a. The EOBW was measured
using an Agilent E8361A 67 GHz vector network analyzer (VNA) and a 40 GHz
GS probe. The signal from port 1 of the VNA was passed through to the device
via a 40 GHz bias tee, which set the DC bias of the modulation-arm. Light from
a tunable laser source (TLS) was input to the device. The modulated optical signal from the output of the modulator was passed through an erbium doped fiber
amplifier (EDFA) to compensate for losses due to the on-chip input and output
GCs. A bandpass optical tunable filter (BPF) was then used to filter out most of
the noise caused by amplified spontaneous emission in the EDFA. An HP 11982A
15 GHz lightwave converter was used to convert the optical signal at the output
of the BPF to an electrical signal before entering port 2 of the VNA. Figure 4.8a
shows the measured S21 of the modulator for a bias voltage of -2 V at two operating wavelengths detuned from resonance (the measured S21 was normalized to
63
the value at 10 MHz). The modulation response for a 1.0 GHz detuning from resonance (blue) has an EOBW bandwidth of 2.6 GHz, which is similar to the cavity
linewidth and confirms that the modulator was indeed limited by the reduced cavity
linewidth due to lithography effects. We also show the response of the modulator
further detuned from resonance, where a peak occurs in the modulation bandwidth
response, extending the EOBW bandwidth to 3.9 GHz. This peak occurs due to intracavity dynamics [108, 143]. While operating at such wavelengths can improve
the bandwidth of the modulator, modulation depths at those wavelengths, i.e., further detuned from resonance, are insufficient for error-free data transmission (see
Figure 4.6c).
a)
VNA
Receiver
DUT
EDFA
BPF
TLS
b)
PPG
DCA + Receiver Plug-in
DUT
EDFA
BPF
TLS
Figure 4.7: Block diagrams of the experimental setups used a) to measure the
modulator EOBW and b) to generate eye-diagrams.
Figure 4.7b shows the block diagram of the experimental setup used to perform
the large signal characterization of the modulator. A pulse pattern generator (PPG)
64
a)
b)
Figure 4.8: a) Measured EOBW of the modulator. The EOBW for a 1.0 GHz
detuning from resonance was 2.6 GHz. b) Optical eye diagram at the
modulator through-port for a 2.488 Gbps, 2 Vpp drive signal.
was used to generate a 2.488 Gbps, 231 -1 pseudo-random binary sequence (PRBS)
with a Vpp of 2 V. The pattern was passed through the bias tee (used to bias the
modulator at -2 V and to combine the AC electrical signal) before being passed to
the modulator via an unterminated GS probe. The modulated optical signal, from
the output of the modulator, was then passed through the EDFA and BPF. The
filtered RF data was then passed into an Agilent 86100A digital communications
analyzer (DCA) mainframe with a 20 GHz HP 83485A optical/electrical plug-in.
The TLS output was detuned from resonance by 0.65 GHz, after setting the resonance wavelength and static operating point using the cavity and modulation-arm
thermal heaters. Figure 4.8b shows the measured eye diagram. Here, we demonstrate open eyes at a baud rate of 2.488 Gbps with an ER of 3.5 dB. The ER of the
modulator could have been improved by also applying the electrical signal across
a second p-n junction segment in the modulation-arm, however, here we show that
a significant eye is achievable due to the high loaded-Q factor of the fabricated
device. Eye-diagrams with larger ERs were possible at shorter wavelengths (see
Figure 4.6a) using a single 210 µm segment (albeit, at a lower baud rate), however,
the EDFA limited the “zero” level of the optical signal, thus limiting the measurable ER of the DCA. As will be discussed, in order to improve the bandwidth of
the modulator, future iterations of the design will need to compensate for lithog65
raphy effects during device design flow and layout by utilizing properly calibrated
lithography models. For higher baud rates, these designs will also require the use
of longer p-n junction segments to achieve the same ER, for the same p-n junction
design, due to the decrease in loaded Q-factor (i.e., the increase in bandwidth). The
drive voltage will depend on the Vπ Lπ of the modulator, which could be improved
by using different junction designs with higher modulation efficiencies such as interleaved [98, 145] or U-junction [146] designs.
4.4.3
Adjacent and Non-Adjacent Resonance Suppression
While we have shown that our modulator has only a single major resonance mode,
and is FSR-free in principle, minor notches are visible in the through-port response
and are a consequence of lithography effects. These notches are the non-fullysuppressed resonance modes, where the contra-DC nulls and ring resonances were
not perfectly aligned. This was due to κ0 deviating from the design value and ∆λnull
(a function of κ0 ) not being exactly 2FSRring . The reduction in κ0 , from the design
value, was due to both lithography smoothing and proximity effects introduced
during device fabrication, which not only altered the shape of the grating-profile,
but also the corrugation depths, the average waveguide widths, and the average
gap between the two grating waveguides [77]. Lithography effects also explain the
shift in the operating wavelength of the tuned, fabricated device to 1530 nm from
the design value of 1550 nm. Accounting for lithography effects to achieve the
desired operating wavelength would also help minimize the power consumption of
the modulator heaters used to set the operating wavelength of the device.
In Figure 4.9, we plot the contra-DC response for our κ0 design value of
6,900 m-1 and the ring response of the cavity. The intersection of the two curves
(indicated by the blue circles in the figure) is the amount of coupling to the cavity
when the contra-DC nulls are optimally aligned to the resonance modes. While
the adjacent modes align directly with the contra-DC nulls (-55 dB coupling to
the ring), due to dispersion, at non-adjacent modes, the contra-DC nulls do not
align perfectly. However, the amount of coupling to the ring saturates at the nonadjacent modes because of the contra-DC’s sinc-like coupling response and the
coupling is reduced from -5 dB at the operating mode to, in the worst-case, -38 dB
66
at a non-adjacent resonance mode. With lithography effects compensated for, and
the optimal alignment achieved, the non-adjacent resonance modes will, clearly, be
highly suppressed.
0
Coupling to the cavity (dB)
-5
-10
-15
-20
-25
-30
-35
-40
-45
1510
1520
1530
1540
1550
1560
1570
1580
1590
Wavelength (nm)
Figure 4.9: Contra-DC response for our κ0 design value of 6,900 m-1 (solidred) and ring response of the cavity (dotted-black). The intersection
of the two curves (blue circles) is the amount of coupling to the cavity
when the contra-DC nulls are optimally aligned to the resonance modes.
The coupling to the cavity saturates at wavelengths far from the operating mode (less than -38 dB, shown by the shaded blue area).
When the contra-DC and ring responses cannot be perfectly aligned, like in our
fabricated modulator with κ0 equal to 1,700 m-1 , we show that the two suppressed
modes adjacent to the operating mode are likely to have the largest magnitudes due
to the sinc-like response of the contra-DC. In Figure 4.5a, we aligned the contraDC and ring responses to completely suppress the right adjacent resonance mode
and to show the worst-case adjacent suppressed mode depth (which in our case,
was located outside of the C-band). Because the left adjacent contra-DC null was
not exactly aligned to a resonance mode, and the contra-DC side lobe is large, here,
67
close to critical coupling, the left adjacent suppressed mode depth is the deepest
(but is still less than 1.75 dB). At non-adjacent resonance modes, due to the sinclike roll-off of the power coupled to the cavity, the suppressed mode depths are
very small as the resonator becomes severely under-coupled regardless of the dropport coupler coupling coefficient. As a result, even when the contra-DC nulls do
not align to non-adjacent resonance modes, the non-adjacent, non-fully-suppressed
resonance mode depths will be very shallow relative to the adjacent depths. The
depths of all non-adjacent, non-fully-suppressed modes were less than 0.80 dB.
While the suppressed mode depths are shallow, the effect of intermodulation
crosstalk [147] needs to be considered. In Figure 4.10a, we plot the measured mode
depth of the left adjacent, non-fully-suppressed mode as a function of p-n junction
bias around the operating point of the modulator. As can be seen in the figure, the
mode depth is less than 1.75 dB, with a worst-case static modulation depth of less
than 0.25 dB for the same 2 Vpp drive voltage used to generate our eye diagrams.
While, here, the worst case modulation depth was 0.25 dB for the left adjacent
mode (see Figure 4.10b), which we aligned outside the C-band, if the operating
resonance mode was aligned symmetrically between the two adjacent contra-DC
nulls, the modulation depth would have been less. Assuming that future modulator
designs can correctly compensate for lithography effects, virtually complete suppression of these adjacent resonance modes should be obtainable. However, the
non-adjacent resonance modes far from the operating wavelength may contribute
to the intermodulation crosstalk due to dispersion, as discussed above. Still, using the modulator parameters obtained from our curve fitting and test structures,
we demonstrate that the crosstalk here is small by simulating the static modulation
depth at the largest (and first observable within the C-band) non-adjacent, nonfully-suppressed mode at around 1554 nm (see Figure 4.5a). Here, with κ0 equal
to 1,700 m-1 , the static modulation depth at 1554 nm was less than 0.01 dB for a
2 Vpp swing, which was expected because of the severe undercoupling of the cavity
at this wavelength (see the discussion above). From this analysis, for our fabricated
modulator, as biased, we expect the crosstalk contribution to be less than 0.01 dB
from the adjacent or any non-adjacent resonance mode in the C-band.
Clearly, based on our analysis, in order to mitigate the channel crosstalk, lithography effects need be taken into account and compensated for during the device
68
a)
b)
~ 0.25 dB
Figure 4.10: a) Measured through-port spectra at the left adjacent resonance
mode for various reverse-bias voltages (with the right adjacent mode
suppressed). b) Static modulation depth as functions of wavelength for
a bias voltage of -2 V and a Vpp swing of 2 V.
design flow to ensure that the adjacent and non-adjacent resonances modes of asfabricated devices are effectively suppressed. Recently, after our modulator design was submitted for fabrication, a lithography model (for the DUV process that
we used) that predicts the shapes of specific, as-fabricated device features, was
demonstrated in the literature [77]. The lithography model was built using a set
of known parameters and calibration measurements obtained from test patterns
that were fabricated using the DUV process. We were able to apply the lithography model post priori and we compared the simulated response of our as-designed
contra-DC (with the lithography model applied) to the measured response of the
as-fabricated, on-chip test structure. Figure 4.11 shows good agreement between
the predicted device performance and the measured device performance. In future
iterations of the modulator design and layout, the lithography model can be applied
during the design flow to help ensure that the as-fabricated device performance will
match the as-design device performance. Examples of this design methodology are
demonstrated in both [2] and [77].
69
Contra-DC Response (dB)
0
Measured
Predicted
-10
-20
-30
-40
-50
-3
-2
-1
0
1
2
3
Wavelength detuning (nm)
Figure 4.11: Measured response of an as-fabricated contra-DC test structure
and predicted response of the as-designed contra-DC after applying
lithography models. The responses are detuned to the central wavelength of the as-fabricated test structure response (1530 nm).
4.5
Summary
In this chapter, we have experimentally demonstrated an FSR-free, MRR-based
modulator with open eyes at a data rate of 2.5 Gbps. The FSR-free response at
the through-port of the modulator was achieved by integrating a grating-assisted,
contra-DC into the microring cavity. The modulator was fabricated using 193-nm
DUV lithography, which affected the contra-DC performance due to lithography
smoothing and proximity effects. This resulted in a large discrepancy between the
as-designed and as-fabricated electro-optic bandwidth of the modulator, limiting
the data rate. Moreover, the lithographic effects introduced non-fully-suppressed
resonance modes in the through-port response. However, we showed that the effect of these non-fully-suppressed modes on channel crosstalk is not substantial
and could be mitigated if lithography models could be used to compensate for the
lithographic effects. Accounting for these lithographic effects will minimize discrepancies between as-designed and as-fabricated modulator performance and will
enable modulators that facilitate higher aggregate data rates in ring-based, singlebus, WDM transmitter architectures that are currently limited by the MRR’s FSRs.
70
Chapter 5
Summary, Conclusions, and
Suggestions for Future Work
5.1
Summary and Conclusions
In this thesis, we have demonstrated SOI, FSR-free, MRR-based filters and modulators that use contra-DCs integrated into the MRR cavity to achieve the FSR-free
responses. We have also analyzed the effects of DUV lithography on the performance of these devices. In Chapter 2, we demonstrated an FSR-free, microringbased filter, with a minimum SMSR (20.8 dB) which is greater the values presented
in previous demonstrations of FSR-free, MRR filters in the literature. Moreover,
we have shown that by integrating an MZI-coupler into to the drop-port region of
the microring cavity, independent control of the fabricated filter’s drop-port coupling coefficient could be achieved. As a result, we have demonstrated a reconfigurable filter bandwidth that can be tuned over a 35 GHz range from 25 GHz to
60 GHz. We have also shown that the device is truly FSR-free at the through-port,
as resonance-induced amplitude and phase responses are virtually non-existent at
the suppressed resonant modes of the MRR. While we have concluded that our
design has advantages over other wide-FSR filters presented in the literature, such
as quadruple Vernier resonators, further work needs to be done to reduce the filter
Ai , nAi , and SMSR values to meet commercials specifications for 100-GHz and
200-GHz spacing DWDM applications. Potential methods to improve the perfor71
mance of MRR-based filters with integrated contra-DCs will be discussed in the
following section. In Chapter 3, we have demonstrated how DUV lithography can
affect the performance of grating-based devices such as contra-DCs. Using lithography models developed for DUV processes, we have simulated and analyzed the
effects of lithography on the performance of an MRR with an integrated contra-DC.
We have shown that if lithography effects are not compensated for during device
design flow, large discrepancies result between the predicted “as-fabricated” and
“as-designed” device performance as regards the device bandwidth, insertion loss,
and adjacent SMSR. We have concluded that if lithography models can be used
to compensate for lithographic effects during device design flow and layout in order to design a contra-DCs in which the as-fabricated device spectral responses
match the expected as-designed spectral responses. Lastly, in Chapter 4, we have
demonstrated a novel, proof-of-concept, MRR-based modulator with an FSR-free
response at its through-port. Here, a contra-DC was integrated into a microring
cavity to achieve the FSR-free response and coupling modulation was used for the
optical signal modulation. We have obtained open eye diagrams at a data rate of
2.5 Gbps. The data rate of the modulator was limited by the small EOBW of the
modulator, which we have demonstrated was a consequence of the effects of DUV
lithography on the contra-DC. While we have demonstrated an FSR-free response
with shallow suppressed mode depths, the effects of the lithography induced, nonfully-suppressed resonances modes on potential channel modulation crosstalk have
also been discussed. We have concluded that if the effects of lithography were
properly compensated for during device design, higher EOBWs could be achieved
and the effect of modulation crosstalk can be minimized, enabling dense channel
spacing in MRR-based WDM transmitters. Future design considerations for the
modulator are discussed in the following section.
5.2
Suggestions for Future Work
In this thesis, while we have demonstrated MRR-based filters for WDM with no
FSR limitations, further work is required to reduce the SMSR of the filter in order
to meet specifications for commercial 100-GHz and 200-GHz spacing DWDM applications. By reducing the SMSR, commercial specifications for the Ai (< 25 dB)
72
Through
Through
Input
Input
…
…
…
…
Drop
Two-stage cascaded contra-DC
Figure 5.1: Schematic of the proposed filter; an FSR-free MRR filter cascaded with a two-stage, series-cascaded contra-DC.
and nAi (< 35 dB) of the filter can be met [148]. Here, we propose that by cascading an FSR-free MRR filter with an N-stage series-cascaded, apodized contraDC-based (SC-contra-DC) [64, 76], devices with larger SMSRs can be achieved.
A block diagram of the proposed device using a two-stage SC-contra-DC is shown
in Figure 5.1. In the proposed filter, by aligning the drop-port passband of the
SC-contra-DC with the operating mode of the MRR, the MRR response outside
of the SC-contra-DC passband will be attenuated by at least the SMSR of the SCcontra-DC. With the SC-contra-DC effectively “cleaning-up” the drop-port signal
of the MRR filter, devices with large Ai s and nAi s can be achieved. In our work, we
demonstrated an SMSR of approximately 21 dB and the work in [76] demonstrated
one- and two-stage filters with SMSRs greater than 20 dB and 40 dB, respectively.
As a result, if the SC-contra-DC passband is designed and aligned correctly, chan-
73
nel isolations greater than 40 dB should be achievable, which would meet commercial specifications. While in Figure 5.1 we show an MRR with a simple directional
coupler in the drop-port coupling region, a tunable MZI-coupler could be used
instead to enable bandwidth reconfigurability.
When designing SOI devices with grating-based components, like contra-DCs,
we have demonstrated that lithography models, calibrated to the specific fabrication process, need to be used during device design flow. As a result, our FSR-free
modulator should be redesigned in order to compensate for the lithography effects.
By accounting for these effects, the fabricated modulator should; 1) have minimal adjacent and non-adjacent non-fully-suppressed mode depths, minimizing the
contributions to the intermodulation crosstalk, 2) a higher data rate due to a cavity
linewidth and EOBWs that matches the desired designed performance metrics. As
previously mentioned, by increasing the cavity linewidth, a larger phase shift in
the MZI-coupler will be required to generate the same extinction ratios that were
demonstrated in this thesis. This will require a redesign of the p-n junction phase
shifters to achieve higher phase shift efficiencies in order to maintain low drive voltages with the higher bandwidth conditions. Moreover, further design optimization
can be done to reduce the insertion loss of the modulator. A full characterization
of the updated modulator should also performed, including measurements such as
bit error rate (BER) testing and further testing to determine the power penalty due
to crosstalk from any non-fully-suppressed resonance modes. Lastly, if large extinction ratios are achievable for OOK, the drive signals can be reconfigured to
demonstrate higher data rates via PAM-4 modulation.
74
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