Subwavelength and diffractive waveguide structures and their
applications in nanophotonics and sensing
P. Chebena, P. J. Bocka,b,c, J. H. Schmida, J. Lapointea, S. Janza, D.-X. Xua, R. Maa, A. Densmorea,
A. Delâgea, B. Lamontagnea, T. J. Hallc, R. Halird, I. Molina-Fernándezd and J.-M. Fédélie
a
Institute for Microstructural Sciences, National Research Council Canada, Ottawa, Canada
b
CRESS Space Instrumentation Laboratory, York University, Toronto, Canada
c
Centre for Research in Photonics, University of Ottawa, Ottawa, Canada
d
ETSI Telecomunicación, Universidad de Málaga, Málaga, Spain
e
CEA, LETI, Minatec, Grenoble, France
ABSTRACT
We review recent advances in subwavelength and diffractive structures in planar waveguides. First, we present a new
type of microphotonic waveguide, exploiting the subwavelength grating (SWG) effect. We demonstrate several
examples of subwavelength grating waveguides and components made of silicon, operating at telecom wavelengths. The
SWG technique allows for engineering refractive index of a waveguide core over a range as broad as 1.5–3.5 simply by
lithographic patterning using only two materials, e.g. Si and SiO 2. This circumvents an important limitation in integrated
optics, which is the fixed value of the refractive indices of the constituent materials in the absence of active tuning
mechanisms. A subwavelength grating fibre-chip microphotonic coupler is presented with a loss as small as 0.9 dB and
with minimal wavelength dependence over a broad wavelength range exceeding 200 nm. It is shown that the SWG
waveguides can be used to make efficient waveguide crossings with minimal loss and negligible crosstalk. We also
present a diffractive surface grating coupler with subwavelength nanostructure, that has been implemented in a Si-wire
evanescent field biological sensor. Furthermore, we discuss a new type of planar waveguide multiplexer with a SWG
engineered nanostructure, yielding an operation bandwidth exceeding 170 nm for a device size of only 160 m  100
m.
Keywords: diffraction grating, subwavelength grating, silicon-on-insulator waveguide, fiber-chip microphotonic
coupler, surface grating coupler and evanescent field sensor.
1. INTRODUCTION
Diffraction effects are suppressed for waves propagating in materials structured at the subwavelength scale.
Subwavelength periodic structures were first used in the late 19 th century by Hertz, when studying the properties of the
newly discovered radio waves with a fine grid of parallel metal wires used as a polarizer. It was not until the 1940s when
electromagnetic wave propagation in a medium structured at the subwavelength scale was first studied, for alternate
layers of a dielectric and a metal1. Although the subwavelength phenomenon has been known and exploited for many
years in free-space optics2,3 and recently also in plasmonics4, little has been reported on using subwavelength periodic
structures in dielectric optical waveguides5-8.
In integrated photonic circuits, the refractive index contrast is usually set by the choice of the material platform. For
example, for silicon photonic circuits the waveguide core and the cladding indices are given by the material constants of
silicon (nSi = 3.5) and silicon dioxide (nSiO2 = 1.44) and waveguide devices must be designed within the constraint of
these fixed values. It is known that periodic dielectric structures with a periodicity smaller than one half of the
wavelength do not diffract any light. Instead, such so-called subwavelength gratings (SWGs) act as homogeneous
effective media with spatially averaged refractive index9,10. We have recently demonstrated the first use of SWGs for
refractive index engineering in microphotonic waveguides, providing a powerful method for controlling the refractive
index of a waveguide core in any specific location of a photonic chip11-17. Importantly, our method only relies on
standard fabrication techniques and can be implemented without any modifications to the chip fabrication process flow.
The structure shown in Fig. 1a exemplifies refractive index engineering of a silicon photonic wire waveguide, as it is
further discussed in Section 2. By etching periodic gaps of a well defined width w and pitch  into a standard silicon
photonic wire an SWG waveguide is formed with an effective core index determined by the duty ratio w/15. Calculation
of the dispersion relation (Fig. 1b) of the segmented waveguide and comparison with the dispersion of an equivalent
photonic wire waveguide with the core refractive index of n = 2.65 confirms theoretically the concept of spatial
refractive index averaging. Experimentally, we have observed waveguiding in such SWG structures with low
propagation loss comparable to the photonic wire waveguides and with a low and nearly wavelength-independent group
index15. Although consistent with Bloch theory, it is fascinating to observe light propagating almost unperturbedly
through so many strong discontinuities.
Figure 1. a) Subwavelength grating waveguide composed of silicon segments on a silicon-on-insulator chip. b)
Dispersion diagram of a SWG waveguide consisting of 150 nm long Si segments separated by 150 nm long gaps
filled with SU-8 polymer (nSU-8 =1.577), for TE polarization. Lower cladding is silicon dioxide (nSiO2 = 1.444) and
upper cladding is SU-8. Dispersion diagram for an equivalent wire waveguide with a core refractive index of 2.65 is
shown as a reference.
Practical implementations of our SWG waveguides are described in Sections 3-6. In Section 3, we present a
subwavelength grating microphotonic fiber-chip coupler which works by gradual modification of the waveguide core
index leading to mode size transformation between a high-index photonic wire and the low-index optical fiber5,12.
Measured coupling loss is 0.9 dB for TE and 1.2 dB for TM polarizations. In Section 4, we discuss a waveguide crossing
with subwavelength grating structure16. The loss per crossing was measured to be as low as 0.02 dB with polarization
dependent loss of <-0.02 dB and crosstalk of less then -35 dB. Ability to intersect waveguides with such low loss and
crosstalk is an important prerequisite for designing complex high density photonic circuits. In Section 5, we demonstrate
a continuously apodized surface grating coupler 17. The device is fabricated in a single etch step, achieving a coupling
efficiency of 3.7 dB, and a 3 dB bandwidth of 60 nm. A subwavelength structure is employed to generate an effective
medium engineered to vary the strength of the grating and thereby maximize coupling efficiency, while mitigating back
reflections at the same time. Finally, in Section 6 we show how the refractive index of a slab waveguide can be
controlled in a specific location of a chip when building sophisticated microphotonic circuits, for an example of a planar
waveguide multiplexer12,18.
2. SUBWAVELENGTH GRATING: A NEW TYPE OF MICROPHOTONIC WAVEGUIDE
We recently demonstrated a new waveguide principle based on the formation of a subwavelength grating (SWG) in a
waveguide core11-15. In contrast to waveguides based on line-defects in 2D photonic crystal lattices, the light is confined
in a SWG waveguide core covered with a cladding material of a lower refractive index, as in conventional index-guided
structures. The core is a composite medium formed by periodically interlacing silicon segments with a material of a
lower refractive index at the subwavelength scale.
Some segmented waveguides have been previously studied numerically19,20 and also experimentally21,22. Since in those
structures spacing between the segments is not subwavelength, application in high-index-contrast waveguides is hindered
by the reflection and the diffraction losses incurred at the boundaries of the different segments. The long-period
segmented waveguides do not support a (theoretically) lossless mode and the light coupling to radiation modes limits
applications of such structures to short propagation lengths and small refractive index discontinuities.
Our subwavelength grating waveguide is unique in that the structure supports a true theoretically lossless mode,
abstracting from fabrication imperfections. By modifying the pitch, width and duty cycle of the subwavelength grating,
the effective index of the medium can be engineered. In our study, we used silicon segments with SU-8 cladding
material; however any materials can be interlaced for specific applications. For example, athermal waveguides can be
designed by interlacing materials with opposite polarity thermo-optic coefficients, while waveguide modulators or lasers
may be implemented by making or interlacing waveguide core segments with a nonlinear optical material. This freedom
in waveguide design suggests that subwavelength grating waveguides can be used in a broad range of applications.
A schematic of a SWG waveguide is shown in Fig. 1a. The grating period, duty cycle and segment dimensions are
chosen to avoid the formation of standing waves due to Bragg scattering and the opening of a band gap near λ = 1550 nm
wavelength. According to this criteria and using finite-difference time-domain (FDTD) and MIT photonic bands
(frequency domain) calculations, the following typical structural parameters were chosen: grating pitch Λ = 300 - 400
nm, segment width w = 300 nm and segment length a = 100 - 150 nm. Details on waveguide design and characterization
can be found in [15].
a a
b
c
Figure 2. a) Mode profile of a Si-wire waveguide (w = 300 nm, SiO2 upper cladding). d) Mode profile of a SWG
waveguide (w = 300 nm, Λ = 300, SiO2 upper cladding) at the center of a 150 nm-long Si segment. e) Field
propagating along the subwavelength grating waveguide (z-direction), excited by the Si-wire waveguide
fundamental mode at λ = 1550 nm, for quasi-TE polarization.
Calculated mode profiles for a 300 nm wide Si-wire waveguide and SWG waveguide are shown in Figs. 2a and 2b,
respectively. The propagating field along the grating is shown in Fig. 2c.
Our subwavelength grating waveguide structures were fabricated using commercially available SOI substrates with a
0.26 µm thick silicon layer and 2 µm thick buried oxide (BOX). Electron beam lithography was used to define the
waveguide layout in high contrast hydrogen silsesquioxane resist, which formed SiO 2 upon electron beam exposure. We
used inductively coupled plasma reactive ion etching (ICP-RIE) to transfer the waveguide pattern onto the silicon layer.
Samples were coated with a 2 µm thick polymer (SU-8, n = 1.577 at λ = 1.55 µm) and cleaved into separate chips and
facets polished.
Propagation loss was estimated by measuring the transmitted power through the loss test structures of SWG waveguides
of different lengths in a range of 0.5 – 3.0 cm. Loss was determined from the slope of a linear fit of transmitted power vs.
SWG waveguide length. Typical SWG waveguide loss measured is 2.6 dB/cm. The PDL is less than 0.5 dB for the
wavelength range 1480 – 1580 nm. It is remarkable that such low loss is achieved for light propagating over a 1 cm
distance through more than 33,000 boundaries between high- and low-refractive-index segments having an index
contrast of Δn ~ 1.9. While this finding is consistent with Bloch mode theory, we also believe that this low loss is a
consequence of the mode delocalization from the composite core with a corresponding decrease in light scattering at
fabrication sidewalls imperfections.
We demonstrate the potential of subwavelength grating waveguides through realization of practical functional
components, as described in the following sections.
3. SUBWAVELENGTH GRATING FIBER-CHIP COUPLER
Our fiber-chip coupler5,7,12 exploits refractive index engineering by subwavelength waveguide structuring to reduce the
effective index mismatch and the associated loss at the fiber-chip coupling interface. The coupler principle was proposed
in ref. [5] and is based on a gradual modification of the waveguide core refractive index and the corresponding mode size
transformation by changing the volume fractions of the Si and SU-8 materials that form the composite waveguide core.
The geometry of the taper shown in Fig. 3a was designed such that at one end of the coupler the effective mode index is
matched to a 450 nm wide silicon strip waveguide for both TE- and TM-like polarizations (nTE = 2.51, nTM = 2.11), while
at the end near the chip facet it is close to that of an optical fibre (n ~ 1.5). Different taper stages with distinct geometries
of silicon segments are used to account for different mode confinement in different regions of the coupler, as shown in
Fig. 3b.
a
from
fiber
2 m
c
Insertion
Lossloss
(dB) (dB)
b
0
SWG W035 P04 TE WG1 Corrected (dB)
-1
SWG W035 P04 TM WG1 Corrected (dB)
-2
TE
SWG W035 P04 TM WG2 Corrected (dB)
-3
SWG W035 P04 TE WG2 Corrected (dB)
-4
SWG W035 P04 TM WG3 Corrected (dB)
TM
-5
SWG W035 P04 TE WG3 Corrected (dB)
-6
-7
-8
1480
1500
1520
1540
1560
1580
Wavelength (nm)
Wavelength
(nm)
Figure 3. a) Subwavelength grating fiber-chip microphotonic coupler. b) The low-confinement section (top) near
the chip edge, along with high-confinement section (center) near the 450-nm wide strip waveguide and
intermediate section (bottom) positioned at ~15 m from the chip edge. c) Transmission spectra of the insertion
loss of a strip waveguide terminated at both ends with a subwavelength grating coupler (two samples; TE and TM
polarizations).
The curves shown in Fig. 3c represent the measurements of 5-mm-long silicon strip waveguides terminated with the
SWG couplers at their inputs and outputs, for TE and TM polarizations. The insertion loss includes the coupling loss and
the propagation loss in the strip waveguide. The intrinsic coupler loss was determined in an independent measurement on
a series of couplers (up to 62) connected back-to-back as -0.23 dB for TE and -0.47 dB for TM polarizations. The total
fibre-to-waveguide coupling efficiency was determined as -0.9 dB for TE and -1.2 dB for TM polarizations. This is the
highest efficiency with minimal wavelength and polarization dependence yet reported for a microphotonic coupler.
The coupler exhibits a high tolerance to the feature size variations that may arise from limited accuracy of the
lithography and etching. The coupling loss was negligibly affected by changing the taper tip width from the nominal 350
nm to 300 nm, with loss penalty of less then 0.1 dB for both polarizations.
4. SUBWAVELENGTH GRATING WAVEGUIDE CROSSING
In optical interconnects, the ability to intersect waveguides with minimal loss and negligible crosstalk is crucial to
facilitate circuit connectivity at a massive scale comparable to state-of-the-art electrical interconnects. However, each
time when a conventional waveguide intersects another waveguide in a planar photonic circuit, a substantial fraction of
light is lost by diffraction at the crossing and it may get coupled as a crosstalk signal to the transverse waveguide. In
[16,24] we demonstrated a solution to this problem by adiabatically transforming a strip waveguide to a subwavelength
grating structure which acts as a non-resonant mode expander in the vicinity of the crossing region, while diffraction is
suppressed as a consequence of the subwavelength scale of the grating. The effective index of both waveguides is
decreased towards the crossing point by reducing the SWG duty ratio and the width of the silicon segments, as it is
schematically shown in Fig. 4a. The mode delocalization from the waveguide core, along with a reduced effective index
of the crossing waveguide, largely decreases the scattering efficiency at the crossing. This was confirmed in our
measurement that showed excellent optical isolation between the two waveguides with a crosstalk below -40 dB, more
than a 25 dB improvement compared to a direct crossing of strip waveguides (260 nm  450 nm).
a
b
c
-5
0.023 dB/crossing, TE
Loss (dB)
-7
-9
0.037 dB/crossing, TM
-11
-13
-15
0
20
40
60
80
Number of crossings
Figure 4. a) Waveguide crossing schematics. Si-wire waveguides are transformed into SWG waveguides near the
crossing region. c) A fabricated SWG waveguide crossing in SOI. d) Measured crossing loss for 0, 1, 5, 10, 20, 40
and 80 concatenated crossings. Loss per crossing is determined as the slope of a linear fit of these measurements.
The fabricated waveguide crossing in SOI is shown in Fig. 4b. In order to quantify the crossing loss, test structures with
multiple (up to 80) waveguide crossings concatenated in series were fabricated. The insertion loss of these structures is
analysed in Fig. 4c, where the loss per crossing is estimated as -0.023 dB from the linear fit for TE polarization, and the
polarization dependent loss is ~0.01 dB. Note that compared to a direct crossing, the loss is decreased at least by a factor
of 30. This is the lowest loss and minimal polarization dependence yet reported for crossings in high index contrast
waveguides. An important practical advantage of this waveguide crossing compared to other designs is that as a binary
structure (the silicon layer has either the full starting thickness of 260 nm, or is completely etched away) it can be
fabricated using a single etch step.
5. SURFACE GRATING COUPLER WITH SUBWAVELENGTH STRUCTURE
Surface grating couplers are a promising fibre-chip coupling solution25,26. They operate by laterally expanding the light
propagating in the waveguide by means of an adiabatic taper, along with diffraction coupling it to (or from) an optical
fibre positioned over the grating. To achieve good coupling efficiency, the grating must exhibit a high directionality
towards the fibre, and the radiated field should match the near-Gaussian field of the optical fibre mode. The ideal
fabrication process would use a single full-etch through the silicon to the buried oxide (BOX) to define both the
waveguides and the grating couplers.
Figure 5. a) Fabricated surface grating coupler with subwavelength structure. b) Field overlaps between the
grating near field and the SMF-28 optical fiber mode, for couplers without (left) and with (right) SWG structure.
FDTD simulation. c) Measured fiber-chip coupling loss for various samples.
In [27] we proposed, for the first time, that coupling strength of a surface grating coupler can be optimized by modifying
the refractive index in the grating region using a subwavelength microstructure. The effective medium is created by fully
etched structures (Fig. 5a) with feature size and periodicity smaller than the operating wavelength. This enables singleetch fabrication of gratings with the optimal strength, and simultaneous apodization to match the radiated field to the
fibre mode (Fig. 5b, right). Two implementations of our concept have recently appeared28,29, using circular holes to
create the effective medium, with a uniform (unapodized) design.
Our continuously apodized surface grating coupler coupler17 was designed and fabricated using a 0.26 μm thick silicon
layer with a 2 μm thick buried oxide (BOX) and air cladding. The effective index was apodized to vary the strength of
the grating to produce a near-Gaussian radiated field (Fig. 5b, right panel). The minimum feature size is 100 nm, for
compatibility with deep-uv lithography. The pitch in the propagation (z) direction was chirped along the grating so that
all grating periods radiate phase-matched. Backreflections are minimized to 0.1% according to our FDTD calculation.
The couplers were successfully fabricated by e-beam lithography and ICP-RIE at the NRC Canada, and also at deep-uv
193 nm CMOS line at CEA LETI. The experimental results for several grating couplers are shown in Fig. 5c, with a peak
coupling efficiency of -3.7 dB. The 3 dB bandwidth is 60 nm. The coupler was successfully implemented in our
evanescent field Si-wire bio-sensor, which requires efficient and robust couplers for TM polarization, where sensitivity is
maximized30,31. More details on our coupler implementations can be found in ref. [32].
6. REFRACTIVE INDEX ENGINEERING IN A SLAB WAVEGUIDE: A NEW TYPE OF
PLANAR WAVEGUIDE MULTIPLEXER
As we showed in previous sessions, in silicon waveguides, media with a wide range of intermediate effective indices can
be engineered by modifying the volume fractions of silicon and cladding material with a spatial accuracy of a few tens of
nanometers simply by lithographic patterning. This control of refractive index in a specific location of a chip is highly
desirable for building sophisticated microphotonic circuits, including optical multiplexers33-35. A new type of waveguide
multiplexer18,12 is shown in Fig. 6a. Making this device is possible using a SWG engineered nanostructure that provides
sufficient optical confinement to make a waveguide, yet have a waveguide boundary that is transparent to light
propagating normal to the boundary. In this multiplexer, the light propagating in the curved strip waveguide is diffracted
by the grating etched in one of the waveguide sidewalls. Curving the waveguide serves the focusing function so that
diffracted light propagates with a convergent wavefront bearing the curvature of the strip waveguide towards the focal
region. Different wavelengths are focused at different positions along the focal curve (Rowland circle of radius 80 m)
where they are intercepted by the receiver waveguides. The subwavelength nanostructure formed in the trench between
the strip waveguide and the slab waveguide combiner is shown in Fig. 6b. The purpose of using the subwavelength
trench is two-fold: Near the strip waveguide an effective material index of n ~ 2 is created. Here, the trench acts as a
waveguide for light diffracted by the grating towards the combiner region, while as a lateral cladding for the strip
waveguide. On the other side of the trench, near the slab waveguide combiner, a triangular SWG structure is used as a
graded-index medium to suppress Fresnel reflection for the light propagating from the trench to the slab waveguide.
Transmission spectra for eleven channels of the spectrometer are presented in Fig. 6c. The achieved maximum-tominimum transmission ratio is as large as ~20 dB, while the loss is approximately -4 dB, allowing for wavelength
filtering with a bandwidth of 170 nm. This is the largest wavelength range yet reported for a miniature spectrometer chip.
The device size is only ~160 m  100 m.
Figure 6. a) Curved waveguide grating multiplexer with subwavelength grating interface. b) SEM image of the
subwavelength nanostructure in the trench between the strip waveguide and the slab waveguide combiner. c) Set
of spectra measured at different output waveguides of the multiplexer (TE polarization).
7. CONCLUSIONS
We demonstrated a new type of optical waveguide based on subwavelength gratings. The potential of SWG waveguides
was shown through realization of practical functional components, including a fiber-chip edge coupler, a surface grating
coupler, a waveguide crossing, and a new type of waveguide multiplexer. Our technique circumvents an important
limitation in integrated optics, that is the fixed value of the refractive indices of the constituent materials in the absence
of active tuning mechanisms. These results suggest that the subwavelength grating waveguides could become important
elements for future integrated photonic circuits.
ACKNOWLEDGEMENTS
The surface grating coupler work was carried out with the support of the Genome and Health Initiative (GHI) at the
National Research Council Canada. P.C gratefully acknowledges support from COST MP0702 action “Towards
Functional Subwavelength Photonic Structures”.
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