# Stress Induced Effects for Advanced Polarization Control in Silicon Photonics Components

Authors: D.-X. Xu; W. N. Ye; S. Janz; A. Delâge; P. Cheben; B. Lamontagne; E. Post; P. Waldron
Journal: Advances in Optical Technologies
 (2008)

---

## Abstract

We review the use of the oxide cladding stress-induced photoelastic effect to modify the polarization dependent properties in silicon-on-insulator (SOI) waveguide components, and highlight characteristics particular to this high index contrast (HIC) systems. The birefringence in SOI waveguides has its origin in the electromagnetic boundary conditions at the waveguide boundaries, and can be further modified by the presence of stress in the waveguiding materials. With typical stress levels inSiO2 films, which are often used as the upper cladding, the waveguide effective index can be altered anisotropically up to the order of 10−3 for ridges with heights ranging from 1 μm to 5 μm. This effect can be used effectively to counter the waveguide geometrical birefringence, allowing the waveguide cross-section profiles to be optimized for design criteria other than null geometrical birefringence. Design strategies are developed for using stress engineering to achieve a variety of functions. Polarization insensitive arrayed waveguide gratings (AWGs), polarization insensitive ring resonators, and polarization splitters and filters are demonstrated using these design principles.


---

## Body

## 1. Introduction

Silicon photonics is a rapidly growing research
field with many important advances in recent years [1–9]. Primarily motivated
by the potential of high-integration density and compatibility with mature CMOS
technologies, silicon-on-insulator (SOI) has been the main material platform
for silicon photonic waveguide components [1, 9]. Along with these benefits,
control and utilization of polarization-dependent properties arise as
a challenge, as well as open new possibilities in advanced designs and functionalities
[10–15].Polarization-dependent
properties have long been an important issue in integrated optics systems. In applications
such as wavelength demultiplexing and high resolution spectroscopy, the shift
in channel wavelength with the polarization state of the incoming optical
signal often compromises the device spectral resolution [8]. One approach to
handle this issue is to produce devices with polarization insensitive
performance. In some cases this approach may not be practical, and then
polarization diversity may be adopted where the signal is divided into
orthogonal polarization states using a polarization splitter and processed
separately. In this paper, we review the characteristics of modal birefringence
in SOI waveguides, with regard to the two main sources of polarization
anisotropy, namely, the geometrical and the stress-induced birefringence [13, 16]. Design methodologies and experimental demonstrations for using the
stress-induced birefringence to achieve polarization-insensitive arrayed
waveguide gratings (AWGs) [13, 17], polarization insensitive ring resonators
[18, 19], and zero-order AWG-based
broadband polarization splitters [20] are presented.


## 2. Waveguide Birefringence: Geometrical Effects

In
planar waveguides, the modal birefringence (the difference in the effective
index for the TM and TE polarizationsΔneff=neffTM−neffTE) results from the
combination of geometrical, compositional, and stress-induced effects. In low index contrast glass
waveguides, the geometrical effect is negligible and the birefringence is primarily
controlled by the residual stress in the waveguide layers. A large body of
research has been devoted to this subject, where the main goal is to reduce the
stress anisotropy in the waveguide core region by adjusting the thermal
expansion coefficients of the cladding and core layers or creating stress
relief features [21, 22]. In high-index contrast waveguides such as SOI where
the light confinement is strong, electromagnetic boundary conditions dictated
by the cross-section geometry of the waveguides have the largest impact on the
waveguide effective index and consequently the birefringence. These geometrical
dependencies have been used to obtain single mode waveguides with large
cross-sections, and to adjust the waveguide geometrical birefringence Δngeo to desired values. In an SOI
ridge waveguide as illustrated in Figure 1, it is possible to minimize the
birefringence by tailoring the waveguide aspect ratio, particularly for waveguides with relatively large cross-sections [10–13]. As the core
size is reduced, typically to ~2 μm and less, it becomes increasingly difficult
to attain the designed birefringence values [13, 16, 17]. Since ridge dimensions also determine
the number of waveguide modes, the minimum usable bend radius, the mode size,
and the coupling between adjacent waveguides, it is often impossible to meet
these different design objectives simultaneously.Figure 1
Schematic cross-section of an SOI ridge waveguide.As
an example, Figure2(a) (dashed lines) shows the dependence of waveguide
geometrical birefringence Δngeo on the etch depth D for
waveguides with vertical sidewalls, ridge height H=2.2μm, and widths of 1.6 and 2.5 μm, respectively. Results for waveguides under
stress (solid lines) will be discussed in Section 3. For a given waveguide
width W, the polarization degeneracy (Δngeo=0) may be achieved at a specific
value of etch depth D. At the birefringence-free point for W=1.6μm near D=1.3μm the change of Δngeo with the fluctuation in the
etch depth is ~1.5×10−4 for ΔD =
±10 nm. When W = 2.5 μm, Δngeo is less sensitive to the
fluctuations in the etch depth (~2×10−5 for ΔD = ±10 nm near D = 1.5 μm), however the birefringence-free
condition cannot be achieved. To reduce the birefringence below the level
required for the state-of-the-art photonic devices (Δneff<10−4) by selecting
and attaining the ridge aspect ratio W/D, dimension control on the order of 10 nm is required for these waveguides [13, 16, 17], which is very difficult in
fabrication.(a) Calculated modal
birefringenceΔneff for waveguides with H = 2.2 μm.
(a) Δneff in ridge waveguides with
vertical sidewalls (θ=90°) as a function of etch depth D.
Waveguide width W = 1.6 and 2.5 μm, cladding thickness tc=0.7 μm,
and film stress σfilm = −100 MPa. (b) Δneff in vertical (θ = 90°) and trapezoidal (θ = 54°) waveguides as a function of the ridge top
width W1, for D = 1.5 μm, tc=0.7 μm, and σfilm = −300 MPa. The dashed curves show the
geometrical birefringence Δngeo (i.e., in the absence of stress),
the solid curves show Δneff including both the geometrical
and stress-induced components.
(a)(b)The
effect of changing the waveguide width on the geometrical birefringenceΔngeo  is shown in Figure 2(b) (dashed
curves), for sidewall angles of 90° and 54°, which represent the profiles
typically obtained by dry and anisotropic wet etching, respectively. Waveguide
sidewall angles strongly affect the mode properties, especially as the sidewall
approaches vertical. With decreasing ridge width for θ = 90°, Δngeo shifts towards positive values
initially, until the waveguide is so narrow that the modes mainly reside in the
etched slab section and the birefringence changes to negative values rapidly.
The birefringence of a trapezoidal ridge waveguide is less susceptible to
changes in the ridge geometry (width and etch depth) as compared to a
rectangular waveguide (i.e., θ = 90°) with
similar cross-section area, as can be observed from the data for a sidewall
angle of 54° shown in Figure 2(b). The geometrical birefringence, however,
remains negative for the entire waveguide width range. For the rectangular
waveguides, an optimal width can be found to satisfy the birefringence-free
condition (zero birefringence at W~2μm). Detailed discussions on the influence of geometrical
parameters can be found in previous publications [16, 17].Even though waveguide
geometries satisfying both the single-mode and birefringence-free conditions can be found in principle, it is
important to be able to implement the designs using existing fabrication
technologies. Using contact-print lithography, waveguide-width variations on the order of 100 nm
can be expected. Using state-of-the-art high resolution lithography methods
such as e-beam direct write or deep UV steppers, dimensional control on the
order of 10 nm is possible but still very challenging. These techniques,
however, are expensive and are not widely available. Because it is difficult to
precisely control the waveguide dimensions due to limitations of the
fabrication techniques, methods of controlling birefringence other than
modifying waveguide geometries are desirable.


## 3. Photoelastic Effect and the Stress-Induced Birefringence

Cladding
layer such as silicon dioxide is usually deposited or grown at elevated
temperatures on the silicon substrate. A (compressive) stress is often found in
the silicon dioxide(SiO2) films, due to the different thermal
expansion coefficients of Si (3.6×10−6K−1) and oxide (5.4×10−7K−1) as well as
intrinsic stress that may exist in the oxide film. When a material is subjected to a stress, the material refractive index
is altered due to the photoelastic effect. The stress-induced changes in the material refractive index are given by
[13, 14, 23]
(1)nx−n0=−C1σx−C2(σy+σz),ny−n0=−C1σy−C2(σz+σx). Here σi(i=x,y,z) is the stress
tensor, ni is the material refractive index in the corresponding
directions, n0 is the (isotropic) refractive index in the absence of
stress, and C1 and C2 are the stress-optic constants. If a
stress (tensor) with axial anisotropy is imposed on an originally optically
isotropic material, a material birefringence is induced:
(2)ny−nx=(C2−C1)(σy−σx).
Stress-optic constants of silicon and
glass are listed in Table 1, as well as those of GaAs for comparison.Table 1
Stress-optic constants of some materials.
Materialλ (μm)C1(10−12Pa−1)C2(10−12Pa−1)Si1.15−11.044.04Silica0.6330.654.5GaAs1.15−18.39−10.63The
stress-inducedmaterial birefringence
in turn causes a stress contribution Δns to the modal birefringence. The
total modal birefringence can be expressed as Δneff=nTM−nTE=Δngeo+Δns. The stress distributions in an
SOI ridge waveguide are shown in Figures 3(a) and 3(b), for SiO2 upper and lower claddings under a compressive stress of  σfilm = −320 MPa (σfilm is the in-plane stress
component in the uniform cladding film far from the ridge), calculated using a finite-element multiphysics solver (FEMLAB). The primarily in-plane stress (Figure 3, x-direction) in the oxide film compresses the Si ridge and results in a
compressive stress in the x-direction (Figure 3(a)) and a higher tensile stress
in the y-direction (Figure 3(b)) in the silicon core. For the waveguide example
shown in Figure 3,  σx≈ −70 MPa and σy≈ 180 MPa at the waveguide center. This stress
anisotropy is the fundamental reason for the stress-induced birefringence. The
corresponding local material birefringence (ny−nx) is shown in Figure 3(c), with
values as large as 4×10−3. These modifications in the material index cause the modal index neffTM to increase and neffTE to decrease with the oxide
thickness and the stress level (Figure 4(a)). The corresponding stress-induced
birefringence thus can
be controlled with two parameters: the oxide thickness tc and the film stress level σfilm, as  shown in Figure 4(b). The stress-induced index variations resulting
from commonly used oxide cladding films are of comparable magnitude to the
geometrical birefringence found in typical SOI ridge waveguides. Depending
on the specific value of the geometrical birefringence Δngeo, the total
modal birefringence may be designed to be zero or other desired values. Figure 5 shows the calculated results for maximum birefringence
that can be induced by a cladding with σfilm = −300 MPa in
waveguides with 2 μm ridge height and different aspect ratios. These
characteristics are the bases for stress engineering in SOI waveguides, and they
can be advantageously employed in many applications.Stress distributions in the
(a)x-direction and (b) y-direction. The ridge height is 2.2 μm, the width is 1.8 μm, and the etch depth is 1.47 μm. The cladding oxide is 1 μm thick with a compressive stress of σfilm = −320 MPa. (c) Stress-induced material
birefringence (ny−nx) corresponding to the stress
distributions shown in Figures  3(a) and  3(b).
(a)(b)(c)(a) Effective index as
a function of the oxide upper-cladding thicknesstc, for different
cladding stress levels σfilm of 0, −200, and −400 MPa,
respectively; (b) total modal
birefringence Δneff as a function of tc and σfilm.
(a)(b)Figure 5
Stress-induced modal birefringenceΔns for ridge
waveguides with different aspect ratios, with H = 2 μm, tc = 2 μm, and σfilm = −300 MPa.


## 4. Experimental Implementations

In the following, we present several
examples of using stress engineering for the control of polarization-dependent properties
of SOI waveguide devices. First, we present polarization insensitive AWG
demultiplexers, where the birefringence in the waveguide array is eliminated by
the proper selection of the oxide cladding stress and thickness [13, 17]. Then
we introduce polarization insensitive ring resonators using multimode interference
(MMI) couplers to achieve polarization insensitive coupling between the bus
waveguide and the ring cavity [18, 19]. Stress-induced birefringence is used to
compensate the round-trip phase difference between the two polarizations. The
last example is a polarization splitter in a zero-order AWG configuration,
where a prism-shaped oxide patch is placed in the arrayed waveguide section to
disperse the TE and TM modes into separate output waveguides. Since this AWG operates
at near zero-order, broadband performance is achieved [20].


### 4.1. Polarization-Independent AWGs

In AWGs,
the polarization-dependent wavelength shiftΔλ=λTM−λTE mainly  arises from the
birefringence of the arrayed waveguides and can be expressed as Δλ≈λΔneff/ng, where ng is the waveguide group index and λ is the
operating wavelength in vacuum. The AWGs used
for this demonstration of polarization compensation using stress engineering
were made on SOI substrates with a silicon thickness of 2.2 μm, with 9
output channels spaced at 200 GHz, and centered at 1550 nm [8, 13, 17] (see Figure 6(a)). The arrayed waveguide gratings of order 40 were formed by 100 waveguides
of width 2 μm. Waveguides were produced using both wet and dry etching methods,
yielding ~54° and nearly vertical sidewall angles, respectively. Waveguide
birefringence simulations were performed using measured waveguide dimensions.
Upper cladding oxide films of different thicknesses were deposited at ~400°C
using PECVD, with a film stress of σfilm = −320 MPa
in the blank films, measured from wafer bowing. Figure 6(b) shows the
calculated and measured dependence of Δλ on the
cladding thickness tc, for both trapezoidal and rectangular
waveguides. Calculated results agree well with experiments for both types of
waveguides, showing that Δλ can be
modified over ~2 nm wavelength range [16]. Figures 6(c) and 6(d) show the
TE and TM spectra of a wet-etched AWG before
and after polarization compensation. The adjacent channel cross-talk is less
than −25 dB. The noncompensated AWG device has a polarization-dependent
wavelength shift of Δλ~0.6nm (Figure 6(c)), arising from the geometrical
birefringence of Δngeo~−1.3×10−3 in the
arrayed waveguide. With an oxide upper cladding film of −320 MPa in stress and 0.6 μm in
thickness, the Δλ was then
reduced to below 0.04 nm for all channels (corresponding to Δneff<1×10−4) (Figure 6(d)). The polarization dependent
loss (PDL) was also found to be negligible in these devices after the
compensation.(a) Optical
image of a fabricated AWG. (b) Polarization-dependent wavelength shift Δλ as a function of the cladding
thickness tc, for AWGs fabricated using wet (waveguide top width W1 = 1.1 μm and bottom width W2 = 3.8 μm) and dry (W1 = 1.85 μm and W2 = 2.0μm) etching to a depth
of D =1.47 μm. The cladding stress is σfilm = −320 MPa. Measured spectra for
an SOI AWG. (c) Measured spectrum for an SOI AWG without the oxide upper cladding. (d) Compensated using a 0.6 μm thick SiO2 claddings with σfilm = −320 MPa. TM (solid) and TE
(dashed).


### 4.2. MMI-Coupled Polarization-Independent Ring Resonators

We also applied the stress engineering
technique to achieve polarization-insensitive ring resonators [18, 19]. Ring
resonators have been used as the building blocks in applications including
add-drop, switching, modulation, and sensing [24–27]. However,
polarization sensitivity is often an obstacle that limits their practical use
[12, 15, 18].The power transmission in the bus waveguide
of a single coupler
ring resonator (Figure7(a)) can be obtained by a generalization of the ring
resonator equations to incorporate the coupler loss [18, 28]:  (3)|T|2=αMMI2[α2−2αtcosϕ+t21−2αtcosϕ+α2t2],where ϕ is the total round trip phase accumulation,
and α2=αMMI2⋅αring2 is the combined
power loss factor including both the ring loss and the coupler loss. The
self-coupling coefficient t2 is the ratio of power transfer from the
input to the output port 1 of the multimode interference (MMI) coupler, as
indicated in Figure 7(b). The resonance extinction ratio is maximum at α2=t2, which is referred
to as the critical coupling condition. A series of transmission minima occur at
wavelengths λm for which the round-trip phase accumulation is integer multiple of 2π. It is apparent that a polarization dependence in the
coupling coefficient t and/or the loss factor α lead
to different resonance quality factors and linewidths for TE and TM input
polarizations. If the waveguides are birefringent, the round trip phase
accumulation ϕ varies with the polarization, and the
resonance wavelengths and free spectral range (FSR) are polarization sensitive.
To achieve polarization independence in a ring resonator, all these factors
need to be addressed.(a) A ring resonator with an MMI coupler. (b) A schematic of the MMI
structure.
(a)(b)Polarization-independent
ring resonator designs using directional couplers have been investigated [12],
but showed long coupler length and very stringent fabrication requirements. We
proposed the use of MMI couplers to achieve polarization-independent light
transfer between the resonator bus and the ring waveguides (Figures 7(a) and 7(b)).
For simplicity, we have chosen the commonly used 2×2 restricted interference coupler with a 50 : 50
splitting ratio between the two output ports [29]. The coupler width is WMMI=3D, where D is the center-to-center separation between the access waveguides
(Figure 7(b)). The resonators are designed with the following ring and access
waveguide dimensions: ridge height H = 1.5 μm, width W = 1.5 μm and 1 μm, and
etch depth H−h = 0.9 μm. A separation of D = 2.5 μm between the access waveguides
is used in the MMI design, based on the considerations of a compact footprint
and ease of fabrication, yielding an MMI width of WMMI = 7.5 μm. The
quality factor of a resonator is determined by the coupler splitting ratio and
the loss in the resonator cavity. MMI designs with variable splitting ratios
have been proposed and demonstrated by other groups and may be used for high-quality
factor resonators [30, 31].The optical field
distribution in the2×2 MMI coupler is shown in Figure 8(a), while Figure
8(b) shows the MMI coupler transfer characteristics in terms of the normalized
power coupled to the fundamental mode in ports 1 and 2, respectively, as a
function of the coupler length. For each polarization, a splitting ratio close
to 50 : 50 is achieved over the range of coupler length LMMI from 82
to 86 μm, with a coupler imbalance of ≤0.05dB. The combined power in the two outputs is the total transmitted power αMMI2, which indicates the
loss through the coupler (with αMMI2 = 1 being
lossless). The optimum coupling length differs by ~2.5μm (or ~3%) between
the two polarizations. As a first approximation, a coupler length of LMMI = 84 μm at the crossing point is used in all our resonator designs, where a
similar excess loss of ~−0.2 dB is found for both polarizations. This
choice is based on the assumption that losses from all other mechanisms are
similar for TE and TM, which is not necessarily the case. In addition to the
coupler excess loss, there are several other mechanisms contributing to the overall
resonator loss. For example, the waveguide propagation loss due to scattering
depends on the optical mode overlap with the roughness at the waveguide
boundaries and is generally polarization dependent. This loss is proportional
to the propagation distance, and therefore to the cavity length of a ring
resonator. Another source is the radiation loss in waveguide bends, as well as
possible losses at discontinuities such as the junctions between the straight
and curved waveguides. These factors need to be considered in the device
design, and detailed discussions can be found in [19].(a) Optical field
distribution in the SOI MMI coupler of7.5μm×84μm in dimensions, with an etch depth of 1 μm. (b) Corresponding normalized power in the
fundamental mode in ports 1 and 2, for the TE and TM polarizations.
(a)(b)Since the stress in SOI waveguides
caused by the cladding layer can be used effectively to control the
birefringence over a wide range, it can be applied to eliminate the polarization
dependence in the ring phase accumulationϕ. The phase
change in the MMI section is 2πneffMMILMMI/λ, plus a constant correction factor which is a multiple integer
of π/2 [32]. Since the stress-induced birefringence
in the ring waveguide Δnsring is much larger
than that in the wider MMI section [16] (i.e., ΔnsMMI≪Δnsring), the difference
in the phase accumulation Δϕ between TM and TE polarizations can be
expressed as [18]:
(4)Δϕ=2πλ[ΔngeoMMILMMI+ΔngeoringL1+ΔnsringL1].Here L1 is the total
length of the narrower ring waveguide sections, L1=L−LMMI=2πR+LMMI. Figure 9 shows the ring resonator phase
difference  Δϕ=ϕTM−ϕTE as a function of the oxide
cladding thickness for two cladding stress levels. Obviously, various
combinations of cladding stress and thickness can be found to adjust  Δϕ to zero.Figure 9
Phase differenceΔϕ=ϕTM−ϕTE as a function of the
oxide cladding thickness for an MMI-coupled ring resonator with a radius R of
200 μm and an oxide cladding stress of −220 and −250 MPa, respectively.We have fabricated MMI-based ring
resonators in SOI wafers with 1.5μm thick silicon at the Canadian Photonics
Fabrication Center (CPFC). SEM images of a fabricated device are shown in Figures 10(a) and 10(b). Standard inhouse PECVD process produces oxide films with −250 MPa stress. Measured transmission spectra
for a MMI-coupled ring resonator with a radius of 200 μm are shown in Figure 10(c) for TE and TM
polarizations. Over the 4 nm scan range, the polarization-dependent wavelength
shift is below 2 pm, which is the laser scan step used in these measurements.
The measured free spectral range (FSR) is ~0.46nm, and the quality factor is Q
~ 15,000. Polarization insensitive operation is achieved in these resonators,
demonstrating the effectiveness of the proposed method for polarization control.(a) SEM image of an MMI-coupled ring resonator. (b) A closeup of the MMI
section. (c) TE and TM transmission spectra of the ring resonator, with an
upperSiO2 cladding of 0.8 μm thick and film stress of σfilm = −250 MPa.


### 4.3. Broadband
Polarization Splitter in a Zero-Order AWG Configuration

Stress-induced
effects can also be used to produce high level of birefringence in selected waveguide
areas. Since the stress-induced index modifications are several orders of
magnitude smaller than the core-cladding refractive index contrast in SOI, the
effect of aSiO2 cladding on mode shape is negligible. Thus there is
little mode mismatch loss or polarization-dependent loss at the junctions
between waveguide sections with and without the cladding. Figure 11 shows a
zero-order AWG where all of the arrayed
waveguides have identical geometrical path lengths [20]. A triangular patch of oxide cladding is placed in the
arrayed waveguide section with a constant length increment ΔL between the adjacent waveguides. The stress
in the waveguide cladding induces a polarization-dependent phase difference in
the light signal propagating in the waveguide array (see Figure 4(a)), causing a
polarization-dependent tilt in the phase front of the light in the free
propagation region (FPR) (see Figure 11(b)). Since all waveguides have the same
physical length, the phase difference for light propagating in the adjacent waveguides
of the arrayed section depends solely on the cladding stress-induced index
change and the patch-length increment. Since the stress-induced index change in
the TE and TM polarization modes has opposite signs for silicon waveguides, the
two modes are spatially displaced in the opposite directions in the focal
region relative to the free propagation region centerline, as shown in Figure 11(b).
With proper placement of the two receiver waveguides along the focal plane, the two
polarizations are spatially separated.Figure 11
(a) Schematic layout of a broadband zero-order
AWG polarization splitter. (b) Geometry of the output FPR with a Rowland
circle configuration.Zero-order
AWG-based polarization splitters were designed and fabricated on SOI wafers,
with a 2.2μm thick silicon core layer. The deposited oxide
cladding film had a thickness of 1 μm, and the measured cladding film stress was
approximately −340 MPa. The overall device size is ~12mm×4mm.
Figure 12(a) shows several fabricated AWG devices with triangular cladding
regions of varied patch sizes. Based on the measured cladding film stress and
thickness, the cladding patch-length increment ΔL between the adjacent
waveguides was set to 16.4 μm to produce the required polarization-dependent
phase front tilt at the output of the waveguide array. Since stress-induced
effects do not vary with wavelength appreciably, and the AWG operates close to
zero order, the performance of the splitter is expected to be wavelength independent
over a large application bandwidth, which was experimentally confirmed. The measured
extinction ratio of the polarization splitter was better than −10 dB for both
output polarizations over the entire tuning range of our laser (1465–1580 nm). Figure 12(b) shows the measured polarization splitter transmission for a wavelength
range of λ = 1537 to 1557 nm. Over this range, the splitter extinction
ratio is <−15dB. The best extinction ratio achieved was −20 dB. Similar
birefringence modification method was also applied in a Mach-Zehnder
interferometer configuration to form polarization splitters and filters [33].(a) A top view of the fabricated
wavelength-independent zero-order AWG polarization splitters and insert expanded SEM image
of the oxide cladding patch in the waveguide array. (b) Measured transmission
as a function of wavelength of a zero-order AWG-based polarization splitter.
(a)(b)


## 4.1. Polarization-Independent AWGs

In AWGs,
the polarization-dependent wavelength shiftΔλ=λTM−λTE mainly  arises from the
birefringence of the arrayed waveguides and can be expressed as Δλ≈λΔneff/ng, where ng is the waveguide group index and λ is the
operating wavelength in vacuum. The AWGs used
for this demonstration of polarization compensation using stress engineering
were made on SOI substrates with a silicon thickness of 2.2 μm, with 9
output channels spaced at 200 GHz, and centered at 1550 nm [8, 13, 17] (see Figure 6(a)). The arrayed waveguide gratings of order 40 were formed by 100 waveguides
of width 2 μm. Waveguides were produced using both wet and dry etching methods,
yielding ~54° and nearly vertical sidewall angles, respectively. Waveguide
birefringence simulations were performed using measured waveguide dimensions.
Upper cladding oxide films of different thicknesses were deposited at ~400°C
using PECVD, with a film stress of σfilm = −320 MPa
in the blank films, measured from wafer bowing. Figure 6(b) shows the
calculated and measured dependence of Δλ on the
cladding thickness tc, for both trapezoidal and rectangular
waveguides. Calculated results agree well with experiments for both types of
waveguides, showing that Δλ can be
modified over ~2 nm wavelength range [16]. Figures 6(c) and 6(d) show the
TE and TM spectra of a wet-etched AWG before
and after polarization compensation. The adjacent channel cross-talk is less
than −25 dB. The noncompensated AWG device has a polarization-dependent
wavelength shift of Δλ~0.6nm (Figure 6(c)), arising from the geometrical
birefringence of Δngeo~−1.3×10−3 in the
arrayed waveguide. With an oxide upper cladding film of −320 MPa in stress and 0.6 μm in
thickness, the Δλ was then
reduced to below 0.04 nm for all channels (corresponding to Δneff<1×10−4) (Figure 6(d)). The polarization dependent
loss (PDL) was also found to be negligible in these devices after the
compensation.(a) Optical
image of a fabricated AWG. (b) Polarization-dependent wavelength shift Δλ as a function of the cladding
thickness tc, for AWGs fabricated using wet (waveguide top width W1 = 1.1 μm and bottom width W2 = 3.8 μm) and dry (W1 = 1.85 μm and W2 = 2.0μm) etching to a depth
of D =1.47 μm. The cladding stress is σfilm = −320 MPa. Measured spectra for
an SOI AWG. (c) Measured spectrum for an SOI AWG without the oxide upper cladding. (d) Compensated using a 0.6 μm thick SiO2 claddings with σfilm = −320 MPa. TM (solid) and TE
(dashed).


## 4.2. MMI-Coupled Polarization-Independent Ring Resonators

We also applied the stress engineering
technique to achieve polarization-insensitive ring resonators [18, 19]. Ring
resonators have been used as the building blocks in applications including
add-drop, switching, modulation, and sensing [24–27]. However,
polarization sensitivity is often an obstacle that limits their practical use
[12, 15, 18].The power transmission in the bus waveguide
of a single coupler
ring resonator (Figure7(a)) can be obtained by a generalization of the ring
resonator equations to incorporate the coupler loss [18, 28]:  (3)|T|2=αMMI2[α2−2αtcosϕ+t21−2αtcosϕ+α2t2],where ϕ is the total round trip phase accumulation,
and α2=αMMI2⋅αring2 is the combined
power loss factor including both the ring loss and the coupler loss. The
self-coupling coefficient t2 is the ratio of power transfer from the
input to the output port 1 of the multimode interference (MMI) coupler, as
indicated in Figure 7(b). The resonance extinction ratio is maximum at α2=t2, which is referred
to as the critical coupling condition. A series of transmission minima occur at
wavelengths λm for which the round-trip phase accumulation is integer multiple of 2π. It is apparent that a polarization dependence in the
coupling coefficient t and/or the loss factor α lead
to different resonance quality factors and linewidths for TE and TM input
polarizations. If the waveguides are birefringent, the round trip phase
accumulation ϕ varies with the polarization, and the
resonance wavelengths and free spectral range (FSR) are polarization sensitive.
To achieve polarization independence in a ring resonator, all these factors
need to be addressed.(a) A ring resonator with an MMI coupler. (b) A schematic of the MMI
structure.
(a)(b)Polarization-independent
ring resonator designs using directional couplers have been investigated [12],
but showed long coupler length and very stringent fabrication requirements. We
proposed the use of MMI couplers to achieve polarization-independent light
transfer between the resonator bus and the ring waveguides (Figures 7(a) and 7(b)).
For simplicity, we have chosen the commonly used 2×2 restricted interference coupler with a 50 : 50
splitting ratio between the two output ports [29]. The coupler width is WMMI=3D, where D is the center-to-center separation between the access waveguides
(Figure 7(b)). The resonators are designed with the following ring and access
waveguide dimensions: ridge height H = 1.5 μm, width W = 1.5 μm and 1 μm, and
etch depth H−h = 0.9 μm. A separation of D = 2.5 μm between the access waveguides
is used in the MMI design, based on the considerations of a compact footprint
and ease of fabrication, yielding an MMI width of WMMI = 7.5 μm. The
quality factor of a resonator is determined by the coupler splitting ratio and
the loss in the resonator cavity. MMI designs with variable splitting ratios
have been proposed and demonstrated by other groups and may be used for high-quality
factor resonators [30, 31].The optical field
distribution in the2×2 MMI coupler is shown in Figure 8(a), while Figure
8(b) shows the MMI coupler transfer characteristics in terms of the normalized
power coupled to the fundamental mode in ports 1 and 2, respectively, as a
function of the coupler length. For each polarization, a splitting ratio close
to 50 : 50 is achieved over the range of coupler length LMMI from 82
to 86 μm, with a coupler imbalance of ≤0.05dB. The combined power in the two outputs is the total transmitted power αMMI2, which indicates the
loss through the coupler (with αMMI2 = 1 being
lossless). The optimum coupling length differs by ~2.5μm (or ~3%) between
the two polarizations. As a first approximation, a coupler length of LMMI = 84 μm at the crossing point is used in all our resonator designs, where a
similar excess loss of ~−0.2 dB is found for both polarizations. This
choice is based on the assumption that losses from all other mechanisms are
similar for TE and TM, which is not necessarily the case. In addition to the
coupler excess loss, there are several other mechanisms contributing to the overall
resonator loss. For example, the waveguide propagation loss due to scattering
depends on the optical mode overlap with the roughness at the waveguide
boundaries and is generally polarization dependent. This loss is proportional
to the propagation distance, and therefore to the cavity length of a ring
resonator. Another source is the radiation loss in waveguide bends, as well as
possible losses at discontinuities such as the junctions between the straight
and curved waveguides. These factors need to be considered in the device
design, and detailed discussions can be found in [19].(a) Optical field
distribution in the SOI MMI coupler of7.5μm×84μm in dimensions, with an etch depth of 1 μm. (b) Corresponding normalized power in the
fundamental mode in ports 1 and 2, for the TE and TM polarizations.
(a)(b)Since the stress in SOI waveguides
caused by the cladding layer can be used effectively to control the
birefringence over a wide range, it can be applied to eliminate the polarization
dependence in the ring phase accumulationϕ. The phase
change in the MMI section is 2πneffMMILMMI/λ, plus a constant correction factor which is a multiple integer
of π/2 [32]. Since the stress-induced birefringence
in the ring waveguide Δnsring is much larger
than that in the wider MMI section [16] (i.e., ΔnsMMI≪Δnsring), the difference
in the phase accumulation Δϕ between TM and TE polarizations can be
expressed as [18]:
(4)Δϕ=2πλ[ΔngeoMMILMMI+ΔngeoringL1+ΔnsringL1].Here L1 is the total
length of the narrower ring waveguide sections, L1=L−LMMI=2πR+LMMI. Figure 9 shows the ring resonator phase
difference  Δϕ=ϕTM−ϕTE as a function of the oxide
cladding thickness for two cladding stress levels. Obviously, various
combinations of cladding stress and thickness can be found to adjust  Δϕ to zero.Figure 9
Phase differenceΔϕ=ϕTM−ϕTE as a function of the
oxide cladding thickness for an MMI-coupled ring resonator with a radius R of
200 μm and an oxide cladding stress of −220 and −250 MPa, respectively.We have fabricated MMI-based ring
resonators in SOI wafers with 1.5μm thick silicon at the Canadian Photonics
Fabrication Center (CPFC). SEM images of a fabricated device are shown in Figures 10(a) and 10(b). Standard inhouse PECVD process produces oxide films with −250 MPa stress. Measured transmission spectra
for a MMI-coupled ring resonator with a radius of 200 μm are shown in Figure 10(c) for TE and TM
polarizations. Over the 4 nm scan range, the polarization-dependent wavelength
shift is below 2 pm, which is the laser scan step used in these measurements.
The measured free spectral range (FSR) is ~0.46nm, and the quality factor is Q
~ 15,000. Polarization insensitive operation is achieved in these resonators,
demonstrating the effectiveness of the proposed method for polarization control.(a) SEM image of an MMI-coupled ring resonator. (b) A closeup of the MMI
section. (c) TE and TM transmission spectra of the ring resonator, with an
upperSiO2 cladding of 0.8 μm thick and film stress of σfilm = −250 MPa.


## 4.3. Broadband
Polarization Splitter in a Zero-Order AWG Configuration

Stress-induced
effects can also be used to produce high level of birefringence in selected waveguide
areas. Since the stress-induced index modifications are several orders of
magnitude smaller than the core-cladding refractive index contrast in SOI, the
effect of aSiO2 cladding on mode shape is negligible. Thus there is
little mode mismatch loss or polarization-dependent loss at the junctions
between waveguide sections with and without the cladding. Figure 11 shows a
zero-order AWG where all of the arrayed
waveguides have identical geometrical path lengths [20]. A triangular patch of oxide cladding is placed in the
arrayed waveguide section with a constant length increment ΔL between the adjacent waveguides. The stress
in the waveguide cladding induces a polarization-dependent phase difference in
the light signal propagating in the waveguide array (see Figure 4(a)), causing a
polarization-dependent tilt in the phase front of the light in the free
propagation region (FPR) (see Figure 11(b)). Since all waveguides have the same
physical length, the phase difference for light propagating in the adjacent waveguides
of the arrayed section depends solely on the cladding stress-induced index
change and the patch-length increment. Since the stress-induced index change in
the TE and TM polarization modes has opposite signs for silicon waveguides, the
two modes are spatially displaced in the opposite directions in the focal
region relative to the free propagation region centerline, as shown in Figure 11(b).
With proper placement of the two receiver waveguides along the focal plane, the two
polarizations are spatially separated.Figure 11
(a) Schematic layout of a broadband zero-order
AWG polarization splitter. (b) Geometry of the output FPR with a Rowland
circle configuration.Zero-order
AWG-based polarization splitters were designed and fabricated on SOI wafers,
with a 2.2μm thick silicon core layer. The deposited oxide
cladding film had a thickness of 1 μm, and the measured cladding film stress was
approximately −340 MPa. The overall device size is ~12mm×4mm.
Figure 12(a) shows several fabricated AWG devices with triangular cladding
regions of varied patch sizes. Based on the measured cladding film stress and
thickness, the cladding patch-length increment ΔL between the adjacent
waveguides was set to 16.4 μm to produce the required polarization-dependent
phase front tilt at the output of the waveguide array. Since stress-induced
effects do not vary with wavelength appreciably, and the AWG operates close to
zero order, the performance of the splitter is expected to be wavelength independent
over a large application bandwidth, which was experimentally confirmed. The measured
extinction ratio of the polarization splitter was better than −10 dB for both
output polarizations over the entire tuning range of our laser (1465–1580 nm). Figure 12(b) shows the measured polarization splitter transmission for a wavelength
range of λ = 1537 to 1557 nm. Over this range, the splitter extinction
ratio is <−15dB. The best extinction ratio achieved was −20 dB. Similar
birefringence modification method was also applied in a Mach-Zehnder
interferometer configuration to form polarization splitters and filters [33].(a) A top view of the fabricated
wavelength-independent zero-order AWG polarization splitters and insert expanded SEM image
of the oxide cladding patch in the waveguide array. (b) Measured transmission
as a function of wavelength of a zero-order AWG-based polarization splitter.
(a)(b)


## 5. Summary

We have reviewed the stress-induced modifications
of the  waveguide effective index for the TE and TM modes and the associated birefringence
which are important for a wide range of commonly employed SOI waveguide
geometries. The significance of these stress-induced effects is now being recognized
in the research community and applied in component development. If not taken
into consideration, these effects can lead to large deviations in device
characteristics from the designed specifications. Fortunately, the use of
cladding stress to correct the waveguide birefringence allows a considerable
degree of freedom in designing SOI waveguides to meet other performance
criteria such as relaxed dimensional tolerance, reduced loss at waveguide bends,
and overall improved device performance. This technique is simple to implement,
and there are no additional process steps required other than the conventional
cladding layer deposition. The stress-induced modifications to the effective
index in SOI waveguides are readily controlled by the stress level and the
thickness of the upper-oxide cladding. We have demonstrated that cladding stress
engineering can be used to achieve polarization insensitivity in AWGs,
spectrometers, and ring resonators, leaving the freedom of optimizing the
waveguide geometry for considerations other than the birefringence. Since the effect of theSiO2 cladding on the mode
profile is negligible, there is little mode mismatch loss or polarization-dependent
loss at the junctions between waveguide sections with and without the cladding.
Therefore, tailored cladding patches can be applied at discrete locations
in a planar waveguide circuit with negligible insertion loss and PDL penalty,
as we demonstrated in the example of a broadband polarization splitter. The
applications of cladding stress-induced effects can be envisioned in a variety
of situations to enhance device functionality, simplify fabrication, and
improve operation tolerance.



---

*Source: 689715-2008-06-22.xml*