# Synthesis of Planar Reflective Gratings for  Silicon Interconnects

Authors: Ronald Millett; Jamie Ramsey; Przemek Bock; Julie Nkanta; Henry Schriemer; Trevor J. Hall; Serge Bidnyk
Journal: Advances in Optical Technologies
 (2008)

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## Abstract

The design and simulations of planar reflective gratings for building optical interconnects in silicon-on-insulator (SOI) were studied for a range of silicon core thicknesses of 0.1 to 10μm. The verticality of the grating facets has been shown to be the main contributing factor to the cumulative
crosstalk  in thick silicon cores. The dispersion property of the slab was found to limit the minimal thickness of the core for polarization-insensitive gratings. The effects of polarization-dependent confinement on optical crosstalk were studied. The findings were used to design and simulate a polarization-insensitive 18-channel coarse wavelength division demultiplexer (CWDM) with a free spectral range of over 600 nm. The CWDM demultiplexer uses a 1.7 μm silicon core and combines a shallow-etch tapered rib structure and multimode silicon channels to produce box-like passbands for integrated receiver applications. The diffraction grating was constructed using double astigmatic point design with phase-corrected grating facets to reduce astigmatism. Optical properties of the planar gratings have been simulated using quasivectorial diffraction grating theory. The simulation results confirm that there is high diffraction efficiency and low optical crosstalk over the entire range of operation. Applications of planar silicon gratings to the synthesis of silicon interconnects are discussed.


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## Body

## 1. Introduction

Over
the past several
decades, data transfer rates over electronic interconnects
have been increasing exponentially following Moore’s law.
The clock speed of silicon-based electronic processors has reached
microwave frequencies of over 4 GHz causing severe problems with the signal
integrity of electronic interconnects. At these frequencies, traditional
stripline interconnects suffer from a fundamental cross-coupling penalty and large
radiation losses. The research in silicon photonics has been driven primarily
by the objective of overcoming the limitations of stripline interconnects. Recently,
several key elements, including silicon lasers, modulators, and photodetectors,
have been realized in silicon using low-cost CMOS-compatible processes
[1, 2].
Further research in silicon-on-insulator (SOI) shows promise for implementing additional
key functionality—demultiplexing—to enable wavelength division multiplexing and
transferring data over multiple channels.
The high index contrast of SOI waveguides also permits smaller device
footprints compared to more weakly guided material systems.Due
to performance limitations, arrayed waveguide grating- (AWG-) based
demultiplexers in SOI have not been able to compete effectively with silica-based
AWGs. Porting AWG technology directly from silica to SOI has been a challenge, mainly
due to high waveguide propagation losses, limited spectral range, strong
polarization dependence, and poor optical crosstalk arising from phase noise in
the delay line region of SOI-based AWGs [3].
In order to overcome AWG limitations in SOI, several research groups have
explored the possibility of using planar reflective gratings as an alternative
to AWGs. To generate diffraction, planar reflective gratings, also known as
Echelle gratings, rely on the optical properties of a 2D silicon slab as
opposed to a phase array of waveguides in AWGs. SOI-based planar reflective
gratings have now been realized with SOI core thicknesses of 0.22 μm [4],
3 μm [5],
and 5 μm [6].
These initial studies are very promising and demonstrate that on-chip insertion
losses of less than 2 dB are readily achievable in both thin and thick core SOI-based
planar gratings [4, 5].In
this paper, we theoretically explore the optical properties of planar reflective
grating demultiplexers based on silicon cores of various thicknesses. We show
that the thickness of the silicon core layer has a profound effect on the polarization
and crosstalk performance of the SOI grating. The results of our findings were
used to synthesize a polarization-insensitive 18-channel coarse wavelength
division demultiplexer (CWDM) with box-like responses based on a planar
reflective grating. The device combines a shallow-etch tapered rib structure
and multi-mode silicon channels. The grating was optimized to reduce aberration
effects. The polarization-insensitive performance of the demultiplexer was
confirmed using quasi-vectorial diffraction theory. Applications of planar
reflective gratings to building silicon interconnects are discussed.


## 2. Planar Reflective Grating Design

The
success of AWGs in meeting the requirements of the multichannel demultiplexer
market has been largely due to the silica platform where AWGs can be fabricated
using shallow etched waveguides in a relatively simple fabrication process. In
spite of a considerably smaller footprint, the fabrication of planar reflective
gratings in silica was more complex compared to AWGs and required additional
research into controlling the verticality and smoothness of the reflective facets.
Contrary to silica, there are a number of well-established processes for
producing deep, smooth, and highly vertical-etched structures in SOI. One of
the key advantages of planar grating devices compared to free-space bulk
gratings is that they are lithographically produced and any grating shape is
readily achievable. Techniques for etching silicon have benefited from recent
advancements in the fabrication of microelectromechanical systems. Planar
reflective gratings in SOI have the potential for monolithic integration with
large-scale electronic-integrated circuits.An
SOI-based planar grating uses a variety of input and output structures, as
shown in Figure1. In a rib-waveguide SOI structure, the fundamental mode of the
waveguide is asymmetrically positioned below the center of the slab core. In
order to improve the waveguide-to-slab coupling, the input waveguide is usually
tapered at the entrance to the slab region. In the slab, the light remains
confined in the vertical direction but expands horizontally until it encounters
a series of reflectors. The grating not only diffracts but also refocuses the
light into the output waveguides, as shown in Figure 1.Figure 1
Architecture of the planar
reflective grating in a silicon-on-insulator optical interconnect. A shallow
etch (0.5μm) defines the input structure, whereas a deep etch (1.7 μm) defines
the output waveguides and grating facets.The
lithographic approach to making planar gratings carries little design
restrictions on the shape of the launching mode or the shapes of the diffracting
elements. Such flexibility in planar grating design has recently resulted in the
successful demonstration of planar gratings with facet widths varying from 4 to
1000μm [4, 7].
Diffractive elements in SOI can be created by either a single
dielectric-to-metal interface [5], a reflective dielectric stack [8],
or using total-internal reflection facets [6].The first planar reflective gratings were realized using the Rowland
configuration [9].
Research into novel grating designs has since yielded a methodology for eliminating
the aberration effects caused by grating facets [10].
Subsequently, a mechanism of compensating for the dispersion of the refractive
index of glass has been discovered, resulting in the successful demonstration
of interleavers [7].A
comparative analysis of both planar reflective gratings and arrayed waveguide
gratings recently performed by Cheben found that the traditional scalar
approach to the simulation of planar gratings is unable to reconcile simulated
and measured data [11].
Numerical difficulties posed by the large number of diffraction orders, deep
triangular grooves with high blaze angles, and small wavelength-to-grating
pitch ratios have made the calculation of diffraction efficiency one of the
most intractable problems of electromagnetic theory.Until
a decade ago, simple relationships between fundamental grating parameters, such
as diffraction order, diffraction angle, resolving power, Rowland circle
radius, grating pitch, were deemed sufficient to model planar reflective
gratings. The linear dispersion strength of a planar grating can be readily computed
through the angle of incidence,α,
and reflected angle, α′ [12]:(1)L∂α′∂λ=Lsin⁡α+sin⁡α′λcos⁢⁡α′[1−λn∂n∂λ], where L is the length of the slab region.
Theoretically, it is possible to use infinite permutations of diffraction
angles and slab lengths to produce gratings with almost identical
characteristics. However, in practice, researchers have realized that
theoretically equivalent gratings can exhibit vastly different performance
characteristics.Vector diffraction theories that
replaced the traditional scalar approach revealed that the shape and
metallization of the grating facets affect both the grating efficiency and
polarization sensitivity. Delâge and Dossou [13]
solved Maxwell’s equations in proximity to the grating facets using a finite-element
method and matched their numerical solution near the grating surface to a
Rayleigh expansion. Their work showed that metallization had a profound impact
on the absolute and relative grating efficiencies of both TE and TM polarized
light.The design of planar gratings in SOI
requires careful studies on the effects of silicon core thickness and grating
verticality on the polarization dependence and optical crosstalk. Particular
consideration should be given to the selection of diffraction angles for the
planar grating in SOI.


## 3. Polarization Dependence of Planar Gratings

The
polarization dependence of the wavelength (PDW) has different origins in AWGs
and planar reflective gratings. PDW in an SOI-based AWG is predominantly caused
by waveguide birefringence in the phase array region. Contributing factors to the
waveguide birefringence include waveguide cross-section variations and stress. Both
of these factors can be used to eliminate modal birefringence in SOI-ridge
waveguides [14].
Consequently, the selection of proper waveguide dimensions and cladding layers
is essential for improving the PDW performance of AWGs.Contrary
to AWGs, the PDW of SOI planar waveguide gratings depends only on birefringence
of the slab and not the waveguides. The geometry of waveguides can be selected
independently, thus providing additional design flexibility in optimizing other
planar lightwave circuit subcomponents, such as fiber-to-waveguide mode converters
and bend waveguide regions.The
modes of an asymmetric slab waveguide can be found using analytical expressions
that assume that the waveguide is infinite in the transverse direction [15].  The three layers of the infinite asymmetric
slab waveguide are a cladding layer of air (n0=1), a core layer of silicon (n1=3.48), and a substrate layer of SiO2(n2=1.445).  The
thickness of the cladding and substrate layers are assumed to be infinite in
these calculations, a good approximation due to the strong modal confinement in
the high-index silicon core.  The
equations for the TM mode are found using the duality relationships between TE
and TM electric and magnetic fields. The computation was performed for a
wavelength of 1.55 μm.The
results of the effective index computations are shown in
Figure2 (left axis).
The effective index of the fundamental slab mode in a silicon core has been
found to depend strongly on the core thickness, due to the high index contrast
of SOI. The birefringence of the slab waveguide becomes greater as the core
thickness decreases, with only the TE mode propagating at core thicknesses of
<0.12 μm. In silica, researchers  have found a way of eliminating the slab
birefringence through a use of a compensator region [16].
In SOI,
the amount of birefringence is orders of magnitude larger.Figure 2
(i) Dependence of the
effective refractive index of the fundamental mode on the core thickness of the
slab for TE- and TM-polarized lights (left axis); and (ii) polarization
dependence of the wavelength as a function of the slab thickness (right axis).Polarization
compensation in SOI is possible for a range of core thicknesses using, for
example, the approach described in [16]. The difficulty associated with this
approach is that a large mode profile mismatch between the slab and compensator
regions can excite undesirable higher modes. This problem has been solved by
Cheben et al. using silicon-oxide-silicon
compensators that can provide sufficiently strong birefringence correction with
minimal field profile mismatch [17, 18].The
present manuscript is limited only to the consideration of planar gratings
containing no polarization compensators. The design and architecture of
compensators is a subject of our present research in this field. A strong slab birefringence
has a profound effect on the optical properties of silicon interconnects based
on planar reflective  gratings.
In Figure2 (right axis), we have computed the
amount of PDW that is caused by slab birefringence. The data clearly shows
that, in devices with a silicon core thickness of <1 μm (PDW=λ⋅Δn/n>10⁢nm), it is not possible to achieve
polarization-independent performance for most practical applications. In a
different approach, it has been suggested that the polarization diversity
scheme can potentially be applied to overcome the polarization dependence of
reflective interconnects [19].
This, however, would likely lead to doubling the number of optical and
electronic subcomponents and would also require integrating polarization
splitters and combiners. The complexity of the polarization diversity scheme
will likely outweigh the benefits of silicon photonic integration for the
majority of applications that require polarization insensitivity.In
addition to PDW, SOI-based devices also experience polarization-dependent loss
(PDL). Nanometer-scale sidewall roughness is the prime cause of polarization-dependent
waveguide loss in silicon waveguides [20].
In AWGs, PDL primarily arises from different waveguide propagation losses
associated with the two polarizations in the phase array region. Planar
reflective gratings, in contrast, require no phase-array waveguides, but rather
a slab region that can be made polarization-insensitive. However, PDL does
arise due to the presence of nonreflecting sidewalls between adjacent grating
facets. The approach to reduce this source of PDL will be discussed later in
this manuscript.


## 4. Optical Crosstalk

Optical
crosstalk also has different origins for AWGs and planar reflective gratings. In
AWGs, the theoretical crosstalk limit depends on the number of waveguides (the
Gaussian field truncation) and waveguide phase errors. The Gaussian field
truncation can be overcome by merely increasing the number of waveguides in the
phase array region. However, controlling the phase noise in SOI waveguides is
very challenging. Even nanometer-scale variations in the waveguide geometry
leads to severe phase distortions. Phase error noise in SOI typically results
in optical crosstalk values unsuitable for most applications [3]. This
limitation underscores the difficulty of implementing the AWG architecture in
SOI.Planar
reflective gratings offer the unique possibility of overcoming the crosstalk
limitations of the SOI platform. The optical crosstalk of planar reflective
gratings is not degraded by waveguide geometry phase errors since diffraction occurs
in the slab region. The slab region typically has a high refractive index and
thickness uniformity. The two main contributors to optical crosstalk in planar
gratings are grating anomalies and facet verticality. A numerical model which
simulates the spectral characteristics of the demultiplexer including grating
anomalies due to the pixilation effect, random stage movement error, and gain
error has already been established and discussed in the literature [21].
In this study, we primarily examine the effects of grating verticality on the cumulative
optical crosstalk.In
a multichannel demultiplexer, the cumulative optical crosstalk arising from a
grating facet tilted byθ degrees from the vertical can be computed by
considering the phase distortion of the mode reflected from the facet. For the
TE mode (and similarly for the TM mode) the mode reflected from a tilted
interface, Etilted,  is given by the input fundamental slab mode, Eslab, multiplied by a
phase-shifting factor(2)Etilted=Eslabei2βytan⁡θ, where y is the coordinate in the growth
direction and β is the slab mode propagation constant.  Crosstalk originates from the fact that the
reflected mode does not perfectly couple with the fundamental slab mode, and
the uncoupled portion of the light can contribute to the crosstalk. Assuming
that all fields are normalized, the amount of cumulative crosstalk can be
estimated by calculating the coupling loss between the reflected mode and the
fundamental slab mode (wavelength dependence is implicit):(3)ηTE=1−|12∫−∞∞Ey,slabHx,tilted*dx|2,ηTM=1−|12∫−∞∞Ex,slabHy,tilted*dx|2.This gives the worst case crosstalk estimate, as some of the reflected mode may
couple to radiation modes and not contribute to the crosstalk. In multichannel
planar grating demultiplexers, the spectral response from each channel, including
side-lobes and other crosstalk limiting features, is very similar if channels
are spectrally shifted by the amount of channel spacing and overlaid [12]. Higher-order
slab modes have different propagation constants and will generally diffract at
different angles, focusing at spatially different locations along the Rowland
circle, resulting in “ghost peaks” appearing in the other channels.
Effectively, each channel will experience crosstalk from a different spectral
window coming from every other channel. Thus, the cumulative optical crosstalk
can be estimated by either adding together crosstalks in different spectral
windows from all the channels, or alternatively performing a spectral integral
of crosstalk coming from a single channel, as given by the above formulas.The
results of our simulations are shown in Figure3. Each curve shows the maximum
vertical tilt angle of the grating permissible for a given silicon core thickness
so as to maintain a particular amount of cumulative crosstalk, from −10 dB to
−40 dB.  From
Figure 3, silicon cores
with a thickness of ~0.3 μm are capable of withstanding the largest grating
facet tilt with the smallest amount of crosstalk. For thicker silicon cores, crosstalk
values become unacceptable even for relatively vertical grating facets (e.g., crosstalk ηTE≈ηTM=−15⁢dB for core thickness of 5 μm and a tilt
angle of θ=0.5∘).Figure 3
Cumulative optical crosstalk as a function of
silicon core thickness and facet tilt angle (relative to vertical) for
different isolation requirements. In order to achieve−30 dB isolation in
1.7-μm-thick silicon slab, the verticality of facets should be controlled to
within ±0.4 degree.Figure3 also shows the polarization
dependence of the cumulative crosstalk. For thinner cores (<0.2 μm),
TM-polarized light is more sensitive to the facet tilt angle, while for larger
core thicknesses TE-polarized light is more sensitive.  For reflective gratings with thick cores
(>10 μm), the TE- and TM-polarized modes are both equally highly sensitive
to the tilt angle.  These results can be
explained by examining the confinement of the optical mode.  As the optical power in the mode becomes more
diffuse in the vertical direction, the edges of the modal field experience a
greater phase shift according to (2), and the mode will become more sensitive
to grating verticality.  The peaks in
Figure 3 occur at core thicknesses where the TE or TM mode is the most
vertically confined.Figure4 shows the confinement in the silicon core of the TE- and TM-polarized
mode.  For thinner cores, where the modes
are only weakly guided, the TM mode is much less confined than the TE mode,
resulting in a greater sensitivity to the tilt angle.  As the core thickness increases, the
TM-polarized light becomes more confined than TE-polarized light, and hence
less sensitive to the tilt angle.  At
core thicknesses above 1 μm, both TE- and TM-polarized modes are almost
entirely confined in the core, and the width of the mode field in the vertical
direction increases as the core thickness increases.  This results in a high sensitivity to the tilt
angle at large values of the core thickness.Figure 4
Confinement factor in the
core layer of TE- and TM-polarized lights versus thickness of the core layer.It is advantageous to use the thinnest
possible core that provides acceptable PDW values (see
Figure2). Thus, the
selection of the core thickness has to be done in conjunction with a specific
application. Irrespective of the core thickness, the ability to etch nearly
vertical grating facets is essential in minimizing the insertion loss and
reducing the optical crosstalk of planar reflective gratings.


## 5. CWDM Demultiplexer Design

We
have applied our findings to design an SOI-based CWDM demultiplexer suited for
use in integrated receiver applications. The CWDM grid is made up of 18
wavelengths defined within a range of 1270 nm to 1610 nm, spaced by 20 nm [22].
CWDM can support various topologies of interconnects—hubbed rings, point-to-point, and passive optical
networks with transmission distances of up to 50 km. The CWDM receivers often
require larger bandwidths that can capture all the specified bitrates and
protocols. We assume that our CWDM demultiplexer is used in conjunction with wavelength
agnostic PINs or avalanche photodiode detectors (APDs) that operate over the
entire ITU CWDM band.On the transmitter side, polarization control is not necessary since laser diodes
are strongly polarized. However, on the receiver side, the incoming signal polarization
is not known a priori, consequently,
receiver demultiplexers should be sufficiently polarization insensitive. From
Figure2, it is  apparent  that to have sufficiently low polarization dependence (PDW
< 2 nm) in a planar reflective grating containing no polarization
compensators, the silicon core thickness should be no less than 1.7 μm.  On the other hand, for the best crosstalk
performance, Figure 3 suggests that the core thickness is as small as possible.
Therefore, to construct the CWDM receiver, we selected the nominal core
thickness of 1.7 μm.The
rib waveguide geometry was chosen to be single mode according to the modified
criterion of Soref et al. [23].  Single-mode operation was confirmed with a
full-vectorial finite-element method.
The nominal ridge width was chosen to be 1.5 μm with a ridge depth of
0.5 μm.  The TM mode profile for this
structure, generated using finite-element analysis, is shown in
Figure 5.Figure 5
The TM mode profile of the
input rib waveguide of the CWDM demultiplexer. Birefringence of the waveguide
does not contribute to the polarization dependence of a planar reflective
grating.The
high-contrast silicon slab considered here supports a large number of higher-order
modes. Consequently, special consideration should be given to the design of the
input taper to prevent higher-order mode excitation. If higher-order modes are
unintentionally excited, it will inevitably lead to the presence of ghost peaks
in the output guides even if the grating facets are perfectly vertical. To overcome
the higher-order mode excitation, the input waveguide incorporates a linear
taper that adiabatically increases the rib width from 1.5μm to 4 μm over a
length of 2000 μm. The length of the slab region was chosen to be 6200 μm. The
slab length is selected to achieve sufficient linear dispersion (as given by (1))
to accommodate the width and separation between the output waveguides.The
selection of the diffraction grating order is dictated by the requirements
imposed by the free spectral range (FSR)
of the device. In general, the overlap between different orders is determined
by(4)(N+1)λ1=Nλ2. In order to accommodate all 18 channels spaced at 20 nm, as required for a CWDM receiver, Δλ=λ2−λ1 should be more than 400 nm. Such a wide-free
spectral range demands the diffraction order to be N = 1, yielding a free spectral range of over
600 nm. While low-diffraction order devices are easily achievable using the
planar reflective grating technology, realizing such wide-free spectral range
device using the AWG architecture would require an impractically large phase
array region that would have severe crosstalk limitations in SOI.The
Rowland circle configuration was chosen as a zero-order approximation to the
position of refractive elements and the plane of the input and output
waveguides. The first-order correction was obtained through the use of standard
double-astigmatic point improvement to the position of the grating facets [11].
In our case, we chose 1270 nm and 1610 nm as astigmatic wavelengths to
compensate for the reduced diffraction efficiency in the end channels. The
energy of light diffracted by the grating was optimized by selecting a blaze
wavelength of 1440 nm.Careful consideration should be given
to the selection of diffraction angles for the planar grating in SOI.
Traditionally, planar reflective gratings in SOI have been selected to have incident
and reflected angles of around 40 degrees [4, 6]. However, building a wide-free
spectral range CWDM demultiplexer at such large diffracting angles would lead
to suboptimally shaped grating facets that are susceptible to corner rounding
and polarization dependence.  While it is
possible to remove reflective material from the nonreflective facets to improve
the grating efficiency, this would require additional postprocessing steps such
as selective metal etch removal.The reduction in the planar grating
diffraction efficiency due to corner rounding is approximately equal to the
ratio between the size of the round corner and the size of the reflective
portion of the facet. It is advantageous to have the size of the reflective
facet much larger compared to the corner rounding. Furthermore, the ratio of
the reflective to nonreflective facet has been shown to be the key for overcoming
PDL in planar reflective gratings [24].
Consequently, the diffraction angle should be low enough to produce
sufficiently wide reflecting facets for ease of manufacturing, while keeping
the size of the nonreflecting facets small enough to eliminate corner rounding
and polarization effects.Our
analysis of the grating parameters yielded a value of 3.5 degrees for the angle
of diffraction. At this diffraction angle, an average size of the reflective
facet is 3μm while the nonreflecting sidewall is only 0.2 μm. This results in
the aspect ratio of the reflecting to nonreflecting facet of 15 : 1, putting a
limit of −0.3 dB on the maximum diffraction efficiency loss due to corner
rounding. The total number of facets was chosen to be 600. This ensured that
well over 99% of the light from the input waveguide is captured by the grating.
Each grating facet was chosen to be an elliptical shape to further reduce
aberration effects. Details of aberration reduction are described in [10].To
achieve a box-like channel profile for the CWDM demultiplexer, the output
waveguides are formed using a 1.7-μm-deep etch with a waveguide width of 8 μm
and a separation between waveguides of approximately 4 μm (see
Figure 1). This
output waveguide structure can support a large number of modes. Since the
proposed device is specifically designed for use in receiver applications, we
assume that the active area of the photodetector is sufficiently large to
absorb all of the light in the multimode guide.To simulate the grating performance, we
used a full-vectorial finite-element method to compute the modes of input and
output guides. An asymptotic approximation for Hankel functions of large
argument was then used to obtain the intensity on the grating facets. This
approximation was used once again to obtain the reflected fieldΘ(λ) on the plane of the output waveguide structures. The demultiplexer
transmission intensity at a specific wavelength was obtained by a convolution
of the diffracted light with the intensity profile of each individual mode φi(λ) in each output multimode output waveguide:(5)T(λ)=∑i〈Θ(λ)∣ϕi(λ)〉.The results of our simulation are
shown in Figure6 for TM polarization. It is worth pointing out that the
diffraction efficiency at the end channels is as strong as the efficiency of
the central channels. This was possible by our selection of the blaze
wavelength of the planar grating to be in the middle of the free spectral range,
and the use of the end wavelengths for astigmatic points. Crosstalk values of
better than −35 dB have been computed for all 18 channels. The 0.5-dB spectral width
of an individual channel was estimated to be 16 nm. Considering that this
device has a projected PDW of 2 nm due to the slab birefringence, centering the
wavelength between the two extreme polarizations can potentially yield 15 nm of
useful bandwidth for each individual channel. Such wide spectral passbands can
be useful for transmitting large-bandwidth data while still allowing for the
temperature drift of the demultiplexer and the transmitter laser diodes. This
work confirms that planar reflective gratings in SOI can be used to achieve
both wide-free spectral range and polarization-insensitive performance.Figure 6
Transmission spectra
of an 18-channel CWDM demultiplexer for TM polarization. No decrease in the
diffraction efficiency was observed for the end channels. Optical crosstalk of
better than−35 dB was achieved.Multiplexing
and demultiplexing light is only one of many possible applications of planar
reflective gratings in silicon interconnects. Planar reflective gratings can
also be used in add-drop filters, repeaters, dispersion compensators, and gain
equalizers. Because of their reflective nature, planar gratings can be very
effective in stabilizing laser sources through wavelength locking. Additional
applications of planar gratings will likely be found in optical clocking
through the use of time domain to frequency domain interferometry in silicon
interconnects.


## 6. Summary

In
summary, we have investigated the optical properties of planar reflective
gratings for building optical interconnects in silicon on insulator for various
silicon core thicknesses. We have shown that the dispersion of the slab can be
controlled through the core thickness selection to produce polarization-insensitive
gratings. The verticality of the grating facets has been found to be the main
contributing factor to the cumulative crosstalk in thick silicon cores. Our
findings were applied towards the design and simulation of an 18-channel coarse
wavelength division demultiplexer that has both a wide-free spectral range and
polarization-insensitive performance. These results demonstrate that planar
reflective gratings can become an essential element in building many silicon
photonics applications.



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