# Subwavelength Grating Structures in  Silicon-on-Insulator Waveguides

Authors: J. H. Schmid; P. Cheben; S. Janz; J. Lapointe; E. Post; A. Delâge; A. Densmore; B. Lamontagne; P. Waldron; D.-X. Xu
Journal: Advances in Optical Technologies
 (2008)

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## Abstract

First implementations of subwavelength gratings (SWGs) in silicon-on-insulator (SOI) waveguides are discussed and demonstrated by experiment and simulations. The subwavelength effect is exploited for making antireflective and highly reflective waveguide facets as well as efficient fiber-chip coupling structures. We demonstrate experimentally that by etching triangular SWGs into SOI waveguide facets, the facet power reflectivity can be reduced from 31% to <2.5%. Similar structures using square gratings can also be used to achieve high facet reflectivity. Finite
difference time-domain simulations show that >94% facet reflectivity can be achieved with square SWGs for 5μm thick SOI waveguides. Finally, SWG fiber-chip couplers for SOI photonic wire waveguides are introduced, including design,
simulation, and first experimental results.


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## Body

## 1. Introduction

Subwavelength
gratings (SWGs) have been known and used for many years [1], most commonly as an alternative
to antireflective (AR) coatings on bulk optical surfaces. The defining property
of an SWG is a pitch that is sufficiently small to suppress all but the 0th
order diffraction, the latter referring to the light that is reflected or
transmitted according to Snell’s law. According to the grating equation for
normally incident light (sinθ=mλ/Λ,
where θ is the angle of diffraction, λ is the wavelength of light, Λ is the
grating pitch, and m is the
diffraction order) diffraction is suppressed for Λ<λ, as the diffraction
angle becomes imaginary for all orders m.
Conceptually, the light propagating through a SWG structure “senses” the
average optical properties of the SWG medium. The SWG can thus be represented
as a locally homogeneous effective medium with optical properties determined by
the grating geometry. The effect of a specific optical coating can be mimicked
by an SWG with an appropriate modulation depth and duty cycle. Effective
multilayer and gradient-index (GRIN)
structures can also be obtained with SWGs. Low reflectivities on optical
surfaces have been demonstrated with SWGs both by a single-layer AR effect as well as by a GRIN effect [2]. More recently, SWG surface
structures that exhibit very high reflectivity over a broad wavelength band have
also been demonstrated [3, 4]. In this paper we discuss the first
implementations of SWG structures in silicon-on-insulator (SOI) integrated planar waveguide circuits.Integrated
planar waveguide circuits are widely used in optical telecommunication systems,
with arrayed waveguide grating (AWG) multiplexers being one of the most complex of such
circuits [5]. Currently, these commercial waveguide devices are typically made
from doped silica glass with a low refractive index contrast. The high-index
contrast (HIC) SOI material system offers the potential of a
significant size and cost reduction of integrated planar waveguide devices,
including AWGs [6, 7]. In addition, new applications are emerging for
miniaturized SOI waveguide
devices. For example, we have recently demonstrated a compact high resolution
microspectrometer [8] and highly sensitive photonic wire evanescent field
sensors (PWEF) with a detection limit of ~20 fg of organic molecules [9, 10]. However,
there are also fundamental challenges of the SOI material system related to the fixed value of the refractive indices of the
constituent materials (Si and SiO2). Since the SWG effect allows one
to engineer artificial materials with intermediate effective indices simply by
lithographic patterning, it has the potential to circumvent this limitation. We
demonstrate this on two specific examples, namely, the control of the Fresnel
reflectivity of the waveguide facets and the fiber-to-chip coupling, both
relying on the SWG effect.The
Fresnel reflectivity of a cleaved SOI waveguide facet is typically ~30%, which is the reflectivity of the Si-air
interface. This comparatively high facet reflectivity causes
Fabry-Pérot cavity effects in SOI planar waveguide devices and also increases the fiber-chip coupling loss. Thus
antireflective facets are often desirable. For some devices, for example,
optical cavities, a facet reflectivity larger than 30% is required. Both AR and
highly reflective (HR) facets can be achieved by the use of thin-film coatings;
however, the use of optical coatings on facets has various drawbacks. For
example, film deposition has to be carried out at the chip level after
cleaving, requiring additional processing and precluding device testing at the
wafer level. Thin film deposition processes can be complex, may reduce yield,
and may require the use of expensive deposition equipment. Furthermore, optical
coatings may become mechanically unstable under thermal cycling, leading to
restrictions on device power and limitation of device lifetime.A major
problem in the design and fabrication of silicon microphotonic devices is the
limited efficiency of optical coupling to silicon waveguides at the
input/output interfaces. Due to the large mode size
disparities, the light coupling between an optical fiber and a silicon
waveguide with a small cross section is largely inefficient. Various solutions
to this problem have been suggested, for example, three-dimensional mode size
transformers, edge [11]
and off-plane [12–15] grating couplers, inversely
tapered waveguides [16] and
GRIN planar waveguide lenses [17],
each having some advantages and drawbacks. A
comparative review of various coupling schemes is contained
in [18]. For
submicron silicon wire waveguides, inverse tapers have emerged as a
particularly efficient coupling method.
Demonstrated coupling losses of inverse
tapers with a minimum width of 0.1 μm  reported in [16]
are 6 dB and 3.3 dB for
TE and TM polarized light, respectively. While this is a remarkable
achievement, a further improvement of the total coupling efficiency is
desirable. Furthermore, the coupling efficiency of inverse tapers is strongly
dependent on the minimum taper width, a fact that results in tight fabrication
tolerances for the taper width.We have
recently proposed the use of the SWG effect as a general tool for waveguide
mode modifications, including light coupling between an optical fiber and high
index contrast waveguides of submicrometer dimensions [19] and modification of
facet reflectivity [20]. In this paper, we review our work but also provide new
experimental and modeling results on the use of SWGs in SOI waveguides. All SWG patterns discussed here, both for facet reflectivity
modification and for fiber-to-chip coupling enhancement, can be fabricated by
standard lithography and vertical etching processes. This has two obvious
advantages. First, devices can be processed at the wafer level before dicing;
and second, shape control of the SWG is limited only by the resolution of the
lithography and pattern transfer. To demonstrate the effects, we have carried
out experiments on SOI waveguides
and compared the experimental results with reflectivity calculations using effective
medium theory and finite difference time-domain (FDTD) simulations.


## 2. Antireflective Waveguide Facets

The AR effect
of specific SWG structures on waveguide facets is analogous to the same effect
on bulk optical surfaces. It can be described using the effective medium theory
(EMT) [21]. According to EMT, a composite medium comprising two different
materials interleaved at the subwavelength scale can be approximated as a
homogeneous medium with a refractive index expressed as a power series in (Λ/λ),
where Λ is the pitch of the SWG and λ is the wavelength of the light. For the
case of a one-dimensional surface grating, the first-order expressions for the anisotropic
refractive index are given by(1a)n∥=(fn12+(1−f)n22)1/2,(1b)n⊥=(fn12+(1−f)n22)−1/2.Equations
(1a) and (1b)
refer to the case of the electric field of the incident light
being parallel or perpendicular to the grooves (see Figure 1), respectively. In
these  equations, n1 and n2 are the refractive indices of the two
media comprising the SWG, and f is
the filling factor, defined as the fraction of material with index n1 in a thin slice parallel
to the surface, as shown in Figure 1. The equations above are valid in the
limit (Λ/λ) →0. Figure 1 shows the geometry of SWGs with
square and triangular shapes at a silicon-air interface (n1=3.5,  n2=1). For square gratings (top left), the filling factor profile is a
step function (left center panel). Using (1a)
and (1b), the refractive index profile, which
is also a step function, is obtained (bottom left).  The effective index in the
grating region is polarization dependent, as per (1a)
and (1b). The TM mode has the electric
field parallel to the grating grooves, corresponding to
(1a) whereas the
electric field of the TE mode is perpendicular to the grooves, corresponding to
(1b). For triangular gratings
(top right in Figure 1), the filling factor
profile is a linearly decreasing function along the depth of the grating
(center right). The corresponding effective index profiles are continuously
decreasing functions across the grating region for both polarizations as shown
in the bottom right panel of Figure 1.Figure 1
Effective medium theory applied to square and triangular SWGs on a Si-air
interface. Top: schematic of the grating geometry. Center: filling factor
corresponding to the square and triangular SWGs. Bottom: resulting effective
refractive index profiles for light with the electric field along the grating
grooves (TM, dashed curves) and perpendicular to the grating grooves (TE, solid
curves).The step
function effective index profile of a square grating is equivalent to that of a
single-layer coating on a silicon surface. The thickness of this effective
layer is given by the modulation depth of the grating and the effective
refractive index can be adjusted between the values of silicon and air by
changing the duty cycle of the SWG. From thin film theory, the requirements for
a single-layer interference AR coating for light crossing the boundary between
two materials of reflective indicesn1 and n2 at normal
incidence are  nfAR=n1n2 and  t=mλ/(4nfAR) where nfAR is the film refractive index, t is the film thickness, and m=1,3,5,… is an odd integer. Thus an AR surface with a square SWG can be
designed by choosing the effective refractive index for a specific polarization
in (1a) and (1b)
equal to the required nfAR.
This determines the filling factor and thus the duty cycle of the grating. The
modulation depth is then determined by the condition above for the AR coating
thickness t.  In contrast to the
square gratings, the antireflective properties of triangular gratings arise
from the GRIN effect, as the
effective refractive index varies continuously between the bulk values of the
two media that comprise the grating, namely, Si and air.Figure2
shows the  scanning electron microscope images of SOI ridge waveguide facets patterned with square and triangular SWGs. These
structures were fabricated with a two-step patterning process on SOI substrates with a Si layer thickness
of 1.5 μm
and a buried oxide (BOX) layer
thickness of 1 μm, as described in [20]. Square and triangular facet patterns
with various dimensions as well as flat reference facets were produced by electron
beam lithography and reactive ion etching (RIE). The facet reflectivity was inferred
from Fabry-Pérot (FP) transmission measurements on waveguides terminated with
SWG facets, as shown schematically in Figure 3. The ridge waveguides have a
width of 1.5 μm, adiabatically tapered to a
width of 4 μm near the facets. This
increased waveguide width at the facet makes is possible to include 10 periods
of the SWG with a pitch of 0.4 μm. The etch depth for the shallow etch (defining
the ridge waveguide) is 0.7 μm, while the deep facet etch is terminated at the
bottom oxide.Scanning electron micrographs of SOI waveguide facets patterned with (a)
square and (b) triangular SWGs.
(a)(b)Figure 3
Schematic top view of a SOI ridge
waveguide terminated at both ends with a SWG (not to scale), as used for
waveguide transmission measurements described in the text.Transmittance
of fabricated waveguides was measured as a function of wavelength nearλ=1.55μm. Propagation loss was determined from the reference waveguides with flat
facets to be 1.7 dB/cm for TE and 5.2 dB/cm for TM polarized light, using the
Fabry-Pérot method. The Fresnel reflectivity of a material with the mode
effective index was used as an approximation for the reference waveguide facet
reflectivity. This value differs from the reflectivity of a Si-air interface by
less than 0.5% for either polarization. The polarization dependence of the
propagation loss is believed to be due to scattering loss from the etched
sidewalls of the waveguides. The reproducibility
of the loss measurement was found to be good with waveguide-to-waveguide fluctuations
of the loss less than 0.5 dB/cm. A comparison of transmission spectra of
waveguides with flat facets and with triangular and square SWG patterned facets
is shown in Figure 4 for TE polarized light. The peak-to-peak grating modulation
depth is 720 nm for the triangular SWG pattern and 270 nm for the square
pattern which has a duty ratio of 61%. The amplitude of the FP fringes is
reduced from 4.5 dB for the flat facets to approximately 0.3 dB and 0.5 dB for
the triangular and square SWGs, respectively. Assuming the same propagation
loss for all waveguides as obtained from the reference measurement on
waveguides with flat facets, the power reflectivities of the triangular and
square SWG facets are calculated to be 2.1% and 3.6%, respectively, from the
amplitude of the observed FP fringes shown in Figure 4.Figure 4
Fabry-Pérot
fringes for the reference waveguide with flat facets and for the waveguides
terminated with antireflective triangular or square SWG structures. The curves
are offset for clarity.For
triangular gratings, the facet reflectivity was measured as a function of the
modulation depth of the SWG for both polarizations and compared with EMT theory for the equivalent grating on a bulk
silicon surface. The results are shown in Figure5. The EMT calculation was carried out by discretizing the continuous effective index
profiles shown in Figure 1 (bottom right) in
steps of 1 nm. The resulting
discrete index profile for each polarization is the same as that of a stack of
1 nm thick films. The reflectivity of the SWG is then calculated as the
reflectivity of this equivalent thin film stack using standard thin film
theory. There is good quantitative agreement of experiment and theory
(see Figure 5). The reflectivity decreases substantially with the grating modulation depth,
as the gradient-index section becomes more adiabatic. The minimum measured
reflectivity of 2.0% for TE and 2.4% for TM polarization is obtained for a
modulation depth of 720 nm, which is the maximum grating depth used in our experiments.
The quoted values are an average over 4 measured samples. According to the EMT calculations, reflectivities below 1% can be
achieved for SWG modulation depths of approximately
1 μm and 2.5 μm for TE and
TM polarized light, respectively. Since the SWG profiles are defined
lithographically, their shape and thus the effective index profile can be
readily engineered for specific requirements (e.g., polarization properties),
in a similar way as for bulk SWG surfaces [22].Experimental and
theoretical results from effective medium theory for the reflectivity of facets
with triangular SWGs as a function of the length of the gradient-index section
(i.e., the grating modulation depth).
(a)(b)For square SWGs (Figure2, left), the lowest measured facet
reflectivity was 3.6% for TE polarized light whereas the TM reflectivity of the
same sample was 23%. Such a large polarization dependence is expected for
square gratings. As discussed above, according to EMT,
the square AR SWGs can be represented as a single-layer AR coating, the
efficiency of which is known to be rather sensitive to the index of the layer.
Since the effective index of the SWG is polarization dependent (Figure 1,
bottom left), optimal AR performance can only be achieved for one polarization
state for a particular SWG duty cycle. The strong polarization dependence of square
SWG facets can potentially be exploited for making polarization
selective waveguide elements.


## 3. Waveguide Facets with High Reflectivity

Subwavelength gratings with high reflectivity have recently been
demonstrated on optical surfaces as a replacement for the top distributed Bragg
reflector in a vertical-cavity surface emitting laser (VCSEL) [23]. In order to
obtain the SWG effect, these gratings need to be separated from the substrate
by a layer of low index material. This was achieved in a VCSEL device by
fabricating a grating freely suspended above the substrate with an air gap of
~1 μm. A similar SWG structure can be envisioned for planar waveguide facets
consisting of a row of vertical posts in front of a flat waveguide facet at a
specific distance (equivalent to the air gap of the VCSEL structure). However,
in such a structure there is no vertical mode confinement in the air gap,
resulting in out-of-plane radiative loss as the light propagates in the air
gap. For a SOI waveguide thickness
of ~1 μm or less, these radiative losses are prohibitive for practical devices,
as we have found with three-dimensional FDTD simulations.Interestingly
though, FDTD simulations show that if a square grating is etched directly into
the facet without a separating air gap, high reflectivities can also be
obtained. The modeled structure is shown in Figure6(a).
It is a 7 μm wide Si
slab waveguide (nSi=3.476) with SiO2 lateral claddings (nSiO2=1.44), terminated at the facet with a
square grating. The grating period is 0.7 μm, the duty cycle is 54% and the
grating modulation depth is 485 nm. The external medium is air (n=1). A
continuous-wave field excitation of a TE (electric field in the plane of the
drawing) waveguide fundamental mode of free space wavelength λ=1550 nm propagating
in the waveguide towards the facet was assumed. The mesh size used was 10 nm
and the simulation was run for a total of 10 000 time steps of Δt=2.2×10−17 seconds. The calculated TE electric field map is
shown in Figure 6(b).
The excitation plane for the waveguide mode source is
indicated in the figure
by a blue line, including the mode propagation direction (arrow). It can be
seen that the transmittance through the grating structure is efficiently
suppressed, hence the mirror effect. Between the excitation plane and the
facet, the forward propagating and the reflected light form a standing wave
interference pattern. To the left of the excitation plane, the reflected mode
propagates unperturbed in the waveguide. The facet reflectivity is calculated
as an overlap integral of the reflected intensity profile in the waveguide
region to the left of the excitation plane with the fundamental TE mode. A
reflectivity value of 97% was obtained for this 2D structure. Figure 6(c) shows
the simulation of light coupling from an external optical fiber to the Si
waveguide. In this case, a light source with Gaussian intensity profile with a
1/e2 width of 10.4 μm (SMF-28
fiber mode), is located at the excitation plane (white line in Figure 6(c)).
The calculated field in the waveguide reveals a strong transverse modulation
with a period half of the grating pitch. This modulation persists almost
unperturbed for several micrometers as the light propagates in the waveguide.
Since the overlap integral of this modulated field with the fundamental mode of
the waveguide is comparatively small, coupling from an external fiber to the
waveguide is inefficient.FDTD simulations of HR SOI facets. (a) Layout used for a typical
simulation. The light and dark blue regions are the silicon waveguide core and
SiO2 lateral cladding, respectively. (b) Simulated TE field map for a
waveguide mode launched at the plane indicated in the figure. (c) TE field map
for an external optical fiber mode coupling into the waveguide.
(a)(b)(c)These
markedly different grating properties for light propagating in opposite
directions may seem surprising, but have a straightforward explanation. Obviously,
diffraction is suppressed on the air side of the grating, sinceΛ<λair. However, the grating is
not subwavelength for light coupled into the Si waveguide, where the first
diffraction order is not evanescent, since Λ>λSi. In our case Λ=700 nm, λair=1.55 μm, and
λSi=λair/nSi=446 nm. This is a
fundamental difference between the HR gratings and the square AR gratings
discussed in the previous section, which have a pitch of Λ=400 nm and are
thus subwavelength both in the Si and in air. It can be shown with rigorous
coupled wave analysis (RCWA) that for a plane wave normally incident from
inside the bulk Si on a surface grating with the same pitch and duty cycle as
our HR facet gratings, both the diffraction efficiency and the transmittance
are extremely small, while the specular (0th order) reflectivity is >99.9%.
Conversely, when the plane wave is incident on such a bulk grating from the air
to Si, the power diffracted into the +1 and −1 diffracted orders is
approximately 98%, with <2% of light reflected or transmitted in 0th order.
The intensity pattern in Figure 6(c) is thus a superposition of the −1
and +1 diffraction orders, while the 0th order is suppressed. This
zero-order suppression effect is commonly employed in phase masks used in the
fabrication of fiber-Bragg gratings [24].The reflectance
of HR gratings on waveguide facets can be estimated from measured FP fringes
similar to the AR measurements discussed in the previous section. The most
notable difference is that fiber-waveguide coupling is now largely inefficient
due to the diffraction effect explained above. In fact, waveguides terminated
with HR facets on both sides were found experimentally to have no measurable
transmittance (T<−60 dB). To circumvent this problem and measure the
internal (Si-air) facet reflectivity, we have used waveguides that are
terminated with an HR grating on the output facet but with a regular flat facet
having a Fresnel reflectivity of 31% on the input side. This way an asymmetric
FP cavity is formed. As in the case of the AR facets, FP fringes can be
observed in the transmission spectra of these waveguides.
In Figure 7, the
spectrum of such an asymmetric cavity waveguide is compared to that of a reference
waveguide terminated on both ends with flat facets. The measured peak-to-peak
fringe modulations are 6.4 dB and 4.2 dB for the respective waveguides. Using a
simple Fabry-Pérot model for the asymmetric cavity, this corresponds to an HR
facet reflectivity of 75%, clearly demonstrating the validity of the HR grating
concept. However, since this reflectivity is significantly lower than the best
results of our 2D FDTD simulations, full 3D FDTD simulations of the HR facet
structures were carried out. These simulations reveal a strong dependence of
the expected reflectivity on mode confinement. For the 1.5 μm thick SOI waveguides with the 0.7 μm pitch gratings used
in our experiments, the highest reflectivity obtained in the 3D FDTD
simulations is 80%, in good agreement with the measurement. For thicker
waveguides with the same facet grating dimensions the achievable reflectivity
increases significantly. For example, 94% reflectivity is expected for 5 μm
thickness according to the 3D FDTD simulations. Physically, the reason for the
mode size effect is the dependence of the grating reflectivity on the incident
angle. With RCWA we find that the grating reflectivity for plane waves drops
from >99.9% to 81% when the angle of incidence is increased from
0° to 10°. Therefore,
the larger range of incident angles contained in a smaller, more localized mode,
results in a lower reflectivity.Figure 7
Measured Fabry-Pérot
fringes in the transmission spectrum of a waveguide with an HR grating on the
output facet. A reference waveguide with flat facets is also shown. The curves
are offset for clarity.


## 4. Fiber-to-Chip Couplers

An original
application of SWGs for fiber-to-waveguide coupling and mitigating losses due
to the mode size mismatch of optical fibers and submicron SOI waveguides has been proposed recently [19]. The
principle of this fiber-chip coupler is based on a gradual modification of the
waveguide mode effective index by the SWG effect. The idea is illustrated in a
schematic side view of a coupler structure in Figure 8. The waveguide mode
effective index is altered by chirping the SWG duty ratio r(z)=a(z)/Λ, where a(z) is the length of the waveguide core segment. Unlike in the case of the AR
and HR SWG structures discussed above, where the direction of light propagation
is orthogonal to the grating vector, here they are colinear, that is, the light
propagates along the grating. Nevertheless, EMT applies to these structures in a similar way. The effective index of the mode
in the SWG coupling structure increases with the grating duty ratio. The duty
ratio and hence the volume fraction of the Si waveguide core is modified such
that at one end of the coupler the effective index is matched to the SOI waveguide while at the other end, near the chip
facet, it matches that of the optical fiber. We
have demonstrated the proposed principle on various SWG coupling structures [19],
using two-dimensional FDTD calculations for an SOI waveguide with Si core thickness of 0.3 μm
with SiO2 cladding. Efficiencies
as large as 76% (1.35 dB
loss) and a negligible return loss (−35 dB, or 0.03%) were calculated for coupling
from a standard optical fiber (SMF-28,
mode field diameter 10.4 μm)
using a 50-μm-long
SWG coupler. Further loss reduction can be expected by advanced design,
including parabolic width tapering and chirping the SWG pitch. The coupling
efficiency tolerance to misalignment is high. Transverse misalignment of ±2 μm
results in an excess coupling loss of only 0.5 dB. The angular misalignment
tolerance is also large, with only 0.24 dB loss penalty for angular
misalignment of ±2 degrees. We
have also demonstrated the reduction of the coupler length down to 10 μm
and found an excess loss of 0.6 dB compared to the 50 μm long coupler discussed above. Unlike
waveguide grating couplers based on diffraction, the SWG mechanism is
nonresonant, and hence intrinsically wavelength insensitive.Figure 8
Schematic of an SWG fiber-to-waveguide
coupler, side view.First SWG
waveguide couplers for SOI photonic wires (PWs) have recently been fabricated in our lab. The dimensions
of the PWs are 0.45μm (width) ×0.26 μm (height). Such thin PW waveguides have
been shown to provide the maximum sensitivity for evanescent field waveguide-based
biosensors [9]. The coupler structures were fabricated on SOI substrates from SOITEC with an Si layer and BOX thickness of 0.26 μm and 2 μm, respectively.
Electron beam lithography with a chemically amplified negative resist (NEB 22 A3) was used to define both waveguides and
SWG couplers in a single step. The pattern was then etched through the Si layer
to the BOX with inductively coupled
plasma RIE. After the resist mask was stripped, a 2 μm thick upper cladding
layer of SU-8 resist with a refractive index of n=1.58 was deposited on the
sample using a standard spin and bake procedure. The samples were then cleaved
and polished as necessary to obtain good facet quality. The ideal SWG coupler structure
described above requires a specific duty cycle at the facet; however, for cleaving
and polishing the facet some tolerance in the exact position of the facet with
respect to the pattern is required. Therefore, the SWG was extended with
constant grating parameters for 400 μm beyond the ideal position of the facet.
This allows the final position of the fabricated facet to be within this
distance from the end of the coupler structure. SEM images of a fabricated coupler
structure are shown in Figure 9. On the left
side, the part of the SWG joining the PW waveguide is shown. The pitch of the
grating is 0.2 μm and the smallest gaps are nominally 50 nm. Due to the
proximity effect in the e-beam lithography, the grating gaps become
successively more closed as the waveguide, which is written with a higher
e-beam dose, is approached. Within a distance of a few periods of the SWG from
the waveguide, the grating is essentially a subwavelength sidewall grating.
This gradual closing of the gaps may in fact be beneficial to the performance of
the coupler, as it reduces the small discontinuity in the effective mode index
as the waveguide transforms into an SWG, making the transition more adiabatic.
Figure 9(b) shows the same coupler at a position closer to the facet. Here the
fabricated structure shows little deviation from the design except for some
corner rounding. To increase the effective index gradient along the SWG
coupler, the width of the SWG segments is tapered from 0.45 μm at the waveguide
to 0.2 μm at the facet.SEM micrographs of a fabricated SOI photonic
wire waveguide with an SWG coupler (top view). (a) The SWG coupler joining
the photonic wire waveguide. (b) Mid-section of the SWG coupler.
(a)(b)Samples
with SWG couplers of varying lengths and taper widths have been fabricated. Two
identical couplers are connected via S-shaped PW waveguides for transmission
measurements. The S-shape helps to reduce the amount of scattered light
reaching the photodetector, as the latter is laterally offset from the light
source. The SWG couplers are compared with inverse tapers of similar dimensions,
as well as untapered waveguides. The inverse taper couplers are adiabatically
tapered waveguides that reach a specific minimum width at the facet [16]. Coupling
loss was inferred from measurements of the waveguide transmittance at a
wavelength λ=1.55 μm using an erbium doped fiber amplified spontaneous
emission (ASE) source with 50 mW
output power. An indium gallium arsenide photo diode was used as a detector. Coupling
loss values were estimated from the measured waveguide transmittance by
correcting for the photonic wire propagation loss, which was determined using
the cut back method on comparable samples to be 9.1 dB/cm and 6.5 dB/cm for TE
and TM polarization, respectively.  The
lowest coupling loss for the SWG couplers of 6.5 dB and 4 dB for TE and TM
polarization, respectively, was obtained for a width of 0.2 μm. The
corresponding values for straight waveguides with a width of 0.45 μm are 18 dB
and 11 dB. The coupling loss of our first coupler is comparable to the loss of
inverse couplers as reported in [16] (6.0 dB and 3.3 dB loss for TE and TM
polarization, respectively), but is achieved for a two times larger width. A
wider taper width implies improved fabrication tolerance to width fluctuations.
We expect the loss can be reduced by further improvements in our design and
fabrication, using a thicker box and/or a wider taper width. Our experiments
provide a first verification of the proposed SWG coupler concept. Also, the SWG
principle experimentally demonstrated in this paper can be generalized to other
types of waveguide modifications including effective index changes and mode transformations,
opening new possibilities for engineering of waveguide properties at the subwavelength scale.


## 5. Summary and Conclusions

We have
reviewed our work in implementing first SWG structures in SOI waveguides. Three types of structures have been
discussed, namely, AR and HR waveguide facets and fiber-chip couplers, all
fabricated using standard fabrication techniques. The AR facets were
demonstrated exploiting either a GRIN effect from triangular SWGs or a single-layer AR effect from square SWGs. The GRIN AR structures were found to be particularly
efficient, with measured facet reflectivities below 2.5% for both
polarizations. These experimental results are in good agreement with EMT calculations. A minimum reflectivity of 3.6%
for the TE mode is reported for square SWGs, including highly polarization
selective properties. HR facets employ a very similar structure to that of
square AR SWG waveguide facets but with different grating parameters. The
0.7μm pitch of the HR grating is large enough that the ±1 orders of
diffraction are allowed in the Si, but are evanescent in air. For light
incident from the air, such gratings act as a zero-order suppressed phase mask.
In the opposite direction (light incident from the waveguide), high specular
reflectivity is observed. We have measured up to 75% reflectivity for facets in
1.5 μm thick SOI waveguides, in good
agreement with 3D FDTD simulations. The FDTD simulations predict that
reflectivities in excess of 95% can be achieved for SOI waveguides with a thickness of 5 μm or more. Finally, the principle, design and
first experimental results on SWG fiber-chip couplers were reviewed. Coupling
losses on the order of ~1 dB can be achieved with these structures according to
FDTD simulations and losses of 6.5 dB and 4 dB for TE and TM polarized light,
respectively, have been demonstrated experimentally. The first results suggest
that the SWG couplers may outperform inverse taper fiber-chip couplers in terms
of fabrication robustness, compactness, and tolerance to misalignment.



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*Source: 685489-2008-07-13.xml*