of 11
Multi-layer silicon nitride-on-silicon
polarization-independent grating couplers
J
ASON
C. C. M
AK
,
1,*
W
ESLEY
D. S
ACHER
,
1,2
H
UANG
Y
ING
,
3
X
IANSHU
L
UO
,
3,4
P
ATRICK
G
UO
-Q
IANG
L
O
,
3,4
AND
J
OYCE
K. S.
P
OON
1
1
Department of Electrical and Computer Engineering, University of Toronto, 10 King’s College Road,
Toronto, Ontario M5S 3G4, Canada
2
Kavli Nanoscience Institute, California Institute of Technology, 1200 East California Blvd, Steele
Laboratory, Pasadena, CA 91125, USA
3
Formerly with Institute of Microelectronics, A*STAR (Agency for Science, Technology and Research), 11
Science Park Road, Singapore Science Park II, 117685, Singapore
4
Advanced Micro-Foundry Pte Ltd., 11 Science Park Road, Singapore Science Park II, 117685, Singapore
*
jcc.mak@mail.utoronto.ca
Abstract:
A polarization-independent grating coupler is proposed and demonstrated in a
3-layer silicon nitride-on-silicon photonic platform. Polarization independent coupling was
made possible by the supermodes and added degrees of geometric freedom unique to the 3-layer
photonic platform. The grating was designed via optimization algorithms, and the simulated
peak coupling efficiency was -2.1 dB with a 1 dB polarization dependent loss (PDL) bandwidth
of 69 nm. The fabricated grating couplers had a peak coupling efficiency of -4.8 dB with 1 dB
PDL bandwidth of over 100 nm.
© 2018 Optical Society of America under the terms of the
OSA Open Access Publishing Agreement
1. Introduction
Grating couplers (GCs) have emerged as effective optical input/output interfaces between standard
optical fibers and silicon (Si) photonic circuits [1
4]. In conventional silicon (Si) photonic
platforms, GCs are formed with the single Si waveguide layer using partially or fully etched
features. One dimensional (1D) Si GCs are highly polarization sensitive, which can be intuitively
explained using the grating equation. For a GC to couple optical power from a waveguide mode
propagating in the chip to an emission angle,
θ
, away from the normal of the plane of the chip, it
must satisfy the phase-matching condition,
k
0
̄
n
e f f
,
m
=
k
0
n
c
sin
θ
+
q
2
π
Λ
,
(1)
where
k
0
is the free-space wavevector of the light,
̄
n
e f f
,
m
is the effective index of mode
m
in the GC,
n
c
is the cladding refractive index of the GC,
Λ
is the grating period, and
q
is an
integer indexing the diffraction order. In a typical periodic 1D GC formed in a single waveguide
layer,
̄
n
e f f
,
m
depends on the grating duty cycle,
f
. It is usually not possible to choose a
duty cycle such that Eq. 1 is simultaneously satisfied for both transverse electric (TE) and
transverse magnetic (TM) polarized modes, i.e., generally,
̄
n
e f f
,
T E
(
f
)
,
̄
n
e f f
,
T M
(
f
)
, leading to
polarization-dependent characteristics.
Therefore, to realize a single layer polarization-independent GC (PI-GC), more degrees of
freedom, beyond
f
, is needed such that TE and TM modes can satisfy the same condition in
the right hand side in Eq. 1. This can be achieved through 2D patterns [5,6], an intersection
of 1D TE and TM gratings [7], or full freedom in the grating geometry [8]. However, thus
far, such PI-GCs have exhibited limited coupling efficiency and bandwidths. Proposals require
back-reflectors [5] or subwavelength features [5,7,8]. Defining the polarization dependent loss
Vol. 26, No. 23 | 12 Nov 2018 | OPTICS EXPRESS 30623
#342025
https://doi.org/10.1364/OE.26.030623
Journal
©
2018
Received
14
Aug
2018;
revised
29
Sep
2018;
accepted
9 Oct
2018;
published
7 Nov
2018
(a)
(b)
Fig. 1. (a) Cross-section of the 3-layer SiN-on-Si platform in this work. Vertical dimension is to
scale. Layer dimensions and refractive index at nominal center wavelength 1310 nm are indicated.
(b) Profiles of the electric (red) and magnetic (blue) fields perpendicular to the plane of the modes
supported by the SiN2, SiN1, and Si etch slab layers. The
n
e f f
of the supermodes are annotated.
(PDL) bandwidth
λ
1
dB PDL
as the bandwidth where PDL is under 1 dB, and
η
PI
to be the
maximum coupling efficiency in either polarization within the PDL bandwidth, to date, the best
experimental demonstration of a PI-GC has a
λ
1
dB PDL
of 12 nm with
η
PI
of -6 dB.
Here, we present 1D PI-GCs for the O-band in the 3-layer silicon nitride (SiN)-SiN-on-silicon
(Si) platform reported in [9] and [10]. The three layers supported 5 confined supermodes which
allowed polarization independent coupling to be realizable using available degrees of freedom.
The PI-GCs were designed by a combination of heuristics and optimization algorithms, achieving
in simulation
η
PI
= -2.1 dB at 1310 nm with
λ
1
dB PDL
= 69 nm. The best fabricated device
had
η
PI
= -4.8 dB at 1306 nm
λ
1
dB PDL
of
>
100 nm. To the best of our knowledge, this is
the highest
η
PI
with largest
λ
1
dB PDL
amongst experimentally realized PI-GCs to date. This
result complements the ongoing work on broadband and high peak coupling efficiency bi-layer
GCs [11–15] and demonstrates the versatility of multi-layer GCs.
This work is organized as follows. In Section 2, we elaborate on the feasibility of polarization
independence in the 3-layer stack, and the optimization process. Section 3 provides experimental
measurements of the fabricated devices. Section 4 compares the results with a representative
selection of polarization independent and polarization splitting gratings from literature, after
which we summarize and conclude.
2. Design
2.1. Polarization independent coupling in a 3-layer GC
Figure 1(a) shows the waveguide layers of the 3-layer platform. To intuitively illustrate why a 1D
PI-GC can potentially be designed, we examine the modes supported by slab waveguides in this
platform. The purpose is to identify whether sufficient degrees of freedom exist to tailor
̄
n
e f f
for
the relevant grating modes such that the modes simultaneously satisfy Eq. 1. Full numerical
simulations need to be carried out for the PI-GC design to account for substrate reflections and the
strong index perturbation (i.e., the guided modes alone do not fully predict the GC performance).
The cross-section consisting of the thin Si etch slab and the two fully etched SiN layers, each
individually single-mode for TE and TM polarizations, supports a total of 6 supermodes (modes
of a system of multiple coupled optical waveguides), as illustrated in Fig. 1(b). To directly
couple light from the multi-layer grating into a single layer waveguide, we consider how the
Vol.
26,
No.
23
| 12
Nov
2018
| OPTICS
EXPRESS
30624
(a)
(b)
(c)
(d)
Fig. 2. (a)-(b): Power profile in the 3-layer region excited from a SiN1 slab waveguide. Outline
of the waveguides are shown in white. Fundamental TE [(a)] and TM [(b)] modes of the SiN1
waveguide excite supermodes of the 3-layer region. No power resides in the Si etch layer for
the TM polarization. (c)-(d): Fraction of power coupled to each supermode corresponding to
fundamental TE [(c)] and TM [(d)] excitation.
supermodes are excited by an input mode from a SiN1 slab waveguide. While a TE input mode
couples into the 3 TE supermodes in the 3-layer region [Fig. 2(a) and Fig. 2(c)], a TM input
mode couples into only 2 TM supermodes [Fig. 2(b) and Fig. 2(d)]. This is because Mode 6 is
not well confined and has very poor overlap with a TM input mode. Therefore, in total, there are
5 modes relevant for polarization independent coupling into an SiN1 slab waveguide.
The 5 relevant modes are matched by 5 degrees of freedom in the geometry of a periodic
3-layer GC that can be used to adjust
̄
n
e f f
,
m
: 1. Fill factor in Si (
f
0
), 2. Fill factor in SiN1
(
f
1
), 3. Fill factor in SiN2 (
f
2
), 4. Spatial offset between the Si and SiN1 features (
o
0
), and 5.
Spatial offset between the SiN1 and SiN2 features (
o
2
). These 5 degrees of freedom allow for the
possibility for
̄
n
e f f
,
m
to be adjusted such that it is equal for all 5 confined supermodes, thus the
potential for polarization insensitive operation.
2.2. Optimization assisted design
While satisfying the system of grating equations is a prerequisite for PI-GCs, their good
performance (e.g., in terms of
η
PI
and
λ
1
dB PDL
) is not guaranteed. Therefore, in addition to
these 5 degrees of freedom that adjust
̄
n
e f f
,
m
, we include the period
Λ
of the grating, and the fiber
position
x
s
and polish angle
θ
in the design process to maximize
η
PI
and
λ
1
dB PDL
. This results
in 8 degrees of freedom for the design of a periodic 3-layer grating. We give a parameterization
in Fig. 3, where we have defined the variables
w
1
=
f
1
Λ
,
g
=
(
1
f
1
)
Λ
,
w
0
=
f
0
Λ
,
w
2
=
f
2
Λ
for
convenience of specifying minimum feature sizes. Apodizing the grating for this parameterization
will result in
2
+
6
N
variables for apodization of
N
teeth.
To develop a design, we used a combination of optimization algorithms and heuristics to
optimize figures of merits (FOM) extracted from direct 2D Finite-Difference Time-Domain
(FDTD) simulations of the design. These 2D-FDTD simulations were set up based on the
parameterization in Fig. 3. The GCs are designed to couple light from an angled polished
SMF-28 fiber into a SiN1 waveguide.
g
,
w
1
,
w
0
,
w
2
are set between minimum allowable features
sizes (0.4
μ
m for
g
, 0.3
μ
m for
w
1
and
w
2
, and 0.18
μ
m for
w
0
) up to coarse features of around
1.3
μ
m corresponding to an upper limit of roughly wavelength per period, beyond which the
Vol.
26,
No.
23
| 12
Nov
2018
| OPTICS
EXPRESS
30625
Fig. 3. Diagram of the 3-layer PI-GC simulation setup and design parameters.
(a)
(b)
Fig. 4. Spectrum of the (a) uniform PI-GC and (b) apodized PI-GC.
resultant grating period would not be efficient for the target wavelength. The offsets
o
0
and
o
2
are allowed to vary approximately over an entire period, within
(−
2
,
0
)
μ
m. Due to substrate
reflections and mode matching, the optimal
θ
cannot be known
a priori
. Therefore, the design
procedure also searched over coupling angles in the range of
θ
∈(
0
,
35
)
without being limited
by the total internal reflection for the cladding-air interface (43.7
). The distance between the
SiN1 waveguide and the center of the fiber is
x
s
, which is bounded between 4 and 7
μ
m. A
Gaussian source with mode field diameter (MFD) corresponding to SMF-28 fiber at 1310 nm
injects 45
polarized light. The TE and TM transmission spectrum of the GC is taken in the SiN1
waveguide using mode overlap integrals.
We first tried to design a periodic 3-layer GC to achieve good coupling efficiency in TE and
TM polarizations simultaneously. We used the average between the TE and TM coupled power
at 1310 nm as the FOM for this design as it was fast to calculate using only one 2D-FDTD
simulation with diagonally polarized light input into the grating. With this FOM, we ran 100
iterations of the particle swarm algorithm [16], using a population of 100 particles initialized
with uniform random sampling. Since this FOM does not account for PDL and
λ
1
dB PDL
, we
visually inspected 20 of the top performing designs to eliminate designs with high PDL or narrow
λ
1
dB PDL
which occur when the TE and TM polarization spectra cross. From this pool of
designs, we identified a design balancing good coupling efficiency and large
λ
1
dB PDL
with low
PDL [see Table 1 and Fig. 4(a)]. Excluding variations of the same design from the same local
optimum, the remaining designs that we had inspected had lower efficiency, higher PDL, or lower
λ
1
dB PDL
.
We then apodized the periodic GC with the goal of further improving
η
PI
and decreasing
the PDL, while maintaining the wide
λ
1
dB PDL
of the periodic GC design. We incrementally
performed the apodization. Multiple rounds of optimization are performed, where we select
Vol.
26,
No.
23
| 12
Nov
2018
| OPTICS
EXPRESS
30626
Table 1. Parameters for the uniform 3-layer SiN-SiN-Si polarization independent GC
g
w
1
o
2
w
2
o
0
w
0
x
s
θ
[nm] [nm] [nm] [nm] [nm] [nm] [
μ
m] [
]
899 830 604 640 604 1047 6 33.9
Table 2. Parameters for the apodized 3-layer SiN-SiN-Si polarization independent GC
g
w
1
o
2
w
2
o
0
w
0
Period
[nm] [nm] [nm] [nm] [nm] [nm]
1
554 890 554 498 554 1246
2
887 907 523 664 600 1051
3
812 829 542 676 762 1015
4
914 874 590 670 505 1138
5
882 856 600 664 664 1103
6
784 925 482 937 678 1415
7
738 916 483 939 590 1155
8
777 930 518 594 702 1298
9
822 792 525 830 568 1484
10
919 776 338 669 587 1237
11
838 862 621 587 575 1306
12
886 1136 548 939 482 1373
13
941 799 569 680 671 1224
14
883 830 572 648 726 1047
several randomly chosen teeth at a time to be varied, with the result from the previous round
as a starting point. At each round, we applied the local optimization algorithm COBYLA [17]
bounded to a small region around each starting point to make gradual improvements to one
of the following FOM: 1. TE coupling efficiency at 1310 nm
η
T E
, TM coupling efficiency at
1310 nm
η
T M
, the standard deviation of the PDL computed at 100 wavelengths between 1260
and 1360 nm
σ
spr ead
which is proportional to PDL over the O-band in linear scale, and 4.
η
log
=
log
10
[
η
T M
/
η
T E
]
which reduces the difference in the TE and TM coupling efficiencies
at the center wavelength in logarithmic scale. At each round, the FOM was selected heuristically
by visual inspection based on the result of the previous round, attempting to balance the increase
of the
η
PI
while minimizing the PDL. We first tried to alternate between increasing
η
T E
and
η
T M
, but this often led to an increased difference between the TE and TM spectra, or a spectral
shift between the two polarizations. Applying the FOMs
σ
spr ead
or
η
log
usually decreased the
Vol. 26, No. 23 | 12 Nov 2018 | OPTICS EXPRESS 30627