City, University of London Institutional Repository
Citation: Barh, A., Rahman, B. M., Varshney, R. K. and Pal, B. P. (2013). Design and
Performance Study of a Compact SOI Polarization Rotator at 1.55 mu m. Journal of
Lightwave Technology, 31(23), pp. 3687-3693. doi: 10.1109/JLT.2013.2286859
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Permanent repository link: https://openaccess.city.ac.uk/id/eprint/12228/
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Abstract—We numerically design a compact silicon (Si) based
polarization rotator (PR) by exploiting power coupling through
phase matching between the TM mode of a Si strip waveguide
(WG) and TE mode of a Si-air vertical slot WG. In such
structures, the coupling occurs due to horizontal structural
asymmetries and extremely high modal hybridness due to high
refractive index contrast of Si-on-insulator (SOI) structure.
Design parameters of the coupler have been optimized to achieve
a compact PR of ~ 135 µm length at the telecommunication
wavelength of 1.55 µm. Maximum power coupling efficiency
(C
m
), which is studied by examining the transmittance of light, is
achieved as high as 80% for both polarization conversions.
Fabrication tolerances and the band width of operation of the
designed PR have also been studied.
Index Terms— Polarization sensitive device, Silicon photonics,
Si-on-insulator (SOI) waveguides, Slot waveguides.
I. I
NTRODUCTION
EVOLUTION
of the semiconductor electronic technology
was only possible due to miniaturization and integration
of millions of transistors into a single VLSI chip. Similar to
this revolution, the only way to reduce the cost of
optoelectronics, which is not limited by electronic speed, is to
make the devices as small as possible and find a material
system for monolithic integration of all components.
One way of reducing the device size is to use a dielectric
material with a refractive index (RI) as high as possible, which
can improve the optical confinement and effectively reduce
the waveguide dimensions. High index contrast also allows
very small bending radius, suitable for increasing number of
components on a chip. Silicon (Si) is the most mature material
for electronics but relatively a newer material for photonics.
However, as the low-cost CMOS facilities can be exploited for
the fabrication, Si photonics is becoming a hot research topic
today. Silicon-on-insulator (SOI) [1-2] can provide large
refractive index contrast between Si core and silica cladding
(~ 3). The basic idea is to use the high RI of Si to shrink the
optical confinement down to sub-wavelength scale and also to
Partial funding by UKIERI is gratefully acknowledged.
Authors Ajanta Barh, Ravi K. Varshney, and Bishnu P. Pal are with the
Department of Physics, Indian Institute of Technology Delhi, Hauz Khas,
New Delhi 110016 India (e-mail: ajanta.barh@gmail.com,
varshney_rk_iitd@yahoo.com, and bppal@physics.iitd.ernet.in, respectively).
B. M. Azizur Rahman is with the School of Engineering and Mathematical
Sciences, City University London, London EC1V 0HB UK (e-mail:
b.m.a.rahman@city.ac.uk).
utilize the fabrication infrastructure of CMOS electronics to
realize high yield, low cost manufacturing [3-5]. Today, Si-
based platforms support the realization of a wide variety of
devices, including high-speed modulators and detectors [6],
low-loss waveguides [7] and other passive and active [8],
linear and non-linear [9] components. Additionally, light from
fiber to Si waveguide (WG) can be coupled by especially
designed tapers or Bragg gratings. Recently, SOI-based nano
sized compact slot optical WG has assumed importance due to
its potential applications [10]. Due to high index contrast at
the interface, electric field normal to the interface shows a
very high discontinuity at the interface with very high optical
confinement inside the low index slot region when the
transverse dimension of the slot is less than the characteristic
decay length of that electric field [10-12].
In general, light input to an integrated optical chip is
randomly polarized. This polarization of light has a great
impact on both photonic circuit design and operation. On the
other hand, though the slot and strip WG dimensions are
small, they are highly polarization sensitive. Thus, for
polarization diversity systems, the problem can be sorted out
by incorporating polarization splitter and polarization rotator
or converter based on these highly polarization sensitive high
RI contrast WGs. The conversion of one polarized mode to the
orthogonal polarized mode can be realized by efficient power
coupling between these two modes at the phase matching or
resonance condition.
Recently, polarization rotator (PR) made of horizontal slot
and strip WG has been reported based on mode evolution [13].
Its fabrication poses difficulty as required proper control of
tapered structure is relatively difficult to realize. Moreover, it
can rotate only one polarization state for one input direction.
Three WGs-based polarization splitter and rotator have been
reported [14-15]. Another approach is made for this TE-TM
conversion based on 2-D photonic crystal slab WG [16]. In
this case though the conversion is good, the structure itself is
complicated. Researchers have also tried to implement TE to
TM convertor by increasing the polarization crosstalk in µ-
bend Si WG [17]. Here also the conversion efficiency is very
high though very sensitive to issues like bend loss, bend angle,
smooth wall of the WG around bent region etc.
In this paper, we propose a design for realizing a PR for
potential application at the optical communication wavelength
of 1.55 µm that should be relatively easy to fabricate as no
tapering is required and the whole structure, made of two WGs
Design and Performance Study of a Compact
SOI Polarization Rotator at 1.55 µm
Ajanta Barh
,
B.
M. Azizur Rahman
,
Senior
Member, IEEE
, Ravi K. Varshney,
and
Bishnu P. Pal,
Senior Member, IEEE
R
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2
(one is a strip and other one is a vertical slot WG), can be
made with a single mask. Moreover, it can rotate both
polarization states for a single input direction (i.e., at the
coupling length (L
c
), TM input in the Si strip WG would yield
TE output from the slot WG and TE input in the slot WG
would yield TM output from the strip WG). Similar concepts
have recently been reported [18-19] to design TE-TM based
polarization splitter/rotator, but detailed analysis of various
WG parameters, the effects of unwanted mode coupling and
their propagation analysis were missing in them. In our
simulations, we have analyzed all the aforementioned
parameters in details along with the tolerance study.
Additionally, our design is optimized both for TE to TM
conversion and vice versa. In the present configuration, we
have shown that it is possible to match and couple two
different polarization states by exploiting efficient coupling
between a Si strip WG and an air-Si vertical slot WG.
Maximum power coupling efficiency (C
m
) ~ 80% is possible
for a device length of 134.5 µm. Device performance is
studied on the basis of fabrication tolerances and operating
band width (BW).
II. T
HEORY
When designing a PR, accurate calculation of the mode
effective indices and modal fields corresponding to
dominating and non-dominating field components for TE-like
and TM-like modes are very important. For high RI contrast
WGs, where the modal hybridness and coupling is very strong,
the full-vectorial mode solver is essential. For our design a full
vectorial finite element method (FV-FEM) was implemented
to analyze the 2-D structure. All the vector fields are
investigated and depending on modal hybridness, TE and TM
modes are identified. In the design process, it is necessary not
only to increase the magnitude of the non-dominant field
components but its profile can be optimized to enhance its
overlap with the dominant field components to achieve the
maximum polarization coupling. As all the H-field
components are continuous across the dielectric interface, H-
field based FV-FEM is used for modal analysis. Based on this
FV-FEM the polarization beat length between the TE-like and
TM-like fundamental modes is calculated.
Study of propagation of these two orthogonal modes is
carried out by “Eigenmode Expansion” method using the
commercially available FIMMPROP software. Eigenmode
Expansion is a rigorous technique to simulate electromagnetic
propagation, which relies on the decomposition of the
electromagnetic fields into a basis set of local
eigenmodes (including all guided and radiation modes) that
exist at the junction of a discontinuity plane. The coefficients
of the eigenmodes were calculated by enforcing the continuity
of the tangential components of electric and magnetic-fields at
the boundaries/junctions. This is fully bi-directional and
vectorial algorithm, making no approximations about the
polarization state of light, and is a rigorous solution to
Maxwell’s Equations [20-21]. Here we have launched TE-like
and TM-like mode as the input at respective WGs and studied
the power propagation along its length.
III. R
ESULTS AND
D
ISCUSSIONS
A. Proposed Design
Our proposed PR is a coupler based on one Si-strip WG and
one Si-air vertical slot WG. The cross-section is shown in Fig.
1. Here two WG’s are implemented on silica (SiO
2
) as the
substrate with air as cover and slot material. However, we can
use any low index compatible materials for the slot region,
such as electro-optic materials for high-speed modulators [6],
doped material to achieve gain [8] or sensing material for
efficient organic/inorganic sensing [22]. Vertical slot WG will
only support a TE mode (E
x
is the dominant component) with
higher field inside the slot region. So, here confinement of the
fundamental TE mode in slot WG and TM mode in strip WG
is considered. Note that, introduction of low index region in
slot WG reduces its effective index of fundamental TE mode
(n
eff
–TE) with respect to n
eff
–TE of strip WG. However this
n
eff
–TE of slot WG becomes more comparable to effective
index of the fundamental TM mode (n
eff
–TM) in strip WG.
Thus by proper tuning of WGs parameters, efficient power
coupling between these two modes is possible exploiting their
extremely high modal hybridness.
We have taken the same height for both the WGs as H and
same width for the high index regions of the slot WG as W
2
.
The width of the strip WG core and low index region of slot
WG are taken as W
1
and W
s
, respectively. The separation
between two WGs is denoted as S (see Fig. 1). Material
dispersion of Si and SiO
2
are incorporated through Sellmeier
formula. Our working wavelength is 1.55 µm, for which the
refractive indices of Si and SiO
2
are 3.47548 and 1.44402,
respectively.
Fig. 1. Schematic transverse view of the proposed polarization rotator.
B. Optimum Structure Parameter
For moderate electric field confinement in the slot, we
choose W
s
as 90 nm. Fabrication simplicity requires same
height (H) for both WGs. Now for sufficient confinement of
TM mode inside the strip WG at 1.55 µm wavelength, H
should be > 200 nm. In this design work, H is fixed at 220 nm,
which is the thickness of most commonly available Si wafer.
On the other hand, maintaining TE as the fundamental mode
in slot WG, W
2
was chosen to be 255 nm for H = 220 nm.
Thus the optimized parameters for the slot WG were W
2
= 255
nm, W
s
= 90 nm, H = 220 nm. In the absence of strip WG, the
n
eff
of the TE mode in this slot WG is 1.53716.
Then we have studied n
eff
for the TM mode of an isolated
strip WG of same height by varying its width (W
1
). For W
1
=
451 nm, the strip WG’s TM mode’s n
eff
becomes equal to n
eff
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of the TE mode of the slot WG (shown in Fig. 2). Fig. 2
reveals that as we increase W
1
, its n
eff
–TM increases and at the
crossing point TM mode for W
1
= 451 nm has the same
effective index (n
eff
) as that of the TE mode for the fixed W
2
and W
s
. Then for the combined coupled structure, using these
optimized dimensions (i.e. W
1
= 451 nm, W
2
= 255 nm, W
s
=
90 nm, H = 220 nm), the variation of n
eff
of the two orthogonal
polarized supermode states were studied as a function of S to
determine the mode exchange regime.
Fig. 2. Variation of n
eff
–TM of strip WG with W
1
in the absence of slot WG.
The horizontal line represents the n
eff
-TE (1.53716) inside the Slot WG in
absence of strip WG.
The three basic parameters to study the supermodes in a PR
are n
eff
, hybridness and coupling length (L
c
). For three
different S values (450 nm, 500 nm, 550 nm), the variation of
above mentioned parameters were studied as a function of
strip WG width (W
1
) and the corresponding variations are
shown in Figs. 3-5, respectively. In Fig. 3, horizontal line
represents n
eff
-TE in the slot (almost constant). Slanted line
represents n
eff
-TM in strip WG, changing as W
1
is increased.
But, they do not cross (similar as any coupled structure), but
around this region both the polarized supermodes go through a
transformation. Near the phase matching condition, two
effective indices are close to each other and the phase
difference between these modes ∆
β
will be smaller. For larger
S, these n
eff
curves come closer due to weaker interactions and
the minimum ∆
β
will be smaller.
Around anti-crossing point, these two modes become
degenerate and they get mixed up. For a quasi-TE mode, the
H
y
component is dominant whereas for a quasi-TM mode, its
H
x
component is dominant. Near anti-crossing the non-
dominant field starts increasing leading to higher modal
hybridness, which can be defined as the ratio of the maximum
values of the H
y
to H
x
field components for the TM and
similarly H
x
/H
y
for the TE mode. In Fig. 4, at lower W
1
, the
mode is near quasi-TM, with H
y
component being much
smaller. So its hybridness is low. As W
1
increases, it travels
through the anti-crossing region leading to stronger mode
mixing and higher hybridness. At a higher W
1
, away from this
anti-crossing region, again hybridness reduces. All the peaks
appear around the mode exchange regime with increasing
value as S decreases. Note that for smaller S, curves are wider
as interaction become easier. Similar results can be obtained
for TE mode also, but not shown here.
Fig. 3. Upper & lower n
eff
variation with strip WG width (W
1
) for three
different S = 450 nm, 500 nm, 550 nm.
Fig. 4. Variation of modal hybridness of the TM mode with W
1
for three
different values of S = 450 nm, 500 nm, 550 nm.
Polarization coupling length of the two modes are defined
as (L
c
= π /│β
1
– β
2
│) where, β
1
and β
2
are the propagation
constants of the TE and TM modes. From Fig. 5 we can infer
that, as S increases, coupling become weaker, and hence, (β
1
–
β
2
) is getting smaller near anti-crossing point, so peak L
c
become larger. From Figs. 4 and 5, it should be noted that as S
is reduced the phase matching value of W
1
reduces. When a
directional coupler is composed of two identical WGs, they
are always phase matched or synchronous. But, for a
synchronous coupler composed of non-identical waveguides,
its phase matching also depends on mutual loading of the
waveguides. Consequently, the phase matching condition for
W
1
value changes with S, as shown here.
The maximum L
c
and variation in maximum power
coupling efficiency (C
m
) with W
1
is shown in Table I. Where
C
m
is the maximum normalized power coupled from one
polarized mode to the other polarized mode. From this table,
we can infer that the L
c
decreases with the decrement of
separation between the two WGs. Additionally, due to
stronger coupling between the two WGs, the supermodes
deviate from just being formed out of linear combinations of
isolated modes (as in weak coupling case) and as a result
progressively less power will be transferred from one WG to
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another and hence C
m
also deceases. Thus there exists a trade-
off between these two parameters. Here we can see that to
achieve ~ 80% power conversion, the minimum separation (S)
would be ≈ 500 nm for which the L
c
becomes ≈ 134.5 µm. We
have therefore focused our further study for S = 500 nm.
Fig. 5. Variation of coupling length (L
c
) with W
1
for three different S = 450
nm, 500 nm, 550 nm.
TABLE
I
P
HASE
M
ATCHING
W
1
,
L
C
AND
C
m
FOR
D
IFFERENT
S
AT
1.55
µm
S (nm) W
1
(nm) L
c
(µm) C
m
(%)
600 454.5 211.51 87.04
550 453 168.45 82.20
500 451 134.50 79.01
450 447 108.01 73.64
400 442 87.16 66.02
C. Supermodes of PR
For further analysis, we have fixed the structure parameters
as W
1
= 451 nm, W
2
= 255 nm, W
s
= 90 nm, H = 220 nm, S =
500 nm. The supermodes of this designed PR are shown in
Figs. 6–8, where the z-component of Poynting vector (P
z
), H
y
and H
x
fields of dominating TM mode in strip WG are
displayed, respectively.
The transverse distribution of the P
z
(x,y) is shown in Fig.
6, which shows evenly distributed powers in the two WGs.
Although maximum amplitudes in two constituent waveguides
are different as their core-sizes were also different,
confinement factors in each WG were also calculated. The
confinement factors in the two WGs for both the supermodes
were similar when the two polarized modes were phase
matched. However, the supermodes were neither quasi-TE nor
quasi-TM, but polarized differently in two constituents WGs
with its H
y
and H
x
components nearly equal (see Fig. 4).
Additionally, their shapes in the two WGs are different as the
waveguides were of different shapes, although phase matched.
However, as this is the phase matched structure, the two
constituent waveguides carry nearly equal amounts of power.
In order to illustrate it, we have plotted H
y
and H
x
fields of the
supermode in Figs. 7 and 8, respectively.
Fig. 7 clearly indicates that H
y
is in the slot region, which
supported the interacting TE mode. Note the two peaks of H
y
field in the slot guide, which is typical for a slot WG [10].
There is a small amount of H
y
in the strip WG. This is an
indication of very high hybridness of the supermode.
Fig. 8 shows the H
x
field of the supermode, which is the
dominating TM mode in strip WG. It is mainly confined in the
strip WG and a small amount of H
x
field lie in the slot WG. It
can be clearly seen that both the signs of H
y
in Fig. 7 and H
x
in
Fig. 8 are positive. Thus it is the even supermode of the whole
structure. For the sake of brevity, the other supermode is not
shown here, whose H
x
and H
y
field components were of
different signs, similar to the field profile of an odd
supermode.
Fig. 6. Amplitude plot of P
z
(x,y) of dominating TM mode in strip WG.
Fig. 7. Amplitude plot of H
y
(x,y) of dominating TM mode in strip WG.
Fig. 8. Amplitude plot of H
x
(x,y) of dominating TM mode in strip WG.
