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976 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 10, MAY 15, 2014
Polarization Rotators in Add-Drop Filter Systems
With Double-Ring Resonators
Guoqiang Chen, Lixue Chen, Weiqiang Ding, Fangkui Sun, and Rui Feng
Abstract— A design of highly integrated polarization
rotators (PRs) with double-ring resonators in add-drop filter
systems is demonstrated theoretically. Based on mode-evolution
theory and 3D finite-difference time-domain simulation, two
vertically stacked microrings with dislocation are designed
and optimized, which efficiently decreases the size of PR to
a double-ring structure with a radius of <3.5 µmforthe
wavelength of 1.55 µm in a silicon-on-isolator system. Numerical
simulations obtain an extinction ratio (ER) of −22 dB and an
insertion loss of 0.07 dB with practical material parameters.
This PR combines the advantages of the periodic spectrum of
ring resonators and add-drop filtering functionality. The method
and result presented here can be valuable for applications in
polarization-diversity circuits.
Index Terms—Integrated optics, polarization rotators,
resonators, microcavity.
I. INTRODUCTION
COMPACT polarization rotators (PRs) are a key
component for future photonic integrated circuits.
PRs are highly desired in order to process orthogonally
polarized light. For this purpose, many types of PRs have
been proposed [1]–[5]. For widely used straight PRs based
on twisted silicon-on-insulator (SOI) structures, a fairly long
conversion length (tens of micrometers) is required to gain
a high extinction ratio [5], [6]. A nonlinear profiled PR can
reduce the conversion length to under 10 micrometers but
demands precise fabrication [4]. Therefore, there have been
increasing interests in optical PRs based on ring resonators,
which offer the intrinsic periodic spectral response [6]–[9].
In the microring PR, the polarization rotation is enhanced at
the resonant frequency, which makes the conversion spectral
response become frequency-dependent [10]. Microring PRs
improve the integration of polarization-diversity circuits, and
enrich the applications of the PR devices [9], [11].
The polarization conversion observed in microrings with a
sidewall angle [7] is explained as a resonant enhancement of
polarization coupling caused by waveguide bends [8], [9], [11].
For PRs based on optical waveguide bends, ring radii of
Manuscript received January 24, 2014; revised February 27, 2014; accepted
March 4, 2014. Date of publication March 6, 2014; date of current version
April 17, 2014. This work was supported in part by the Natural Science
Foundation of China under Grant 11004041 and in part by the National Basic
Research Program of China under Grant 2013CB328702.
The authors are with the Physics Department, Harbin Institute of
Technology, Harbin 150001, China (e-mail: gqchen.china@gmail.com;
clx@hit.edu.cn; wqding@hit.edu.cn; fksun@hit.edu.cn; fengrui_0223@
163.com).
Color versions of one or more of the figures in this letter are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LPT.2014.2310251
Fig. 1. (a) Schematic of the polarization rotator consisting of input bus
waveguide, output horizontal slot waveguide and double-ring resonators with
dislocation. The input TE polarized light in the bus waveguide is converted
into the TM mode in the microring, and output from the drop-port in the
slot waveguide. (b) Sectional view of half-ring in the double-ring resonators
of (a), which converts polarized modes from the TE mode in bottom ring to
the TM mode in horizontal slot region. (c), (d) and (e) indicate the electric
field evolution along the double-ring resonators.
∼20–∼200 μm are required to increase the hybridization
of the modes and hence the conversion efficiency, which
are undesirable in compact photonic integrated circuits.
Large free spectral range (FSR) also requires smaller radii.
However, decreasing of radius results in exponential increase
of radiation loss [9]. Therefore, it is highly desired to design
a PR with a small bending radius, while allowing a very
limited radiation loss.
In this letter, we propose an ultra-compact PR based on
the 4-port add-drop filter systems with vertically stacked
double-ring resonators [12]–[14]. The dislocation between the
vertically stacked double-ring resonators forms a twist along
the angular transmission as shown in Fig. 1. According to
the mode-evolution theory [1], the polarized modes can be
1041-1135 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
CHEN et al.: PRs IN ADD-DROP FILTER SYSTEMS 977
converted through the twist between the bus waveguide and
the slot waveguide [15], therefore it can efficiently convert the
quasi-transverse-electric (quasi-TE) mode in the straight bus
waveguide to the quasi-transverse-magnetic (quasi-TM) mode
in the horizontal slot waveguide, or vice versa. Numerical
simulations by three dimensional (3D) finite-difference time-
domain (FDTD) methods demonstrate an extinction ratio of
−22 dB and a FSR of 32 nm with the ring radius of only
3.5 μm.
II. DESIGN OF THE DOUBLE-RING PR
The schematic structure of the PR is shown in Fig. 1(a).
The device consists of two vertically stacked rings separated
by a thin slot layer with a thickness Tslot. The bottom ring is
horizontally coupled to the input bus waveguide. The top ring
is smaller than the bottom ring, and vertically aligned to the
bottom ring at the side of slot waveguide (filtering port), as
shown in Fig. 1(b). The radius of top ring is Ru=Rb−WC/2,
where Rbis the radius of bottom ring and WCis the width
of bus waveguide. The angular dislocation of the two layers
of rings can be regarded as a gradual change from a bus
waveguide to a slot waveguide. Therefore, the dislocation also
induces a twist along the angular propagation of light. Based
on the mode evolution theory, the twist along the propagation
direction rotates the polarization, and induces couplings among
the polarized modes.
Once coupled into the bottom ring from the input bus
waveguide, the polarized light propagates from the TE polar-
ized bottom ring to the TM polarized slot between the double-
ring resonators. The first-half ring acts as a PR similar to
previous designs based on mode-evolution theory [1], and
the only difference is that light propagates along the angular
direction in the double-ring PR investigated here. Through
the twist of half-ring from the bus waveguide to the slot
waveguide, the TE mode in the bottom ring is converted into
the TM mode in the slot region, and converted back to the TE
mode through the other half-ring as shown in Fig. 1(c)–(e).
The converted TM mode at the resonant frequency is coupled
to the output slot waveguide. These vertically stacked double-
rings with dislocation combine the spectral performance of
ring resonators and polarization-mode rotation.
The strip waveguides and rings are silicon structures
embedded in SiO2cladding (the slotted regions are also
filled with SiO2). The refractive indices of Si and SiO2are
nH=3.48 and nL=1.46, respectively, around the wavelength
of 1.55 μm. The thicknesses of the horizontal slot and the
strip waveguide are designed to be Tslot =20 nm and
TSi =200 nm, respectively. The widths of the input bus
waveguide and slot waveguide are WCand WS. The width
of both rings at the side of slot waveguide is set equal to
WS. The width of the bottom ring is equal to WCat the
side of bus waveguide. The microring and channel waveguide
are phase-matched and have the same propagation constant.
The mode conversion in the half-ring [see Fig. 1(b)] also
requires being phase-matched. The TE mode in the bottom
ring and the TM mode in the slotted double-ring should have
the same propagation constant. Therefore the optimized widths
Fig. 2. Polarization-conversion efficiency at resonant frequency for various
Tslot values of 20 nm, 30 nm and 40 nm, and the FSR as a function of
microring radius Rbis shown also to the right y axis.
of WCand WSare designed to be WC=290 nm and
WS=230 nm, which ensure the polarized mode propagation
constants βTM =βTE.
III. CHARACTERISTICS OF POLARIZATION ROTATOR
The polarization-conversion efficiency mainly depends on
the conversion length and the coupling coefficient between
microring and bus/slot waveguide. There are also several other
factors that affect the coupling slightly, such as the microring
radiative loss, the scattering losses from the microring sidewall
roughness, and the microring internal losses due to different
mechanisms including material loss [16]. The polarization
rotation is primarily dependent on the conversion length of
PRs, which means a larger radius is demanded. Fig. 2 plots the
polarization-conversion efficiency as a function of microring’s
radius for different slot thickness Tslot at the resonant fre-
quency around 1.55 μm. To keep the polarization conversion
efficiency no smaller than 0.95, the radii of microring should
be larger than 3.5 μmforTslot =20 nm. With a fixed
radius Rb, the polarization conversion decreases as the Tslot
increases [17] as seen in Fig. 2. With larger Tslot such as 30 nm
and 40 nm, we need much larger radii (i.e. longer conversion
length) to achieve complete polarization conversion.
High conversion efficiency with large radii is, however, at
the cost of small FSRs, which can be demonstrated by [18]
FSR ≈λ2/2πngR(1)
where λis the wavelength, ngis the group refractive index
of the microring mode, and Ris the ring radius. The inverse
dependence of FSR on radius Rbis also shown in Fig. 2.
In the case that Tslot =20 nm, the FSR of double-ring
deceases with Rbfollowing the 1/Rdependence.
Another concern affecting the choice of the radii of micror-
ing is the radiative and scattering loss. The scattering loss
caused by the roughness of sidewalls is ignored in our simu-
lation. Microrings with small radii have a large radiative loss.
Therefore the radius of the microring should not be too small
in order to keep a high quality factor, which will be discussed
in the next section.
At the resonant wavelength of 1.532 μm, the power transfer
from the TE- to TM-polarized mode is shown in Fig. 3.
978 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 10, MAY 15, 2014
Fig. 3. Energy density distribution for the TM and TE modes at the resonant
wavelength of 1.532 μm.
Fig. 4. Transmission spectra of different output channels: (a) the blue solid
line represents the rotated TM mode and the red dashed line represents the
TE mode from the drop-port; (b) the red dashed line represents the TE mode
and the blue solid line represents the TM mode from the though-port. The
thickness of the horizontal slot is Tslot =20 nm, and the thickness of the
single ring is TSi =200 nm. The radius of bottom ring is Rb=3.5μm.
The rotated TM mode can be seen enhanced in half ring
(converted from the TE mode coupled from the input bus
waveguide) and diminished in the other half (converted back
to the TE mode). The rotated TM mode is coupled into
the horizontal slot waveguide and output from the drop-port.
Fig. 4(a) shows the rotated TM mode and the TE mode spectra
at the drop-port with Tslot =20 nm and TSi =200 nm.
Fig. 4(b) shows the transmission of the filtered TE mode
and TM mode at the through-port. These spectra indicate a
resonant peak which keeps the ER as high as −22 dB at the
Fig. 5. (a) Insertion loss and ER of both TE-TM (solid line) and TM-TE
(dashed line) conversions at the resonant frequency as a function of horizontal
slot thickness. (b) ER versus the TSi variations with different Tslot.
wavelength of 1.532 μm. This also verifies that the TE-TM
polarized modes conversion occurs at the resonant frequency
of the microring. The normalized converted TM mode can
be as high as 0.967. The FSR can be kept at 32 nm with
Rb=3.5μm.
IV. QUALITY FACTOR AND INSERTION LOSS
Although double-ring resonators with dislocation can rotate
polarization modes, the coupling between polarized modes
limits the quality factor of ring resonator. The coupling loss of
PR induces a Qrot in addition to intrinsic Qint and coupling
induced Qcpl in conventional single-ring resonators with one
polarization [19], [20]. Thus, the quality factor of microring is
given as Q−1=Q−1
int +Q−1
rot +Q−1
cpl,whereQint consists of
the radiative loss, the surface scattering loss and the surface
absorption (ignored in our simulation); Qrot is attributed to
the coupling between polarized modes; Qcpl is attributed to
the coupling between the resonator and the strip waveguides.
The quality factor can be calculated by
Q=2πfresϕ(2)
where ϕis the attenuation constant of power in the resonator
and fres is one resonant frequency. By measuring the power
attenuation in the resonator, we can obtain that the Qint in the
double-ring resonators with Rb=3.5μm is over 105,which
is much larger than Qcpl and Qrot. Therefore the contribution
of Qint in the total Qcan be negligible. The loaded quality
factor in our double-ring resonators without dislocation is
2.2×103, and is mainly attributed to the Qcpl . The double-
ring PR has a loaded Qof 800 as shown in Fig. 4. Therefore
CHEN et al.: PRs IN ADD-DROP FILTER SYSTEMS 979
Qrot =1.2×103has a major influence on the loaded Qwith
Rb=3.5μm. This is the result considering the TM mode as
the output signal.
In Fig. 5(a), the slot thickness dependence of insertion loss
is shown. The insertion loss in PR is correlated with the ratio
of the rotated TM mode to the input power, corresponding to
the rotation Qrot. The loss increases with the slot thickness
with Tslot increasefrom20nmto60nmwithafixedRbof
3.5 μm. The rotation Qrot decreases with Tslot, and becomes
the major part of the loaded Qin the case that the polarization
conversion is significantly below 1. Thin slot waveguides will
improve the quality factor and polarization rotation; therefore
the horizontal slot between the two stacked rings demands to
be thin enough. Due to possible fabrication errors, we give an
analysis on the ER variations caused by Tslot and TSi variations
as shown in Fig. 5(b). The ER is more sensitive to Tslot rather
than TSi. Considering the horizontal slot thickness is largely
limited by fabrication in practice, we set the thickness Tslot to
be 20 nm in this letter.
The polarization conversion of this microring PR structure
is reversible, as shown in Fig. 5(a). As we have discussed the
TE-to-TM conversion, the TM mode input from the horizontal
slot waveguide can also be converted into the TE-mode output
in the bus waveguide with a high ER and a low loss. When
Rb=3.5μmandTslot =20 nm, the loss in the TE-TM
conversion is 0.07 dB, and 1.6 dB in the case of the TM-TE
conversion. Although not as high as −22 dB in the forward
TE-to-TM conversion [5], the ER of the backward TM-to-TE
conversion obtains a decent −16 dB at resonance.
V. CONCLUSION
In conclusion, we have presented an ultra-compact polar-
ization rotator consisting of vertically stacked double-ring
resonators with dislocation. The mechanism of this micror-
ing polarization rotator is analyzed using the mode-evolution
theory: polarized modes are rotated when propagating along
the angular direction. The conversion is introduced by the
dislocation of the two rings. The combination of double-
ring resonators and a polarization rotator provides a periodic
response spectrum for the rotated mode; meanwhile increases
the integration and reduces the size of PR. Numerical sim-
ulations using 3D FDTD verified the performances of the
structure. For the radius of 3.5 μm, this PR can provide
an extinction ratio exceeding −22 dB, and an insertion loss
below 0.07 dB for the TE-to-TM rotation. Polarization rotators
based on ring resonators are frequency selective. They can be
exploited in applications in the field of wavelength-division-
multiplexing (WDM) systems with polarization-sensitive com-
ponents, polarization-interleaved transmission systems [21]
within a spectral range of interest and polarizationdiversity
schemes.
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