Embedded ring resonators for microphotonic
Lin Zhang,1,* Muping Song,1,2Teng Wu,1Lianggang Zou,2Raymond G. Beausoleil,3and Alan E. Willner1
1Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
2Department of Information and Electronic Engineering, Zhejiang University, Hangzhou, Zhejiang, 310027, China
3Hewlett-Packard Laboratories, 3000 Hanover Street, Palo Alto, California 94304, USA
* Corresponding author: firstname.lastname@example.org
Received June 12, 2008; revised July 23, 2008; accepted July 25, 2008;
posted July 29, 2008 (Doc. ID 97157); published August 25, 2008
We propose a new type of optical resonator that consists of embedded ring resonators (ERRs). The resonators
exhibit unique amplitude and phase characteristics and allow designing compact filters, modulators, and
delay elements. A basic configuration of the ERRs with two rings coupled in a point-to-point manner is dis-
cussed under two operating conditions. An ERR-based microring modulator shows a high operation speed up
to 30 GHz. ERRs with distributed coupling are briefly described as well. © 2008 Optical Society of America
OCIS codes: 130.3120, 230.3990, 230.5750.
In recent years microresonators have exhibited great
design flexibility and unique advantages for achiev-
ing various compact devices, including lasers, modu-
lators, switches, filters, delay elements, signal pro-
cessing units, and sensors. Much progress has been
made in designing and fabricating these sophisti-
cated devices by employing multiple rings that are
cascaded in a parallel , serial , 2D-arrayed ,
or vertically coiled  configuration, as shown in Fig.
1. However, a cascade of many ring resonators may
require an increased chip size.
In this Letter, we propose an embedded configura-
tion as another way to cascade the ring resonators.
Typically, the rings are embedded with coupling in ei-
ther a point-to-point or distributed manner, as shown
in Fig. 1. The embedded ring resonator (ERR) may
enable a smaller footprint and unique amplitude and
phase characteristics. For example, the ERR struc-
ture can produce an electromagnetically induced
transparency (EIT)-like effect that could be used for
high-speed modulation up to 30 Gbits/s, which is
hardly achieved using previously reported EIT-like
microring structures [5–7].
For an ERR with point-to-point coupling, as shown
in Fig. 2(a), one can derive its transfer function using
coupled mode theory . For simplicity, the coupling
coefficients at A and B are set to be the same, while
the coupling coefficients at C and D are the same as
well. We obtain transfer functions at “through” and
2exp?j?2? − 1?/A,
TFthrough= ?r1+ ?1
2exp?j?2? − r2
2?1 + r1
A = ?1
2exp?j?1? + ?2
2exp?j?2?? + 1.
Coupling is assumed to be lossless. ?r1,t1? and ?r1,t2?
represent the amplitude coupling coefficients be-
tween the outer ring and the waveguides and be-
tween the two rings, respectively, satisfying r1
=1 and r2
the outer and inner rings, while ?1and ?2are ampli-
tude transmission coefficients within the quarter
round-trip in the outer ring and half round-trip in the
inner ring, respectively. The two rings have their own
resonance wavelengths ?R1and ?R2, satisfying n·L1
=m1·?R1and n·L2=m2·?R2, where n is the effective
refractive index; L1and L2are perimeters of the
outer and inner rings; and m1and m2are integer
numbers. When ?R1and ?R2are set to be the same,
the ERR has two typical working regimes:
(i) m1−m2is an even number (here, m1=46, m2
=32), in which case the transfer function at the
through port features a doublet in amplitude re-
sponse. As shown in Fig. 2(a), two notches occur at
wavelengths ?1and ?3that are equally shifted from
the common resonance wavelength ?2of the two
rings. Finite-difference time domain (FDTD) simula-
tions for the TE mode show the symmetric and anti-
symmetric field distributions at coupling areas A and
B in Fig. 2(b), excited at wavelength ?1and ?3, re-
2=1. ?1and ?2are round-trip phases in
and embedded ring resonators.
(Color online) Structures of previously proposed
OPTICS LETTERS / Vol. 33, No. 17 / September 1, 2008
0146-9592/08/171978-3/$15.00© 2008 Optical Society of America
spectively. In this case, waveguide width is 300 nm
and waveguide spacing in four coupling areas is
160 nm. The size of the ring resonators are set to
match integers m1=46 and m2=32.
(ii) m1−m2is an odd number (here, m1=47, m2
=32), in which case the through-port transfer func-
tion shown in Fig. 2(a) features an EIT-like profile
centered at wavelength ?2. With an input continuous
wave at ?2, the FDTD simulation shows that half of
the inner ring is brighter than the other half, as il-
lustrated in Fig. 2(b). This is because the phase dif-
ference between the two optical waves traveling over
a half round-trip of the two rings is ?m1−m2?? and
The ERR is characterized with varied coupling co-
efficients between the waveguide and the outer ring
and is compared to single- and double-ring resona-
tors . When m1−m2is an odd number (m1=47,
m2=32), the normalized output power at resonance
wavelength at the through port increases with the
coupling in Fig. 3. The power coupling coefficient be-
tween the two rings is set to be 0.13, and the loss is
2.23 dB/cm. The group delay can be enhanced in an
EIT-like profile. Compared to a single- or double-ring
resonator with the same structural parameters, the
group delay is increased by ten times using ERRs.
However, we note that the resonance linewidth also
becomes ten times narrower, so the delay-bandwidth
trade-off still holds. ERR structures have a Vernier
effect, and the overall free spectral range (FSR) can
be designed by changing individual FSRs of the two
and FSR2, and alsotheirratio
FSR2/FSR1. An effective FSR extension has been re-
ported by embedding a small ring into a bigger one
with an output waveguide vertically coupled to the
inner ring .
ERRs can be used for high-speed digital modula-
tion as well. When the electrical design of a microring
modulator is improved , the modulation speed is
limited in the optical domain by the photon lifetime
of the resonator that determines how fast light can be
coupled into and out of the resonator. For a single-
ring modulator, weak coupling allows increasing cav-
ity Q and generating good extinction ratio by apply-
ing relatively low voltage, but this limits modulation
speed. For example, in 10 Gbits/s modulation, the
power coupling coefficient between the ring and the
waveguide has to be ?0.02 (for a 5 ?m radius) to ob-
tain a 10 GHz linewidth (i.e., cavity Q=19,000). In
contrast, an ERR can have a 10 GHz resonance in the
EIT-like profile, even if all power coupling coefficients
are up to 0.13 (i.e., cavity Q=?1500). The narrow
profile results from the interaction of two low-Q reso-
nators, which greatly relaxes the limitation on
modulation speed imposed by the photon lifetime.
As shown inFig. 4(a),
semiconductor capacitor is integrated onto the inner
ring with a carrier transit time of 16 ps, the reso-
nance peak can be shifted for intensity modulation by
applying a voltage of 4.5 V and thus varying the re-
fractive index of the inner ring , which is corre-
sponding to a frequency shift of ?10 GHz of the inner
ring ??m2?2?10−3?. One may not want to drive the
two rings at the same time, because this costs more
driving power, needs a different drive voltage for
each ring, and requires very accurate fabrication of
two electrodes. A dynamic model is developed from
 to simulate the performance of this modulator.
Figure 4(b) shows eye diagrams for 20, 25, and
30 Gbits/s intensity modulations in comparison with
a 30 Gbits/s signal generated by a single-ring modu-
lator with the same linewidth and drive voltage. The
ERR-generated 30 Gbits/s
larger eye-opening with an extinction ratio of
signal exhibits much
Fig. 2. (Color online) An ERR with point-to-point coupling
and its frequency responses at the through port for (i) m1
−m2=even and (ii) m1−m2=odd. (b) Mode distributions
with cw inputs at wavelengths ?1 and ?3 for m1−m2
=even and ?2for m1−m2=odd.
sion, and delay versus coupling between the waveguide and
the ring, compared to single- and double-ring resonators.
m1−m2is an odd number, normalized transmis-
September 1, 2008 / Vol. 33, No. 17 / OPTICS LETTERS
16.7 dB, which indicates that an error-free detection
(bit error rate ?10−9) can be obtained. Silicon ERR-
based EIT enables digital modulation at even
30 Gbits/s with an extinction ratio of ?11 dB by ap-
plying 4.5 V voltage, which is hardly achieved using
previously reported EIT-like microrings. This ERR-
based modulator could be tolerant to a variation of
coupling coefficients. We examine the generated sig-
nal quality at 30 Gbits/s when the power coupling co-
efficient at the B area is changed by ±5%, which
causes asymmetric coupling between the two rings.
As shown in Fig. 4(c), the signal eye diagram remains
almost unchanged for the variation of the coupling
coefficient by 10% in total, and the signal Q factor is
16.7, 16.6, and 16.3 dB. This good stability can be at-
tributed to the fact that this ERR used here for signal
modulation is made highly overcoupled by increasing
coupling coefficients, and a relatively small perturba-
tion to coupling coefficients can hardly change the
resonator to undercoupling.
ERRs can interact with each other by distributed
coupling. They exhibit EIT-like profiles if m1−m2is
odd and are expected to be useful as modulators as
well. Concentric structures have been proposed
[13–15] to form a single resonator with desired prop-
erties, in which mode distributions in all the rings
contain the same number of optical cycles. In our
case, ERRs can have different working regimes. We
choose a radius of 2.4 ?m ?m1=27? for the outer ring
and shrink the inner ring. When the inner-ring ra-
dius is 2.06 ?m, symmetric and antisymmetric
modes are formed as shown in Figs. 5(a) and 5(b). In
this case, the two rings form a single resonator. Field
distributions are captured at 5 ps. The symmetric
mode mainly stays in the outer ring and is built
quickly (i.e., a low cavity Q), while the antisymmetric
mode is mostly concentrated in the inner ring with a
higher Q. In contrast, as the inner ring is shrunk, ow-
ing to the phase difference between the two traveling
modes, each ring becomes an independent resonator
that has its own mode number. There are ?m1−m2?
power-fluctuated areas, separated by solid lines in
Figs. 5(c) and 5(d), where the inner-ring radius is
1.96 and 1.86 ?m with m2=22 and 21, respectively.
Different from a well-separated mode pattern of the
inner ring in Fig. 5(c), the inner ring has an almost
uniform field distribution in Fig. 5(d).
The authors thank M.-J. Chu for helpful discus-
sions. This work is sponsored by Army Nanophoton-
ics program and HP Labs.
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Fig. 5. (Color online) Mode distributions in the ERRs with
distributed coupling. m1=27. (a),(b) m1=23, for symmetric
and antisymmetric modes. m1=?c? 22 and (d) 21 correspond
to independent resonator modes
coupling is used for high-speed modulation. (b) Signal eye
diagrams at 20, 25, and 30 Gbits/s, as compared to the sig-
nal generated by a single-ring modulator with the same
linewidth and drive voltage. (c) Signal quality is examined
when the coupling coefficient at the B area is changed by
(Color online) ERR-based EIT effect with strong
OPTICS LETTERS / Vol. 33, No. 17 / September 1, 2008