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Embedded ring resonators for microphotonic

applications

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: linzhang@usc.edu

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 [1], serial [2], 2D-arrayed [3],

or vertically coiled [4] 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 [8]. 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

“drop” ports

2t1

TFdrop= ?1

2r2exp?j?1/2???2

2exp?j?2? − 1?/A,

TFthrough= ?r1+ ?1

4r1exp?j?1???2

2?2t3

2r1r2

2exp?j?2? − r2

2?exp?j??1+ ?2?/2?

2?

+ ?1

2?1 + r1

2exp?j?2/2??/A,− ?2

A = ?1

4?2

2r1

2?2r1t3

2??1

2exp?j??1+ ?2??

+ 2?1

2exp?j??1+ ?2?/2?

− r3

4r1

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+t1

2

2+t2

2=1. ?1and ?2are round-trip phases in

Fig. 1.

and embedded ring resonators.

(Color online) Structures of previously proposed

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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

m1−m2is odd.

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 [9]. 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

rings, FSR1

andFSR2, and also their ratio

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 [10].

ERRs can be used for high-speed digital modula-

tion as well. When the electrical design of a microring

modulator is improved [11], 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 showninFig.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 [12], 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

[9] 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

whenametal-oxide-

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.

Fig. 3.

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-

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11.5 dB.

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

The corresponding signal

Q

factor is

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

Fig. 4.

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

±5%.

(Color online) ERR-based EIT effect with strong

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OPTICS LETTERS / Vol. 33, No. 17 / September 1, 2008