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OPTICS LETTERS / Vol. 33, No. 17 / September 1, 2008
Embedded ring resonators for microphotonic applications Lin Zhang,1,* Muping Song,1,2 Teng Wu,1 Lianggang Zou,2 Raymond G. Beausoleil,3 and Alan E. Willner1 1 Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA Department of Information and Electronic Engineering, Zhejiang University, Hangzhou, Zhejiang, 310027, China 3 Hewlett-Packard Laboratories, 3000 Hanover Street, Palo Alto, California 94304, USA *Corresponding author:
[email protected]
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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 discussed 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 achieving various compact devices, including lasers, modulators, switches, filters, delay elements, signal processing units, and sensors. Much progress has been made in designing and fabricating these sophisticated 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 configuration as another way to cascade the ring resonators. Typically, the rings are embedded with coupling in either 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 structure 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
Coupling is assumed to be lossless. 共r1 , t1兲 and 共r1 , t2兲 represent the amplitude coupling coefficients between the outer ring and the waveguides and between the two rings, respectively, satisfying r12 + t12 = 1 and r22 + t22 = 1. 1 and 2 are round-trip phases in the outer and inner rings, while 1 and 2 are amplitude 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 R1 and R2, satisfying n · L1 = m1 · R1 and n · L2 = m2 · R2, where n is the effective refractive index; L1 and L2 are perimeters of the outer and inner rings; and m1 and m2 are integer numbers. When R1 and R2 are set to be the same, the ERR has two typical working regimes: (i) m1 − m2 is an even number (here, m1 = 46, m2 = 32), in which case the transfer function at the through port features a doublet in amplitude response. As shown in Fig. 2(a), two notches occur at wavelengths 1 and 3 that are equally shifted from the common resonance wavelength 2 of the two rings. Finite-difference time domain (FDTD) simulations for the TE mode show the symmetric and antisymmetric field distributions at coupling areas A and B in Fig. 2(b), excited at wavelength 1 and 3, re-
TFdrop = 12t12r2 exp共j1/2兲关22 exp共j2兲 − 1兴/A, TFthrough = 兵r1 + 14r1 exp共j1兲关22 exp共j2兲 − r22兴 + 122t32共1 + r12兲exp关j共1 + 2兲/2兴 − 22r1r22 exp共j2/2兲其/A, A = 1422r12 exp关j共1 + 2兲兴 + 2122r1t32 exp关j共1 + 2兲/2兴 − r32关14r12 exp共j1兲 + 22 exp共j2兲兴 + 1. 0146-9592/08/171978-3/$15.00
Fig. 1. (Color online) Structures of previously proposed and embedded ring resonators. © 2008 Optical Society of America
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Fig. 3. m1 − m2 is an odd number, normalized transmission, and delay versus coupling between the waveguide and the ring, compared to single- and double-ring resonators.
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 2 for m1 − m2 = odd.
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 − m2 is an odd number (here, m1 = 47, m2 = 32), in which case the through-port transfer function 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 illustrated in Fig. 2(b). This is because the phase difference between the two optical waves traveling over a half round-trip of the two rings is 共m1 − m2兲 and m1 − m2 is odd. The ERR is characterized with varied coupling coefficients between the waveguide and the outer ring and is compared to single- and double-ring resonators [9]. When m1 − m2 is 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 between 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 and FSR2, and also their ratio
FSR2 / FSR1. An effective FSR extension has been reported 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 modulation 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 singlering modulator, weak coupling allows increasing cavity Q and generating good extinction ratio by applying 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 obtain 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 resonators, which greatly relaxes the limitation on modulation speed imposed by the photon lifetime. As shown in Fig. 4(a), when a metal-oxidesemiconductor capacitor is integrated onto the inner ring with a carrier transit time of 16 ps, the resonance peak can be shifted for intensity modulation by applying a voltage of 4.5 V and thus varying the refractive index of the inner ring [12], which is corresponding to a frequency shift of ⬃10 GHz of the inner ring 共⌬m2 ⬇ 2 ⫻ 10−3兲. 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 modulator with the same linewidth and drive voltage. The ERR-generated 30 Gbits/ s signal exhibits much larger eye-opening with an extinction ratio of
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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 = 共c兲 22 and (d) 21 correspond to independent resonator modes
Fig. 4. (Color online) ERR-based EIT effect with strong coupling is used for high-speed modulation. (b) Signal eye diagrams at 20, 25, and 30 Gbits/ s, as compared to the signal 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%.
11.5 dB. The corresponding signal Q factor is 16.7 dB, which indicates that an error-free detection (bit error rate ⬍10−9) can be obtained. Silicon ERRbased EIT enables digital modulation at even 30 Gbits/ s with an extinction ratio of ⬎11 dB by applying 4.5 V voltage, which is hardly achieved using previously reported EIT-like microrings. This ERRbased modulator could be tolerant to a variation of coupling coefficients. We examine the generated signal quality at 30 Gbits/ s when the power coupling coefficient 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 attributed to the fact that this ERR used here for signal modulation is made highly overcoupled by increasing coupling coefficients, and a relatively small perturbation 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 − m2 is 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 properties, 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 共m1 = 27兲 for the outer ring and shrink the inner ring. When the inner-ring radius 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, owing to the phase difference between the two traveling modes, each ring becomes an independent resonator that has its own mode number. There are 共m1 − m2兲 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 discussions. This work is sponsored by Army Nanophotonics program and HP Labs. References 1. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999). 2. J. E. Heebner, R. W. Boyd, and Q-H. Park, J. Opt. Soc. Am. B 19, 722 (2002). 3. Y. M. Landobasa, S. Darmawan, and M.-K. Chin, IEEE J. Quantum Electron. 41, 1410 (2005). 4. M. Sumetsky, Opt. Express 12, 2303 (2004). 5. S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, IEEE Photon. Technol. Lett. 11, 1426 (1999). 6. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004). 7. S. J. Emelett and R. A. Soref, Opt. Express 13, 7840 (2005). 8. A. Yariv, Electron. Lett. 36, 321 (2000). 9. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997). 10. I. S. Hidayat, Y. Toyota, O. Torigoe, O. Wada, and R. Koga, Mem. Fac. Eng. Okayama Univ. 36, 73 (2002). 11. S. Manipatruni, Q. Xu, and M. Lipson, Opt. Express 15, 13035 (2007). 12. C. A. Barrios and M. Lipson, J. Appl. Phys. 96, 6008 (2004). 13. L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999). 14. J. Scheuer and A. Yariv, Opt. Lett. 28, 1528 (2003). 15. Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, Opt. Express 16, 4621 (2008).
