Electro-optic phase matching in a Si photonic crystal slow light modulator using meanderline electrodes

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1 ol. 26, No Apr 2018 OPTICS EXPRESS Electro-optic phase matching in a Si photonic crystal slow light modulator using meanderline electrodes YOSUKE HINAKURA,* YOSUKE TERADA, HIROYUKI ARAI, AND TOSHIHIKO BABA Department of Electrical and Computer Engineering, Yokohama National University, 79-5Tokiwadai, Hodogaya-ku, Yokohama , Japan *hinakura-yosuke-zm@ynu.jp Abstract: We demonstrate a Si photonic crystal waveguide Mach Zehnder modulator that incorporates meander-line electrodes to compensate for the phase mismatch between slow light and RF signals. We first employed commonized ground electrodes in the modulator to suppress undesired fluctuations in the electro-optic (EO) response due to coupled slot-line modes of RF signals. Then, we theoretically and experimentally investigated the effect of the phase mismatch on the EO response. We confirmed that meander-line electrodes improve the EO response, particularly in the absence of internal reflection of the RF signals. The cut-off frequency of this device can reach 27 GHz, which allows high-speed modulation up to 50 Gbps Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: ( ) Integrated optics devices; ( ) Modulators; ( ) Photonic crystal waveguides. References and links G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, and D. J. Thomson, Silicon optical modulators, Nat. Photonics 4(8), (2010). D. J. Thomson, F. Y. Gardes, S. iu, H. Porte,. Zimmermann, J. M. Fedeli, Y. Hu, M. Nedeljkovic, X. Yang, P. Petropoulos, and G. Z. Mashanovich, High Performance Mach-Zehnder-Based Silicon Optical Modulators, IEEE J. Sel. Top. Quantum Electron. 19(6), (2013). H. Xu, X. i, X. Xiao, Z. i, Y. Yu, and J. Yu, Demonstration and Characterization of High-Speed Silicon Depletion-Mode Mach Zehnder Modulators, IEEE J. Sel. Top. Quantum Electron. 20(4), (2014). X. Tu, K. F. Chang, T. Y. iow, J. Song, X. uo,. Jia, Q. Fang, M. Yu, G. Q. o, P. Dong, and Y. K. Chen, Silicon optical modulator with shield coplanar waveguide electrodes, Opt. Express 22(19), (2014). H. Yu and W. Bogaerts, An Equivalent Circuit Model of the Traveling Wave Electrode for Carrier-DepletionBased Silicon Optical Modulators, J. ightwave Technol. 30(11), (2012). J. Shin, S. R. Sakamoto, and N. Dagli, Conductor oss of Capacitively oaded Slow Wave Electrodes for High-Speed Photonic Devices, J. ightwave Technol. 29(1), (2011). R. Ding, Y. iu, Y. Ma, Y. Yang, Q. i, A. E. J. im, G. Q. o, K. Bergman, T. B. Jones, and M. Hochberg, High-Speed Silicon Modulator With Slow-Wave Electrodes and Fully Independent Differential Drive, J. ightwave Technol. 32(12), (2014). D. Patel, S. Ghosh, M. Chagnon, A. Samani,. eerasubramanian, M. Osman, and D.. Plant, Design, analysis, and transmission system performance of a 41 GHz silicon photonic modulator, Opt. Express 23(11), (2015). Y. Terada, T. Tatebe, Y. Hinakura, and T. Baba, Si Photonic Crystal Slow-ight Modulators with Periodic p n Junctions, J. ightwave Technol. 35(9), (2017). Y. Hinakura, Y. Terada, T. Tamura, and T. Baba, Wide spectral characteristics of Si photonic crystal MachZehnder modulator fabricated by complementary metal oxide semiconductor process, Photonics 3(2), 17 (2016). K. Hojo, Y. Terada, N. Yazawa, T. Watanabe, and T. Baba, Compact QPSK and PAM modulators with Si photonic crystal slow light phase shifters, IEEE Photonics Technol. ett. 28(13), (2016). T. Tamura, K. Kondo, Y. Terada, Y. Hinakura, N. Ishikura, and T. Baba, Silica-clad silicon photonic crystal waveguides for wideband dispersion-free slow light, J. ightwave Technol. 33(7), (2015). K. Kubota, J. Noda, and O. Mikami, Traveling wave optical modulator using a directional coupler inbo3waveguide, IEEE J. Quantum Electron. 16(7), (1980). I. Kim, M. R. T. Tan, and S. Y. Wang, Analysis of a new microwave low-loss and velocity-matched III- transmission line for traveling-wave electrooptic modulators, J. ightwave Technol. 8(5), (1990). # Journal Received 9 Mar 2018; revised 16 Apr 2018; accepted 17 Apr 2018; published 19 Apr 2018

2 ol. 26, No Apr 2018 OPTICS EXPRESS G. E. Ponchak, J. Papapolymerou, and M. M. Tentzeris, Excitation of coupled slotline mode in finite-ground CPW with unequal ground-plane widths, IEEE Trans. Microw. Theory Tech. 53(2), (2005). 1. Introduction Silicon (Si) photonics have become a standard platform for integrating functional photonic devices with optical interconnects owing to the strong optical confinement of Si waveguides, high accuracy, reproducible, and low cost mass production using complementary metal oxide semiconductor (CMOS) processing. For their use as optical interconnects, modulators with high speed, small size, low loss, low power consumption, and large operating wavelength and temperature tolerances are important. Mach Zehnder modulators (MZMs) exploit carrier depletion in p-n doped Si rib waveguides. These devices allow high speed and large tolerances in wavelength and temperature [1 8] and have been used in commercial systems because of these practical advantages. However, they require a long phase shifter of the order of several millimeters, which increases the device size and power consumption. Our research group has studied photonic crystal waveguide (PCW) MZMs, which enhance the phase shift Δφ in proportion to the slow-light group index n g. This allows a reduction in the length of the phase shifter, which also reduces power consumption [9 11]. A PCW can produce a wide range of n g from <10 to ~100 by structural tuning [12]. The group index can be set between 20 and 30 to balance the advantages of slow light, a sufficiently wide working spectrum, and moderately low propagation loss. This value is five to seven times larger than n g in Si rib waveguides. attice-shifted PCWs (SPCWs), which feature specific rows of holes that are shifted in the photonic crystal slab along the waveguide, can produce low dispersion slow light over a wide working spectrum of Δλ = nm. By employing a wavy p-n junction, a large phase shift Δφ can be obtained with a fast operating speed. 32 Gbps modulation has been obtained with an extinction ratio ER = 3 db and an excess modulation loss M = 1 db using a phase shifter of length = 200 μm and drive voltage pp = 1.75 [9]. A large value of the group index potentially reduces the operating voltage, but it simultaneously degrades the frequency response because of the electro-optic (EO) phase mismatch [10]. The modal index for an RF signal, n RF, ranges from 2 to 6 [4,5,7], which is much different from n g 20 for slow light. Therefore, the phase of the modulated slow light deviates from the RF signal phase as the waves propagate. The mismatch becomes large as the frequency increases, ultimately degrading the frequency response. Several studies have discussed the compensation of the phase mismatch in MZMs based on Si, inbo 3, and III- semiconductors [6 8,13,14]. One may consider to use capacitively-loaded slow-wave electrodes, which has been studied for phase or impedance matching [6 8]. However, n RF in these electrodes is 6 at most, which is not sufficiently high to offset the phase mismatch. An increasingly efficient phase matching scheme is needed to use slow light in MZMs at high operating speeds. In addition, we have previously observed a peculiar local minimum in the frequency response of such devices [10]. This minimum is likely caused by unwanted coupled slot-line (CS) modes in the RF signal, which are excited owing to the imbalance of the electric potential between the ground (G) electrodes placed on both sides of the central signal (S) electrode [15]. This dip must be suppressed because it obscures the EO phase mismatch, which makes compensating for that mismatch increasingly difficult. Xu et al. suppressed this minimum by commonizing the ground electrodes with wire bonding [3]. The device proposed in this paper employs meander-line electrodes to suppress the phase mismatch and improve the frequency response of a Si photonic crystal slow light MZM. The meander-line electrodes delay the RF signals by simply extending the electrode length. In the device s preparation, we first discuss an experimental test that confirms that commonized ground electrodes suppress the unwanted spectral local minimum, and then we focus on a design that compensates for the phase mismatch between the RF and slow light signals. We theoretically and experimentally determine the manner in which the frequency response is degraded by the phase mismatch and the manner it is compensated by the meander-line

3 ol. 26, No Apr 2018 OPTICS EXPRESS electrodes. We finally optimize the meander-line electrodes considering the reflection of RF signals at the ends of the phase shifters. 2. Device fabrication We fabricated prototypes using a standard Si photonics CMOS process with a 200-mmdiameter silicon-on-insulator (Si thickness of 210 nm), KrF excimer laser exposure (λ = 248 nm), and phase shift masks with resolution less than 130 nm. Figure 1 shows the p-n doped and SiO 2 -cladded PCW MZMs that were fabricated. The Al coplanar waveguide (CPW) comprises a signal electrode and a pair of ground electrodes sandwiching the signal electrode. Termination resistors were not included in the design to simplify the device layout. In device (a), the ground electrodes are independent, while in devices (b) and (c), they were commonized. We used PCWs without lattice shifts to take advantage of the gradually increasing n g spectrum, which allows us to test a range of slow light group indices by varying the wavelength. We set the lattice constant a = 400 nm, the hole diameter 2r = 190 nm or 220 nm, and phase shifter length = 200 μm. The design also employs a simple linear p-n junction. Although the interleaved and wavy junctions we have studied in the past effectively increase Δφ [9], a linear junction is appropriate for evaluating the phase mismatch because the frequency response is constrained less by the RC time constant. The p- and n-type doping concentrations were N A = cm 3 and N D = cm 3, respectively. p + and n + doping was performed for the metal contacts at a concentration of N A + = N D + = cm 3. The doping sites were spaced at 4-µm intervals across the p-n junction to avoid strong free carrier absorption. Also, 36.5-μm long TiN heaters were integrated inside the SiO 2 cladding above the PCWs so that we could tune the initial phase using the thermo-optic effect. Fig. 1. Fabricated Si PCW MZMs. (a) Normal electrode device without commonizing grounds.in the inset, the p- and n-doped regions are colored. (b) Normal electrode device with commonized grounds. (c) Meander-line electrode device with commonized grounds. Insets show the details of a bend in the meander-line electrode and the separated p-n junction. For device (c), we introduced meander-line electrodes of length d and RF index n d as the signal electrodes in the CPWs. Similar to the electrodes at the PCW phase shifter, the Si layer was left intact and a metal contact was formed below the meander-line electrode. However, n d is different from n RF because of the no doping in this region; we assumed n d = 2 and n RF = 4, referring to [7]. The phase mismatch at the end of the phase shifter was given by δφ = 2πf [(n g n RF ) n d d ]/c. where f is the frequency of RF signals. We set d = 1186 μm to make δφ =

4 ol. 26, No Apr 2018 OPTICS EXPRESS when n g = 15.9 for slow light. Although the device footprint is increased by these electrodes, it is still much smaller than rib waveguide devices, and its width is comparable to the total width of probe pads. In the meander-line electrodes, we placed a corner reflector at each bend, which minimizes the impedance change and suppresses the reflection of RF signals. We separated the p-n junctions before and after the meander-line electrodes to maintain the continuity of the PCW and Si slab so that the waveguide loss is almost the same as it is for devices (a) and (b). The typical on-chip loss of a 200-μm p-n doped PCW is ~5 db, including the coupling loss from Si-wire waveguides [9,10]. 3. Ground commonization To test the effects of the commonized ground electrodes, we measured the reflection parameter S 11 using an RF vector network analyzer (NA, Anritsu R), as shown in Fig. 2(a). At low frequencies, S 11 is close to 0 db; this means that the reflection is nearly complete owing to the absence of electrical termination. At high frequencies, S 11 decreased owing to the loss of the RF signals. Without ground commonization, a local minimum and maximum were observed at f = 17 GHz and f = 23 GHz, respectively. We previously found that the frequency of this maximum corresponds to a minimum in the EO frequency response [10] and that it is similar to the minimum caused by the CS mode [3]. In the two groundcommonized devices, the minimum and maximum disappeared and the response was smooth, thus indicating that the CS mode was suppressed. Comparing the two ground-commonized devices, the S 11 of the meander-line electrode device was db lower than that of the normal electrode device. This difference might be explained by the transmission loss over the round trip of RF signals in the long delay line, including the sum of weak radiation from the 24 bends. We also consider that the leakage current between the signal and ground electrodes in the delay line may contribute to this difference. However, the excess loss of one-way transmission is 1.5 db/2 = 8% at the most. 4. Theoretical electro-optical response Fig. 2. Measured S 11 of fabricated devices. Next, we theoretically analyze the EO frequency response of the modulator. Figure 3 shows transmission models of the two types of electrodes that were tested. When we define the voltages of forward and backward propagating waves as f and b, the voltage (z,f) at position z and frequency f is expressed as follows: ( z, f) = e + e, (1) f γz γz b γ = α + jβ, and (2) RF 2π fn c RF β =, (3) RF

5 ol. 26, No Apr 2018 OPTICS EXPRESS Fig. 3. Calculation model of (a) normal electrode device, and (b) meander-line electrode device. where γ, α and β RF are the complex propagation constant, attenuation constant, and propagation constant of RF signals, and c is the speed of light. Considering the RF reflectivities at the start and end points of the phase shifter, Γ g and Γ, for the model in Fig. 3(a), (z,f) is represented as follows: γz γz 2γ γz γz 2γ ( +Γ ) ( +Γ ) Z e e Z e e ( z, f) = = in g 0 g 2 2 ( )(1 ) ( )(1 ), γ γ Z + Z +Γ e Z + Z Γ Γ e g in 0 g g (4) Z Z Z Z Γ = Γ = Z + Z Z + Z 0 g 0, and g 0 g 0, (5) Z 1+Γ e 2γ = Z in 0 2γ 1 Γ e, (6) where Z g is the internal impedance of the signal generator, Z 0 is the characteristic impedance of the phase shifter, and Z in is the impedance on the right side from z = 0. From the velocity difference between RF signals and slow light pulses, the effective voltage for modulating the slow light, eff, is represented as follows: ( jβo γ) z ( jβo + γ) z 2γ +Γ 0 g Z e e ( z, f) = ( )(1 ) eff 2γ Z + Z Γ Γ e 0 g g and (7) 2π fn g β = (8) o To calculate the modulation depth over the entire phase shifter, we derive the average voltage ave as follows [5,13,14]: c jϕ+ jϕ 2γ ( sin cϕ +Γ sin cϕ + ) dz Z e e e 0 eff 0 g ( f) = = ave 2γ Z + Z Γ Γ e 0 g g ( )(1 ) and (9) ( β jγ o ) = (10) ± ϕ ± 2 Furthermore, we consider the p-n doped PCW as a simple RC circuit consisting of the series electrical resistance R pn and capacitance C pn at the p-n junction. The appropriate transfer function G(f) is represented as follows: 1 G( f) = (11) 1 + j2 π f( Z + R ) C g pn pn

6 ol. 26, No Apr 2018 OPTICS EXPRESS We define the frequency response of the average voltage, η(f), as follows: The EO response S 21 is represented as follows: ave η ( f ) = (12) ave ( f) G( f) (0) G(0) S ( f)[db] = 20 log η( f) (13) For the meander-line electrode device in Fig. 3(b), we consider the phase changes before (0 z /2) and after the middle of the line (/2 z ) separately and assume that in the delay line as φ d. The effective voltages eff1 and eff2 are shown as ( z, f ) ( jβo γ) z { +Γ 0 g ( jβo + γ) z 2γ j2ϕd} Z e e = eff 1 2γ j2ϕd ( Z + Z )(1 Γ Γ e ) 0 g g ( z, f ) ( jβo γ) z jϕd 0 g{ +Γ ( jβo + γ) z 2γ jϕd} Z e e = eff 2 2γ j2ϕd ( Z + Z )(1 Γ Γ e ) 0 g g 2π fn (0 z / 2) (14) ( /2 z ) (15) d d ϕ = (16) d From Eqs. (14) and (15), similar to the normal electrode, we derive the following: c /2 ( ) dz dz 0 eff1 /2 eff2 f = + ave /2 /2 (17) jϕ+ j3ϕ+ jϕ j3ϕ+ jϕd ϕ j2ϕ 2 d jϕd 2 2 γ ϕ Z e + e sin c +Γ e e + e sin c 0 g 2 2 = 2γ j2ϕd 2( Z + Z )(1 Γ Γ e ) 0 g g The EO frequency responses are calculated from Eqs. (9) and (18) with c = m/s and = 200 μm. We set R pn = 60 Ω and C pn = 50 ff, as obtained from the previously reported simulations [9], n RF = 4 and n d = 2 [4,5,7], considering the doping and un-doping in the phase shifter and delay line, respectively, and neglecting the attenuation, i.e., α = 0, and reflection at z = 0, i.e., Γ g = 0. We assume Z 0 and Z g to be independent of the frequency so that their effect is eliminated by the normalization in Eq. (11). Figures 4(a) and 4(b) show the results for the normal electrode devices with Γ = 1 and Γ = 0, respectively. S 21 is degraded as the value of n g increases. A sharp dip appears at f = 38 GHz for n g = 40, and it shifts to a low frequency for a large value of n g. This dip is caused by the inversion of eff against the modulated light in the phase shifter. No marked differences are observed between Γ = 1 and Γ = 0, except the different depths of the dip and the slight improvement of the response with Γ = 0. Figures 4(c) and 4(d) show the results for the meander-line device with d = 1186 μm. The dip appears at f < 40 GHz even if n g = 55. This shows that the delay line effectively compensates for the phase mismatch. The response is particularly improved when Γ = 0. For example, the response of the meander-line device with n g = 35 appears to be the same as that of the normal electrode devices with n g = 22. Even when Γ = 1, the response is improved by the meander line at f > 30 GHz, but a slow valley appears at f = GHz, which degrades the cut-off frequency f 3dB. This slow valley is caused by the cancelation of forward and backward RF signals, which is made increasingly evident owing to the large phase shift in the delay line. Figure 5 summarizes f 3dB for various Γ. When Γ > 0.25, f 3dB decreases as d increases; therefore, the meander-line electrodes degrade performance somewhat. When Γ 0.25, f 3dB (18)

7 ol. 26, No Apr 2018 OPTICS EXPRESS shows a maximal value for certain d. For Γ = 0 and d = 0.8 mm, f 3dB = 27 GHz is possible, which allows for 50 Gbps modulation. Fig. 4. Calculated S 21 of the EO frequency response for = 200 μm, α = 0, Γ g = 0, n RF = 4. (a), (b) Normal electrode device. (c), (d) Meander-line electrode device of d = 1186 μm, n d = 2. (a), (c) Γ = 1, (b), (d) Γ = 0. Fig. 5. Calculated f 3dB for = 200 μm, Γ g = 0, n d = 2, n RF = 4, n g = 20, and various Γ. 5. Measurement of electro-optical response While measuring the EO frequency responses, we applied small amplitude sinusoidal signals to a single channel of the fabricated ground-commonized devices from the NA through a bias tee and an RF probe. Modulated light was input to an OE converter (Anritsu MN4765, >70 GHz) after passing through an erbium-doped fiber and a tunable band pass filter (BPF), after which the signal was returned to the NA. The optical phase difference between the two arms of the device was tuned to 90 by the TiN heaters. Figures 6(a) and 6(b) show the results for the normal electrode device and the corresponding n g spectrum as measured via the modulation phase shift method using a dispersion analyzer (Alnair abs CDA2100). n g changed from 22 to a value higher than 70 over the measured wavelength range. The spectral dip caused by the phase mismatch did not appear in the range n g < 32, while it appeared for n g > 34, which is consistent with our calculations. Figures 6(c) and 6(d) show the results for the

8 ol. 26, No Apr 2018 OPTICS EXPRESS meander-line device. The dip caused by the phase mismatch was suppressed up to n g = 69, while the slow valley appeared at f = GHz. These results were consistent with the calculation for Γ = 1, which is the case in the fabricated device with no electrical terminations. 6. Conclusion Fig. 6. (a), (c) Measured EO frequency response and (b), (d) corresponding n g spectrum. (a), (b) Normal electrode device, (c), (d) Meander-line electrode device. DC = 2. In this paper, we proposed a PCW MZM with meander-line electrodes that suppress the phase mismatch between slow light and RF signals. While preparing this device, we first measured the frequency response of devices fabricated with Si photonics CMOS processing and confirmed that the CS mode of RF signals that deforms the frequency response is suppressed by commonizing the ground electrodes. We also confirmed that the one-way transmission loss of the meander-line electrode is as low as 0.75 db. Then, we theoretically compared devices with normal and meander-line electrodes and concluded that the meanderline device achieves a high cut-off frequency at 27 GHz, which will allow operation at 50 Gbps. We confirmed a clear correspondence between our theoretical expectation and preliminary experimental results. In the measurements, the emergence of a slow valley caused by the reflection of RF signals slightly degraded the cut-off frequency. We aim to achieve a sufficiently high cut-off frequency by optimizing the electrode terminations, which we leave for future work. Some groups have already demonstrated high speed devices over 40 Gbps in Si photonics, but they used a phase shifter of as long as mm having a large optical loss of 9 15 db [2,3]. We expect our device to achieve 50 Gbps operation with a much shorter phase shifter of 200 μm and a moderate loss of ~6 db [9,10]. Funding New Energy and Industrial Technology Development Organization (NEDO) (project #P13004).

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