Robust phase-shift-keyin Silicon photonic modulator Donald Adams, * Abdelsalam Aboketaf, and Stefan Preble Microsystems Enineerin, Rochester Institute of Technoloy, 77 Lomb Memorial Dr., Rochester, New York 1463, USA * dbaeen@rit.edu Abstract: Here we propose a robust silicon modulator that seamlessly enerates phase shift keyed data. The modulator has very low insertion loss and is robust aainst electrical amplitude variations in the modulatin sinal; specifically a 50%-00% variation in modulatin amplitude leads to only a π/9 variation in output optical phase, correspondin to only ± 10% variation in the differentially detected sinal. This yields a ~.5dB enhancement in SNR over OOK (on-off-keyin) formats. 01 Optical Society of America OCIS codes: (130.310) Interated optics devices; (130.4110) Modulators; (130.5990) Semiconductors. References and links 1. A. Shacham, K. Berman, and L. Carloni, Photonic networks-on-chip for future enerations of chip multiprocessors, IEEE Trans. Comput. 57(9), 146 160 (008).. D. Miller, Device requirements for optical interconnects to Silicon chips, Proc. IEEE 97(7), 1166 1185 (009). 3. C. Xu, X. Liu, and X. Wei, Differential phase-shift keyin for hih spectral efficiency optical transmissions, IEEE J. Sel. Top. Quantum Electron. 10(), 81 93 (004). 4. L. Xu, W. Zhan, Q. Li, J. Chan, H. L. R. Lira, M. Lipson, and K. Berman, 40-Gb/s DPSK data transmission throuh a Silicon microrin switch, IEEE Photon. Technol. Lett. 4(6), 473 475 (01). 5. Y. Din, J. Xu, C. Peucheret, M. Pu, L. Liu, J. Seoane, H. Ou, X. Zhan, and D. Huan, Multi-channel 40 Gbit/s NRZ-DPSK demodulation usin a sinle Silicon microrin resonator, J. Lihtwave Technol. 9(5), 677 684 (011). 6. R. Kou, K. Yamada, H. Nishi, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, DPSK demodulation with a sinle Silicon photonic nanowire waveuide, in 8th IEEE International Conference on Group IV Photonics (GFP), (011), pp. 33 35. 7. L. Zhan, J. Y. Yan, M. Son, Y. Li, B. Zhan, R. G. Beausoleil, and A. E. Willner, Microrin-based modulation and demodulation of DPSK sinal, Opt. Express 15(18), 11564 11569 (007). 8. P. Don, C. Xie, L. Chen, N. K. Fontaine, and Y. K. Chen, Experimental demonstration of microrin quadrature phase-shift keyin modulators, Opt. Lett. 37(7), 1178 1180 (01). 9. J. Lloret, R. Kumar, S. Sales, F. Ramos, G. Morthier, P. Mechet, T. Spuesens, D. V. Thourhout, N. Olivier, J. Fédéli, and J. Capmany, Ultra-compact electro-optic phase modulator based on III-V-on-Silicon microdisk resonator, Opt. Lett. 37(1), 379 381 (01). 10. K. Padmaraju, N. Ophir, Q. Xu, B. Schmidt, J. Shakya, S. Manipatruni, M. Lipson, and K. Berman, Error-free transmission of DPSK at 5 Gb/s usin a Silicon microrin modulator, in 37th European Conference and Exposition on Optical Communications, OSA Technical Diest (CD) (Optical Society of America, 011), paper Th.1.LeSaleve.. 11. G. Barbarossa, A. M. Matteo, and M. N. Armenise, Theoretical analysis of triple-coupler rin-based optical uided-wave resonator, J. Lihtwave Technol. 13(), 148 157 (1995). 1. R. A. Soref and B. R. Bennett, Electrooptical effects in Silicon, IEEE J. Quantum Electron. 3(1), 13 19 (1987). 13. S. Manipatruni, R. K. Dokania, B. Schmidt, N. Sherwood-Droz, C. B. Poitras, A. B. Apsel, and M. Lipson, Wide temperature rane operation of micrometer-scale Silicon electro-optic modulators, Opt. Lett. 33(19), 185 187 (008). 14. M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Youn, Adiabatic resonant microrins (ARMs) with directly interated thermal microphotonics, in Conference on Lasers and Electro- Optics (009), paper CPDB10. 15. Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, 1.5 Gbit/s carrier-injection-based Silicon microrin Silicon modulators, Opt. Express 15(), 430 436 (007). 16. A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharpin, and A. L. Gaeta, Tailored anomalous roup-velocity dispersion in Silicon channel waveuides, Opt. Express 14(10), 4357 436 (006). #165779 - $15.00 USD Received 9 Mar 01; revised 4 Jun 01; accepted 10 Jul 01; published 17 Jul 01 (C) 01 OSA 30 July 01 / Vol. 0, No. 16 / OPTICS EXPRESS 17440
17. A. Biberman, S. Manipatruni, N. Ophir, L. Chen, M. Lipson, and K. Berman, First demonstration of lon-haul transmission usin Silicon microrin modulators, Opt. Express 18(15), 15544 1555 (010). 1. Introduction Efficient optical interconnects are one of the most promisin application of Silicon photonics [1,]. The fundamental element of any optical interconnect is the electro-optic modulator, and there have been many successful demonstrations of amplitude based silicon modulators [1,]. However, phase encoded modulation has been required for the advancement of all communication technoloies. For example, while amplitude modulation was used in optical fiber communications for decades, by the beinnin of the last decade there was a rapid transition to phase based encodins due to the exponentially increasin bandwidth requirements of the internet [3]. Silicon photonics is experiencin a similar demand for bandwidth and will also need to move towards usin phase encodins [1,]. There are several reasons that phase modulation is preferred over amplitude modulation: (1) Maximization of sinal/noise; () Minimization of nonlinear effects; (3) Maximization of channel efficiency (which translates to increased system bandwidth). As a result phase encoded sinals on silicon chip have received increasin attention. There have been several recent studies of the transmission, switchin and receivin of phase encoded sinals [4 6]. In addition, there have been initial developments in silicon modulators for phase encodin. The first compact microrin based phase modulator was proposed in [7], and usin this desin hih speed binary phase-shift keyed (BPSK) and quadrature phase-shiftkeyed (QPSK) modulators were demonstrated in [8 10]. However, in all cases the devices required precise voltae inputs, and had hih insertion loss. Here we propose a completely new approach for realizin a compact binary phase modulator. Our desin is based on a sinle rin resonator, with a key output confiuration that enables low insertion loss, and robust hih speed phase modulation. Usin this desin it will be possible to realize all of the advantaes of phase encodin, particularly the ~3dB enhancement in SNR over OOK [3]. In addition, our desin can be extended to the realization of advanced phase encodin formats, such as QPSK and quadrature amplitude modulation (QAM).. Binary phase encodin usin rin resonators In order to understand how a rin resonator can be used to modulate phase, consider the spectral response of a rin resonator with a throuh and drop port: ( + j ) R 1 (1) ( α+ jβ) π R c1c e α β π Y throuh c c e = X 1 Y drop X ( + j ) R 1 () ( α+ jβ) π R 1 α β π s s e = 1 c c e where R is the radius of the rin, c 1, = 1 κ 1,, s 1, = κ 1,, κ 1, represents the power couplin ratio at the throuh and drop ports respectively, α is the waveuide amplitude attenuation coefficient of a curved waveuide of radius R, and β = π n λ is the waveuide propaation constant where n is the waveuide roup refractive index. First we consider the case of a sinly coupled rin response which is obtained by settin κ = 0 (see Fis. 1(a) 1(c)). This confiuration is identical to those found in [7 10] and realizes the requisite 0 and π phases for BPSK by operatin at two equal amplitude points of an over-coupled resonance. However, this scheme inherently requires precise control of the modulation sinal as experimentally observed in [8 10]. #165779 - $15.00 USD Received 9 Mar 01; revised 4 Jun 01; accepted 10 Jul 01; published 17 Jul 01 (C) 01 OSA 30 July 01 / Vol. 0, No. 16 / OPTICS EXPRESS 17441
In contrast, consider a rin resonator with equal throuh and drop ports ( κ = κ 1 ). As shown in Fis. 1(d) 1(f), when the resonator is off-resonance, the optical power passes to the throuh port and experiences no phase shift, and when the rin is on resonance, the optical power passes to the drop port and experiences a π phase shift. Therefore, by combinin the throuh and drop port outputs it is possible to realize an optical sinal with the required 0 and π phases for BPSK. Fi. 1. (a) Sinly coupled rin confiuration. (b) Spectral amplitude response and (c) spectral phase response of the sinly coupled rin. A π phase-shift can be induced by operatin at two opposite points, with equal amplitude, on the resonance curve. (d) Dually coupled rin confiuration. (e) Spectral amplitude response and (f) spectral phase response of the dually coupled rin. To achieve PSK operation the phase shifted sinal should be on one output not two, therefore the throuh and drop ports must be combined. Rather than combinin the throuh and drop ports with a y-splitter or directional coupler (which will induce 3db of loss) we propose to connect the throuh port output to the drop port input, which we will refer to as a feed-throuh waveuide (see Fi. (a), path l ). This will ensure that the device has a minimal insertion loss. A riorous derivation of the spectral response of this device can be found in [11], and yields: Y ( α+ jβ) l ( α+ jβ) l ( α+ jβ)( l1+ l + l3) jβl ( c1c e s1s e + e ) e = ( α+ jβ) l3 ( α+ jβ) l1 ( α+ jβ) l 1 1 1 1 1 ( ) X e s s e c c e where l 1 l and l 3 represent the lenths of waveuide from coupler to coupler as shown in Fi. (a). In [11] it was also shown that optical loss will be minimized first by settin κ 1 equal to κ, and second by adjustin the lenths l 1 l and l 3 such that: (3) π n 1 3 1 3 ( ) ( ) β l + l = l + l = Mπ λ π n 3 3 ( ) ( ) β l + l = l + l = Mπ λ (4) (5) #165779 - $15.00 USD Received 9 Mar 01; revised 4 Jun 01; accepted 10 Jul 01; published 17 Jul 01 (C) 01 OSA 30 July 01 / Vol. 0, No. 16 / OPTICS EXPRESS 1744
where M and N are even numbers. For the case where l = l1+ l3, each resonance will be optimally coupled. This is shown in Fis. (b) (d) with l1 = π 5µ m, l3 = π 5µ m, l = π 5µ m, and n = 4.1. The amplitude response is nearly constant with respect to wavelenth, with a very small dip, <5% for 3dB/cm loss in a 5µm radius rin as shown in Fi. (c). Consequently, the device allows low loss phase modulation operatin at two points: on-resonance (π) and off-resonance (0). Fi.. (a) Rin resonator PSK modulator. (b) The rin s wideband spectral amplitude response shows only one phase matched resonance (c) spectral amplitude and (d) phase response of the phase matched resonance. These operatin points ensure sinificantly more robust PSK modulation because the (0), off-resonance condition, can be realized over a wide rane of wavelenths, sinificantly reducin requirements on the electronic control of the device. However, it should be noted that these operatin points could in theory be achieved with a sinle coupled rin resonator. However a close inspection of Eq. (3) reveals a subtle advantae of the dual-coupled desin. Assumin κ = κ 1 << 0.5 then small index chanin effects in waveuide sections l 1 and l 3 will lead to lare chanes in the resonant wavelenth of the device, whereas small index chanin effects in waveuide section l will lead to small chanes in the resonant wavelenth of the device. Effectively this can be thouht of as rantin a course tunin and fine tunin mechanism for the resonant condition of the device, respectively. Since the exact resonant condition reatly affects the on resonance phase (π), the symbol distance and ultimately the SNR, a hih-sensitivity tunin mechanism will ensure practical deployment of this device. Fi. 3. (a) FDTD simulation of a narrowband off-resonance input. (b) FDTD simulation of a narrowband on-resonance input; note the normalized optical amplitude in the rin is actually much reater than. As an additional verification of the results, finite-difference-time-domain (FDTD) simulations were performed. As shown in Fis. 3(a) 3(b), when the rin is on resonance the majority of the power passes into the rin (drop port); whereas when the rin is off resonance the majority of the power passes throuh the feed-throuh waveuide. #165779 - $15.00 USD Received 9 Mar 01; revised 4 Jun 01; accepted 10 Jul 01; published 17 Jul 01 (C) 01 OSA 30 July 01 / Vol. 0, No. 16 / OPTICS EXPRESS 17443
3. Modulation via free-carrier injection/extraction In principle, the proposed device could be made to function with any index chanin effect. Here we will focus on the predominant modulation effect available in Silicon - the free-carrier plasma dispersion effect [1]. It is well known that free-carrier modulation can be performed in a variety of ways, includin injection/extraction with a p-i-n diode, depletion reion modulation with a reverse biased diode, and others. As will be shown, injection/extraction with a p-i-n diode complements the optical desin of the device. Specifically under forwardbias conditions there will be a sinificant carrier concentration, more than sufficient to shift the resonator to the (0) phase point. And in extraction, very few carriers will be present, ensurin that the (π) phase condition is met, provided thermal effects can be corrected for [13,14]. In contrast depletion reion modulation with a reversed biased diode could be used, but is challenin since the effect is relatively weak, in comparison to injection. While it is potentially faster than injection based devices, it requires careful desin of the waveuide and diode which is beyond the scope of this work. Chare injection by a p-i-n diode into a Silicon waveuide was modeled usin the chare dynamics model found in [15]. Fiure 4(a) shows the averae carrier density as a function of forward bias when the carrier response has evolved for 1ns, 00ps, and 100ps after the voltae has been applied (a step function is used). In order to obtain the optical response of the device first we calculate the chane in the phase of the device for various index chanes, as seen in Fi. 4(c). This was obtained usin Eq. (3), with the substitutions: n = ni + dn, and α = αi + dα, where n = 4.1 and α 0.69 are the roup index and amplitude i i = attenuation coefficients of the waveuide without carriers, and d α and dn are the chane in absorption and index as a function of carrier concentration (Fi. 4(b)) [1]. Additionally l1 = π 5µ m, l3 = π 5µ m, l = π 5µ m and κ = κ 1 = 0.0. The model assumes that the device is on resonance when no carriers are present in the rin. Fi. 4. (a) Forward Biased p-i-n junction current as a function of voltae for a 1ns, 00ps and 100ps rise time. (b) Refractive index chane as a function of carrier density [11]. (c) The output phase of the proposed device as a function of waveuide index chane. (d) The output phase of the proposed device as a function of voltae. By combinin Fis. 4(a) 4(c), we obtain the proposed device output phase as a function of input voltae. As shown in Fi. 4(d), this phase has a sharp response near threshold, and remains relatively constant otherwise. Therefore the device is robust aainst voltae variation for both the 0 and π phase condition. However as the switchin speed increases the response widens, as expected, since the carrier response does not reach a steady state. This can be optimized in any iven desin by makin tradeoffs in the quality factor of the rin and power requirements. 4. Performance In order to further quantify the robustness of the device we have simulated the effect of drastically varyin input voltae on the response. Because Eq. (3) assumes steady-state operation, this simulation uses the followin temporal equation model of the device: #165779 - $15.00 USD Received 9 Mar 01; revised 4 Jun 01; accepted 10 Jul 01; published 17 Jul 01 (C) 01 OSA 30 July 01 / Vol. 0, No. 16 / OPTICS EXPRESS 17444
y ( t ) = c x ( t ) + s r ( t ) (6) 1 1 1 1 3 y ( t ) = c x ( t ) + s r ( t ) (7) 1 π n x ( t ) = exp α+ j l y 1( t T ) λ π ( n + dn) r1 ( t ) = exp α+ dα+ j l1 s1x 1( t T1) + c1r3 ( t T1) λ ( ) (8) (9) π ( n + dn) r3 ( t ) = exp α+ dα+ j l3 s x ( t T3) + c r1 ( t T 3) λ ( ) where r 1,3 are the electric-field in the rin in the correspondin sections l 1 and l 3, T = l n c, c is the speed of liht, and dα and dn are determined usin the previously 1,,3 1,,3 described p-i-n diode models, with a 10Gbps modulatin input. Fiure 5(a) shows the input voltaes, ranin from 50% to 00% variation of optimal performance for the device, for both square wave and sine wave inputs in order to characterize variations in rise/fall time. The correspondin carrier concentration chane is shown in Fi. 5(b) and its effect on output optical phase is shown in Fi. 5(c). Despite lare variation in input voltae and carrier concentration the output optical sinal remains relatively constant (phase varies by <π/9, which as explained next will only derade SNR by only 0.5dB). This is for three reasons: (1) the 0 phase symbol can be achieved over a wide rane of operatin points due to the flat transfer function seen in Fi. 4(d). () The π phase symbol is realized when the diode is effectively off, makin it insensitive to voltae variations. While the π phase symbol will still be sensitive to thermal fluctuations, this is an issue of all microrin based modulators and a variety of techniques have been employed to minimize this [13,14]. (3) The feed-throuh waveuide enables hih sensitivity tunin of the relative phase between the two symbols, ensurin maximum symbol distance. (10) Fi. 5. (a) Modulatin voltae input (50-00% of optimal) with square wave and sine wave (~100ps rise) sinals. (b) Averae carrier concentration in the waveuide. (c) Optical output amplitude and (d) optical output phase of the proposed device. (e) Sinal amplitude resultin from differential detection. Levels yield a.5db ± 0.db output. To evaluate the performance of this device in a PSK interconnect system we have modeled a standard differential detection scheme (e.. where a one-bit time delayed #165779 - $15.00 USD Received 9 Mar 01; revised 4 Jun 01; accepted 10 Jul 01; published 17 Jul 01 (C) 01 OSA 30 July 01 / Vol. 0, No. 16 / OPTICS EXPRESS 17445
interferometer is used to interfere adjacent symbols) [3]. The results are seen in Fi. 5(d), where the 10Gbit/s optical output (Fi. 5(c)) is differentially detected. It is seen that the differentially detected sinal amplitude spans ± 0.9 ± 0.05, which in part is achieved by tunin the phase in the feed-throuh waveuide to π/9 to counteract the minor phase offset in hih speed operation. Therefore, the proposed device directly ains a.5 db enhancement in SNR over OOK, which is comparable to measured results in commercial rade PSK based telecommunication systems [3]. The amplitude variations in the output sinal are also of importance in evaluatin the performance of the modulator, and are shown in Fi. 6(a). It is seen that there are peaks and dips, which inherently are caused by the build-up and release of enery in the rin resonator. Firstly, these amplitude fluctuations correspond to the bit transitions and minimally impact the differentially detected sinal in Fi. 5(d). They can also potentially be used for clockrecovery, as is the case in Mach-Zehnder based PSK modulators [3]. Secondly, the amplitude variations correspond to points where the phase makes transitions as seen in Fi. 6(b), which leads to chirp in the optical sinal. This can also be represented by the complex plane diaram (Fi. 6(c)), which demonstrates that the chirp of the π-to-0 transition is considerably larer than the 0-to-π transition. However, while chirp is of a concern in telecommunication systems with lon lenths fiber, it is much less sinificant for chip-scale optical interconnect applications. Specifically by takin the temporal derivative of the phase output the maximum chirp of the modulator when operatin at 10 Gbit/s was determined to be ~40GHz. The larest dispersion in Silicon waveuides is considerably less than 10000ps/nmkm [16], and with propaation lenths on the order of only centimeters this would only yield a sinal shift <100fs, which is neliible at 10 Gbit/s. Lastly, the amplitude variations could induce nonlinear effects. However, we expect these will be minimal since similar amplitude spikes in microrin based OOK modulators have been shown to have a minor impact [1,17]. Reardless we expect the nonlinearities will be even less than with OOK since the amplitude is considerably more constant in PSK. 5. Conclusions Fi. 6. (a) Optical output amplitude of the PSK modulator. (b) Phase output with the two transitions hihlihted (0 to pi; pi to 0) (c) Complex plane transition diaram. Here we have presented a novel microrin phase-shift-keyed modulator. It realizes low insertion loss while bein relatively insensitive to modulation variations. This will allow for hih speed performance over a wide rane of operatin conditions. Additionally even thouh the proposed device produces a BPSK sinal, it can be easily be extended to more complicated QPSK and QAM desins [8]. #165779 - $15.00 USD Received 9 Mar 01; revised 4 Jun 01; accepted 10 Jul 01; published 17 Jul 01 (C) 01 OSA 30 July 01 / Vol. 0, No. 16 / OPTICS EXPRESS 17446
Acknowledments The authors would like to thank Dr. Gernot Pomrenke, of the Air Force Office of Scientific Research for his support under FA9550-10-1-017. #165779 - $15.00 USD Received 9 Mar 01; revised 4 Jun 01; accepted 10 Jul 01; published 17 Jul 01 (C) 01 OSA 30 July 01 / Vol. 0, No. 16 / OPTICS EXPRESS 17447