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On-Chip All-Optical Switching and Memory by Silicon Photonic Crystal Nanocavities

On-Chip All-Optical Switching and Memory by Silicon Photonic Crystal Nanocavities Hindawi Publishing Corporation Advances in Optical Technologies Volume 2008, Article ID 568936, 10 pages doi:10.1155/2008/568936 Review Article On-Chip All-Optical Switching and Memory by Silicon Photonic Crystal Nanocavities Masaya Notomi, Takasumi Tanabe, Akihiko Shinya, Eiichi Kuramochi, and Hideaki Taniyama NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi 2430198, Japan Correspondence should be addressed to Masaya Notomi, notomi@will.brl.ntt.co.jp Received 23 December 2007; Accepted 13 April 2008 Recommended by D. Lockwood We review our recent studies on all-optical switching and memory operations based on thermo-optic and carrier-plasma nonlinearities both induced by two-photon absorption in silicon photonic crystal nanocavities. Owing to high-Q and small volume of these photonic crystal cavities, we have demonstrated that the switching power can be largely reduced. In addition, we demonstrate that the switching time is also reduced in nanocavity devices because of their short diffusion time. These features are important for all-optical nonlinear processing in silicon photonics technologies, since silicon is not an efficient optical nonlinear material. We discuss the effect of the carrier diffusion process in our devices, and demonstrate improvement in terms of the response speed by employing ion-implantation process. Finally, we show that coupled bistable devices lead to all-optical logic, such as flip-flop operation. These results indicate that a nanocavity-based photonic crystal platform on a silicon chip may be a promising candidate for future on-chip all-optical information processing in a largely integrated fashion. Copyright © 2008 Masaya Notomi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION As has been studied in various forms, all-optical switches can be realized using optical resonators, where a control It used to be a great challenge to tightly confine light in a optical pulse induces a resonance shift via optical nonlinear wavelength-scale volume, which had limited the capability of effects. For such a resonator-based switch, there is a two- photonics technologies in various aspects. Recently, however, fold enhancement in terms of the switching power if a an optical resonator with ultrahigh-Q (∼1 million) and small cavity with a high-Q is employed. First, the light small volume (∼(λ/n) ) becomes possible by employing the intensity inside the cavity should be proportional to Q/V . state-of-the-art photonic crystal technologies [1–6]. Figure 1 Second, the required wavelength shift is proportional to shows an example of high-Q nanocavities, which we have 1/Q. In total, the switching power should be reduced recently demonstrated in silicon photonic crystals. This by (Q /V ), which can be significantly large for photonic particular cavity shows a theoretical Q of over 10 and crystal nanocavities [9]. Although the switching mechanism an experimental Q of 1.3 million with a mode volume itself is basically similar to that of previous resonator- of 1.5(λ/n) [4, 7]. These values are hardly available in based switches, such as nonlinear etalons [10], this large optical systems other than photonic crystals. Various forms enhancement has had an important impact on optical of light-matter interactions are expected to be enhanced integration since most optical switching components require in such high-Q nanocavities having large Q/V ratio [8]. too much power for realistic integration. Furthermore, in the case of carrier-induced nonlinearity or thermo-optic Among them, in this article, we focus on application to all- optical switching and memory operations based on optical nonlinearity, the smallness of the device naturally leads nonlinear interaction. Especially for this, we investigate all- to fast operation speed, since the relaxation time of such optical operations based on carrier-induced nonlinearity and processes normally depends on the size. As we will show examine the features of photonic crystal nanocavities for below, this advantage is significant for wavelength-sized such applications. cavities. 2 Advances in Optical Technologies Q = (1.28 ± 0.06) × 10 1.2pm c1-hole c2-hole c3-hole 1575.336 1575.34 Wavelength (nm) (a) (b) Q = (1.34 ± 0.08) × 10 τ :1.12 ns 12 34 Time (ns) (c) Figure 1: Width-modulated, line-defect photonic crystal cavities. (a) Cavity design. The cavity has the theoretical Q. The hole shifts are typically 9 nm (red holes), 6 nm (green holes), and 3 nm (blue holes). (b) Spectral measurement of a nanocavity fabricated in a silicon hexagonal air-hole photonic slab with a = 420 nm and 2r = 216 nm. The transmission spectrum of a cavity with a second-stage hole-shift. The inner and outer hole-shifts are 8 and 4 nm, respectively. (c) Time-domain ring-down measurement. The time decay of the output light intensity from the same cavity as (b). Details can be found in the reference. In addition, resonator-based optical switches are well 2. ALL-OPTICAL BISTABLE SWITCHING BY known to exhibit optical bistability [10] and thus they can THERMO-OPTIC NONLINEARITY be used for optical memory and all-optical logic [11]. Such functionality is one of the most important functions missing As described above, photonic crystal nanocavities have a from existing photonic devices. Thus, we believe that all- promising potential for all-optical switching applications. optical bistable switches based on photonic crystal cavities To experimentally confirm this, we have investigated all- are important candidates for future optical integration. optical bistable switching operations employing the thermo- In this paper, we investigate all-optical switching and optic nonlinearity induced by two-photon absorption (TPA) memory action in silicon photonic crystal nanocavity in silicon [12]. For this study, we employed an end- devices. First, we study the switching action using thermo- hole shifted four-point Si photonic crystal cavity integrated optic nonlinearity. Next, we investigate similar switch- with input/output photonic crystal waveguides (shown in ing action using much faster carrier-plasma nonlinearity. Figure 2(a))[13, 14]. Figure 2(b) shows transmission spectra Thirdly, we analyze the effect of carrier relaxation process in with various input power at 1.5 μm wavelength region. the switching action and made an attempt to further decrease As clearly seen in the graph, the transmission spectrum the relaxation time by ion implantation. Furthermore, we is shifted to longer wavelength (red-shifted). This shift is demonstrate bistable memory action employing basically the due to thermo-optic nonlinearity induced by two-photon same nanocavity devices and present an example of design absorption in the cavity. At input power higher than for on-chip all-optical logic circuits consisting of two bistable 10 μW, there is an abrupt kink in the spectrum. This nanocavities. kink corresponds to bistable switching. To see this more Intensity Transmission Masaya Notomi et al. 3 Red shifted −1 −2 1567.5 1568 1568.5 1569 1569.5 Wavelength (nm) 400 μW(4 dB) 25 μW(16 dB) 250 μW(6 dB) 10 μW(20 dB) 160 μW(8 dB) 2.5 μW(26 dB) 100 μW(10 dB) 250 nW (36 dB) 63 μW(12 dB) (a) (b) δ: detuning Red shift −1 1 2 10 10 Input power P (μW) IN δ = 0pm 100 pm 20 pm 120 pm 40 pm 140 pm 60 pm 160 pm 80 pm 180 pm (c) Figure 2: All-optical bistable switching in a silicon hexagonal air-hole photonic crystal nanocavity (end-hole shifted four-point defect cavity) realized by the thermo-optic nonlinearity induced by two-photon absorption in silicon. (a) Schematic of the sample and a scanning electron micrograph of the sample. a = 420 nm, 2r = 0.55a. The radius of end-holes of the cavity is 0.125a. V = 0.102 μm . The radius of end-holes of the waveguide is 0.15a. (b) Intensity-dependent transmission spectra taken by a tunable laser in the upsweep condition. Q in the linear regime is 33400. (c) Output power versus input power for various detuning values. The nonlinear regime starts from 10 μW, and the bistable regime starts from 40 μW. directly, we measured the output power as a function of This value is remarkably smaller that of bulk-type thermo- the input power at various detuning conditions, as shown optic nonlinear etalons (a few to several tens mW) [15] in Figure 2(c). Now, it is clear that this device exhibits and also smaller than that of recent miniature-sized thermo- bistable switching. The most noteworthy point regarding this optic silicon microring resonator devices (∼0.8 mW) [16]. In switching is its switching power, which is as small as 40 μW. addition, it is important to note that TPA occurs only in the Output power P (μW) OUT Output power (μW) 4 Advances in Optical Technologies Relaxation time measurement mode A (CW probe) Switch-on time measurement mode B (ON→OFF) δ (pump): 0 (nm) OFF 0 300 δ (probe): 0.38 (nm) −7dBm −7.6dBm −8dBm −1 200 −8.6dBm −2 t ∼ 100 ns −3 0 200 400 600 800 600 800 1000 1200 Time (ns) Time (ns) Stored energy = 4pJ (a) (b) Switch-on time measurement Critical slowing down 0 50 100 150 200 Time (ns) Incident energy =∼ 11 pJ (c) Figure 3: Temporal response of thermo-optic switching. (a) Switch-off. Temporal response of the probe output. At t = 800 nanoseconds, the pump signal was switched off. The input instantaneous power for the pump is 64 μW. The pulse width and period are 400 nanoseconds and 40 microseconds. The exponential fit gives a decay time of approximately 100 nanoseconds. (b) Switch-on operation for various input power. (c) Incident energy required for the switch-on operation estimated from the product of the incident energy and the time required for switch-onin(b). cavity (the linear absorption of silicon at this wavelength is which is normally required for signal processing. Since negligible), and, therefore, we can easily integrate this device bistable switching for one resonant mode should influence with transparent waveguides in the same chip. the transmission intensity of the other resonant mode in Our cavity shown in Figure 2(a) was intentionally de- the same cavity, we can easily realize such operation. As signed to have two resonant modes, and, therefore, we we reported in [12], we observe basically similar bistable can perform all-optical switching using independent two switching behavior in the relation between the input power inputs with different wavelengths (signal and control), for the control mode and the output power for the signal Output (probe) (in scale) Input energy (pJ) Output power (a.u.) Masaya Notomi et al. 5 NOT type switching (ON to OFF) AND type switching (OFF to ON) 0.1 0.1 0.01 0 200 400 600 800 1000 0 1000 2000 3000 4000 5000 Time (ps) Time (ps) U (U ) in eff U (U ) in eff 1042 (38) fJ 450 (16) fJ 298 (11) fJ 47 (2) fJ 859 (31) fJ 291 (11) fJ 206 (8) fJ 413 (15) fJ 156 (6) fJ 369 (13) fJ 666 (24) fJ 112 (4) fJ (a) (b) Figure 4: All-optical switching in a silicon photonic crystal nanocavity (end-hole shifted four point cavity) realized by carrier-plasma nonlinearity induced by two-photon absorption in silicon. Q for the control mode is 11500, and Q for the signal mode is 23000. (a) AND- type switching at various control pulse energies with the detuning of −0.3 nm. (b) NOT-type switching at various control pulse energies with no detuning. Each line is shifted by 500 picoseconds. Model calculation Experimental result 1 S On 50 (ps) 293 (ps) 267 (ps) 54 (ps) τ = 50 ∼ 100 (ps) 0.1 0.1 S × 10 Off S × 10 τ = 80 (ps) 0.01 0.01 −200 0 200 400 600 −200 0 200 400 600 Time (ps) Time (ps) δ =−0.45 (nm) δ =−0.45 (nm) δ = 0(nm) δ = 0.01 (nm) (a) (b) Figure 5: Comparison between the rate-equation analysis and measurement result. We modeled the cavity resonance as a Lorentzian function whose center wavelength is shifting in proportion to the carrier density. (a) Calculation. (b) Experiment. mode. This operation is basically what we expect for the so- Although the bistable operation itself is similar to that called all-optical transistors, and will be basis for various of nonlinear etalon switches, these photonic crystal switches logic functions. The detail of this operation is described in can be clearly distinguished in terms of the operating power [12]. For example, we demonstrated that we can amplify an and capability for integration. The mode volume of this AC signal using this device. cavity is only approximately 0.1 μm . This small footprint Signal transmission (a.u.) Signal transmission (a.u.) 6 Advances in Optical Technologies itself is of course advantageous for integration, but it is parameter condition. In this calculation, we assumed the also beneficial for reducing the switching speed because carrier relaxation time of 80 picoseconds. This suggests that our device is limited by the thermal diffusion process. To the effective carrier relaxation time for this all-optical switch demonstrate these characteristics, we measured temporal is in the range between 50 to 100 picoseconds. This fast response of the operation for switch-off and switch-on carrier relaxation may be attributed to the short diffusion processes, as shown in Figures 3(a) and 3(b). The relaxation time for generated carriers. Note that the photon lifetime time of our switch is approximately 100 nanoseconds, which of our cavity is approximately 10 picoseconds, and thus is much shorter than that of conventional thermo-optic the operation speed of our device is limited by the carrier switches (∼milliseconds). This amazingly fast thermo-optic relaxation time. This carrier relaxation time is much shorter switching is primarily due to the smallness of our cavity. In than that in other silicon photonic microdevices [18]. That addition, we can estimate the required switching energy from is, the small footprint of the device is again effective in the switch-on measurement. The deduced smallest value is as improving the operating speed. smallas11 pJasshown in Figure 3(c). 4. EFFECT OF CARRIER RELAXATION PROCESS ON 3. ALL-OPTICAL SWITCHING BY SWITCHING OPERATION CARRIER-PLASMA NONLINEARITY In Section 3, we demonstrate that silicon all-optical switches These thermo-optic nonlinear bistable switches clearly based on carrier-plasma nonlinearity can operate at a demonstrate that large Q/V photonic crystal cavities are significantly fast speed, which is attributed to the fast carrier very effective in improving the operation power and speed. relaxation process. We regard that this fast carrier relaxation However, the speed itself is still not very fast, which is limited is possibly due to the fact that the diffusion process is an by the intrinsically slow thermo-optic effect. To realize much efficient relaxation channel for nanocavities. To verify this faster all-optical switches, here we employ another nonlinear explanation, we performed numerical simulations for the effect, namely, the carrier-plasma effect [17]. This process is carrier diffusion process in silicon photonic crystal cavities also based on the same TPA process in silicon. Thus most of [19]. In this simulation, we assumed an initial carrier dis- the arguments concerning their advantages are similar to that tribution determined from the optical intensity distribution for thermo-optic nonlinearity. For this experiment, we used of the cavity mode, and numerically solved two-dimensional similar photonic crystal cavity devices with a control pulse diffusion equations with assuming a realistic photonic input. If the duration of the control pulse is sufficiently short, crystal cavity structure which is the same as that used in we can avoid thermal heating and may be able to observe only the experiment. The side-wall nonradiative recombination carrier-plasma nonlinearity. In fact, we observed a clear blue process at the air-hole surface is incorporated in the equation shift in the resonance when we injected a 6-picosecond pulse as effective surface recombination rate (S), and the effect into this device, which is consistent with the expected shift of the top-surface nonradiative recombination process is induced by the carrier-plasma nonlinearity. Figure 4 shows incorporated as an effective carrier lifetime parameter which the time-resolved output intensity for the signal mode when is determined from another calculation for a simple slab. a 6-picosecond control pulse is input [17]. We observed clear We calculated the time-dependent resonance wavelength all-optical AND-type switching from OFF to ON for the shift using instantaneous carrier concentration in the cavity. detuning of 0.45 nm (Figure 4(a)) and NOT-type switching The calculated snapshots of the carrier distribution at t from ON to OFF for the detuning of 0.01 nm (Figure 4(b)). = 0, 8, and 24 picoseconds are shown in Figures 6(a), The required switching energy is only a few hundred fJ, 6(b),and 6(c). These snapshots clearly show that the initial which is much smaller than that of ring-cavity-based silicon distribution is rapidly spread as a result of diffusion. This all-optical switches [18]. If we take the coupling efficiency rapid diffusion results rapid switching recovery. Figure 6(d) between the cavity and waveguide into account, the actual shows the calculated shift of the resonance wavelength for the cavity. The initial wavelength shift caused by the carrier pulse energy used for the switching is less than 10 fJ. This extremely small switching energy is attributed to large Q/V plasma shift is recovered quickly. As shown in the figure, ratio in our cavity. the nonradiative recombination does not seriously affect the The switching time of our device is approximately initial recovery. Therefore, we believe that the fast operation from 50 picoseconds to 300 picoseconds depending on the of our optical switches is explained by the rapid carrier detuning and control pulse energy. Considering the fact diffusion process. that the carrier lifetime in silicon is normally very long If we wish to increase the operation speed further, (∼microseconds), this switching time is also surprisingly we have to somehow decrease the carrier relaxation time. fast. This apparently indicates that the switching time is Although there are several ways to do so, we have recently not limited by the carrier recombination time of bulk employed an Ar-ion implantation process in order to silicon. We analyzed the switching behavior employing introduce extremely fast nonradiative recombination centers simplified rate equations for the photon and carrier density into silicon. If the carrier recombination time becomes faster in a photonic-crystal nanocavity incorporating the effective than the diffusion time, we can expect an improvement in the carrier relaxation time. We found that this simple model operation speed. When we implanted silicon photonic crystal + 14 −2 can reproduce the experimental result fairly well. Figure 5 nanocavity switches with Ar dose of 2.0 × 10 cm and shows simulated and experimental results for the same an acceleration voltage of 100 keV, we observed a significant Masaya Notomi et al. 7 2 2 1 1 0 0 −1 −1 −1 0ps 8ps 24 ps −2 −2 −2 −2 −10 1 2 −2 −10 1 2 −2 −10 1 2 x (μm) x (μm) x (μm) 17 17 16 16 16 16 03.8 × 10 7.5 × 10 03.1 × 10 6.3 × 10 02 × 10 4 × 10 −3 −3 −3 Electron density (cm ) Electron density (cm ) Electron density (cm ) (a) (b) (c) 0.15 0.1 S = 0cm/s 0.05 S = 8 × 10 cm/s 0 50 100 150 200 Time (ps) (d) Figure 6: Numerical simulation of carrier diffusion process for a silicon end-hole-shifted photonic crystal cavity. (a), (b), (c) snapshots of the carrier distribution at t = 0, 8, 24 picoseconds. (c) Shift of the resonance wavelength for the cavity as a function of time with the sidewall nonradiative recombination rate S = 0and S = 8 × 10 cm/s. improvement in switching speed as shown in Figures 7(a), 5. ALL-OPTICAL MEMORY OPERATION 7(b). The implantation condition was carefully determined AND LOGIC CIRCUIT so as to keep almost the same cavity Q but to significantly decrease the carrier lifetime in the cavity. In the case of In the same way as thermo-optic switching, carrier-plasma detuning for an NOT gate (Figure 7(a),itwas reducedfrom switching also provides bistable operation. Figure 8 shows 110 picoseconds to 50 picoseconds. In the case of detuning bistable operations realized by employing a pair of set and for an AND gate, the switching time was reduced from reset pulses [21]. When a set pulse is fed into the input 220 picoseconds to 70 picoseconds (Figure 7(b))[20]. As waveguide, the output signal is switched from OFF to ON shown in Figure 7(c), the ON/OFF ratio is mostly the same and remains ON even after the set pulse exits (green curve). between two conditions. In addition, the required switching When a pair of set and reset pulses is applied (as shown in energy was almost the same as that without the implantation. Figure 8(a)), the output is switched from OFF to ON by the Although the reduction of the carrier lifetime may lead to set pulse and then ON to OFF by the reset pulse (blue curve). increase in the switching energy, this change is not significant This is simply a memory operation using optical bistability. as far as the carrier lifetime is longer than the photon lifetime The energy of the set pulse is less than 100 fJ, and the DC bias and the control pulse length (which was the case in our input for sustaining the ON/OFF states is only 0.4 mW. These experiment). These results clearly demonstrate the effect small values are primarily the results of the large Q/V ratio of of ion-implantation on the improvement in the switching the photonic crystal cavity. It is worth noting that the largest speed. Q/V should always result in the smallest switching power, y (μm) Wavelength shift (−nm) y (μm) y (μm) 8 Advances in Optical Technologies but the operation speed can be limited by Q. In the present Ion-implanted situation, the switching speed is still limited by the carrier 70 ps relaxation time, and thus a large Q/V is preferable. In the 220 ps case when the photon lifetime limits the operation speed, we have to choose appropriate loaded Q for the required speed. Even in such a case, it is better to have high unloaded Q because loaded Q can be controlled by changing the cavity- 0.1 waveguide coupling, and high unloaded Q means low loss of the device. The best design of out device would be a device with the smallest volume, the lowest transmission loss, and the designated loaded Q (depending on the operation speed). The lowest loss with the designated loaded Q can be Non-ion-implanted obtained only when we employs an ultrahigh unloaded Q 0.01 cavity. Compared with other types of all-optical memories, −200 0 200 400 600 800 this device has several advantages, such as small footprint, Time (ps) low-energy consumption, and the capability for integration. (a) The fact that all the light signals used for the operation are transparent in waveguides is important for the application, 0.5 which is fundamentally different from bistable-laser-based 0.4 Non-ion-implanted optical memories. 0.3 In the above, we showed that a single photonic crystal cavity coupled to waveguides functions as a bistable switch or a memory. If we couple two or more bistable cavities, 0.2 Ion-implanted 110 ps we can create much more complex logic functions [11], in 50 ps the same way as with transistor-based logic in electronics. As an example, here we show our numerical design for 0.1 an all-optical flip-flop consisting of two bistable cavities integrated in a photonic crystal. It has been proposed that all- optical flip-flops be realized by using two nonlinear etalons with appropriate cross-feedback [22], but this proposal is unsuitable for on-chip integration. Here, we propose a −200 0 200 400 600 800 different design using two photonic crystal nanocavities [23]. Time (ps) A typical example of flip-flop operation in the high- (b) speed information processing is a retiming circuit, which corrects the timing jitter of an information bitstream and synchronizes it with the clock pulses. This function is normally accomplished by high-speed electronic circuits, but 0.8 if it can be done all optically, it will be advantageous for future ultrahigh-speed data transmission. Here, we propose 0.6 a simple flip-flop design for realizing the retiming function. Figure 9(a) shows a design for the retiming circuit. The 0.4 coupled cavities (C1 and C2) have one common resonant mode (λ = 1548.48 nm, Q = 4500) extended to both 2 2 0.2 cavities and two modes (λ = 1493.73 nm, Q = 6100, 1 1 and λ = 1463.46 nm, Q = 4100) localized in each cavity. 3 3 Here, we use two bistable switching operations for C1 and −100 1000 C2. The cross-feedback is realized as follows. C1 is switched Input energy (fJ) ON only when λ and λ are both applied (P 1and P 2 1 2 IN IN are ON). C2 is ON only when λ are applied (P 3isON) 3 IN Non-ion-implanted and simultaneously λ is supplied from C1 (which means C1 Ion-implanted is ON). Thus the output signal of λ (P 3) becomes ON 3 OUT (c) only if P 3 is turned ON when C1 is already ON in advance. IN These results achieve retiming process. We set P 1and P 3 IN IN Figure 7: All-optical switching for samples with and without ion- as two different clock signals as shown in Figure 9(b),and implantation. (a) NOT-type switching. (b) AND-type switching. assume P 2 to be bit-stream NRZ (nonreturn-to-zero) data IN (c) Signal transmission at the time when the control pulses enters with finite timing jitter. The resultant P 3isprecisely OUT the cavity. The ON/OFF contrast of the signal is shown in relation synchronized to the clock signals and is actually an RZ to the input control pulse energy. The circles are the minimal (return-to-zero) data stream converted from P 2 with jitter transmission for the nonimplanted sample, and the squares are for IN the implanted sample. corrected. Transmittance (a.u.) Transmittance (a.u.) Modulation depth Masaya Notomi et al. 9 P 1 P 2 OUT OUT Control 0.1 Reset C1 Set 0.01 C2 −200 0 200 400 600 800 1000 1200 1400 Time (ps) (a) P P 3 D OUT (a) ON Data (λ2) OFF Clock (λ1) Clock (λ3) 0.1 0.6 0.4 0.2 0.01 0 200 400 600 −200 0 200 400 600 800 1000 1200 1400 Time (ps) Time (ps) (b) Signal input Set ON Figure 9: All-optical retiming circuit based on two bistable cavities. Set ON/OFF (a) Design based on a hexagonal air-hole 2D photonic crystal with (b) a = 400 nm and 2r = 0.55 a. Two waveguides in the upper area (P and P ) are W1 and the other two in the lower area (P and P )are C B D Figure 8: All-optical bistable memory operation in a silicon W0.8. (b) Simulated operation. photonic crystal nanocavity (end-hole shifted four-point defect cavity) realized by the carrier-plasma nonlinearity induced by two- photon absorption in silicon. Q for the control mode is 7640, and Q for the signal mode is 12400. (a) Injected control light consisting operation may be possible after the optimization since our of a pair of set and reset pulses. (b) Output signal intensity as a rough estimation shows that a single cavity switch can function of time for three different cases: with no set/reset pulses operate at sub-mW input power for the similar condition. In (red curve), with set pulse only (green curve), and with set and reset addition, if we manage to employ the carrier-plasma effect pulses (blue curve). for this operation (as was done in Figure 8), we can expect further decrease in terms of the input power. In addition to this work, we have reported another design of all-optical logic circuit which is mostly equivalent to an SR We designed this function in a photonic crystal slab flip-flop employing two bistable cavities [8]. system, and numerically simulated its operation using the FDTD method. The structural parameters are shown in the figure caption. We assumed realistic material parameters 6. SUMMARY (3) −19 2 2 (with a Kerr coefficient χ /ε = 4.1 × 10 (m /V ), a typical value for AlGaAs) and the instantaneous driving Recent rapid progress in photonic crystal nanocavities power is assumed to be 60 mW for all three inputs. is enabling low-power, all-optical switching and memory Figure 9(b) shows three input signals (a data stream with actions on a silicon chip. We have shown that our experimen- jitter, and two clock pulses), and the output from P (P 3). tal demonstration of all-optical switching operation using D OUT As seen in this plot, P 3 is the RZ signal of the input thermo-optic nonlinearity and carrier-plasma nonlinearity, OUT with the jitter corrected. We confirmed that the operation both based on two-photon absorption in silicon. For both speed corresponds to 50 GHz operation. Note that this work cases, we observed significant decrease in the switching was intended to demonstrate the operation principle and power (energy) and also significant increase in the switch- the structure has not yet been optimized. We expect ∼mW ing speed. In this article, we numerically investigated the Input power (a.u.) Output power (a.u.) Transmittance (P 3) OUT 10 Advances in Optical Technologies diffusion process concerning photonic-crystal nanocavities, photonic crystal slabs,” Optics Express, vol. 12, no. 8, pp. 1551– 1561, 2004. which is fundamentally different from that in conventional [15] G. R. Olbright,N.Peyghambarian,H.M.Gibbs,H. optical devices with much larger size. Moreover, we have A. MacLeod, and F. Van Milligen, “Microsecond room- demonstrated their potential for optical logic by a com- temperature optical bistability and crosstalk studies in ZnS bination of bistable elements. 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Tanabe, A. Shinya, et al., “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Optics Express, vol. 15, no. 26, pp. 17458–17481, 2007. [9] M. Soljaci ˇ c ´ and J. D. Joannopoulos, “Enhancement of nonlin- ear effects using photonic crystals,” Nature Materials, vol. 3, no. 4, pp. 211–219, 2004. [10] H. M. Gibbs, Optical Bistability: Controlling Light with Light, Academic Press, Orlando, Fla, USA, 1985. [11] S. D. Smith, “Optical bistability, photonic logic, and optical computation,” Applied Optics, vol. 25, no. 10, pp. 1550–1564, [12] M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high- Q photonic-crystal nanocavities,” Optics Express, vol. 13, no. 7, pp. 2678–2687, 2005. [13] S. Mitsugi, A. Shinya, E. Kuramochi, M. Notomi, T. Tshchizawa, and T. 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On-Chip All-Optical Switching and Memory by Silicon Photonic Crystal Nanocavities

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Copyright © 2008 Masaya Notomi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Publishing Corporation Advances in Optical Technologies Volume 2008, Article ID 568936, 10 pages doi:10.1155/2008/568936 Review Article On-Chip All-Optical Switching and Memory by Silicon Photonic Crystal Nanocavities Masaya Notomi, Takasumi Tanabe, Akihiko Shinya, Eiichi Kuramochi, and Hideaki Taniyama NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi 2430198, Japan Correspondence should be addressed to Masaya Notomi, notomi@will.brl.ntt.co.jp Received 23 December 2007; Accepted 13 April 2008 Recommended by D. Lockwood We review our recent studies on all-optical switching and memory operations based on thermo-optic and carrier-plasma nonlinearities both induced by two-photon absorption in silicon photonic crystal nanocavities. Owing to high-Q and small volume of these photonic crystal cavities, we have demonstrated that the switching power can be largely reduced. In addition, we demonstrate that the switching time is also reduced in nanocavity devices because of their short diffusion time. These features are important for all-optical nonlinear processing in silicon photonics technologies, since silicon is not an efficient optical nonlinear material. We discuss the effect of the carrier diffusion process in our devices, and demonstrate improvement in terms of the response speed by employing ion-implantation process. Finally, we show that coupled bistable devices lead to all-optical logic, such as flip-flop operation. These results indicate that a nanocavity-based photonic crystal platform on a silicon chip may be a promising candidate for future on-chip all-optical information processing in a largely integrated fashion. Copyright © 2008 Masaya Notomi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION As has been studied in various forms, all-optical switches can be realized using optical resonators, where a control It used to be a great challenge to tightly confine light in a optical pulse induces a resonance shift via optical nonlinear wavelength-scale volume, which had limited the capability of effects. For such a resonator-based switch, there is a two- photonics technologies in various aspects. Recently, however, fold enhancement in terms of the switching power if a an optical resonator with ultrahigh-Q (∼1 million) and small cavity with a high-Q is employed. First, the light small volume (∼(λ/n) ) becomes possible by employing the intensity inside the cavity should be proportional to Q/V . state-of-the-art photonic crystal technologies [1–6]. Figure 1 Second, the required wavelength shift is proportional to shows an example of high-Q nanocavities, which we have 1/Q. In total, the switching power should be reduced recently demonstrated in silicon photonic crystals. This by (Q /V ), which can be significantly large for photonic particular cavity shows a theoretical Q of over 10 and crystal nanocavities [9]. Although the switching mechanism an experimental Q of 1.3 million with a mode volume itself is basically similar to that of previous resonator- of 1.5(λ/n) [4, 7]. These values are hardly available in based switches, such as nonlinear etalons [10], this large optical systems other than photonic crystals. Various forms enhancement has had an important impact on optical of light-matter interactions are expected to be enhanced integration since most optical switching components require in such high-Q nanocavities having large Q/V ratio [8]. too much power for realistic integration. Furthermore, in the case of carrier-induced nonlinearity or thermo-optic Among them, in this article, we focus on application to all- optical switching and memory operations based on optical nonlinearity, the smallness of the device naturally leads nonlinear interaction. Especially for this, we investigate all- to fast operation speed, since the relaxation time of such optical operations based on carrier-induced nonlinearity and processes normally depends on the size. As we will show examine the features of photonic crystal nanocavities for below, this advantage is significant for wavelength-sized such applications. cavities. 2 Advances in Optical Technologies Q = (1.28 ± 0.06) × 10 1.2pm c1-hole c2-hole c3-hole 1575.336 1575.34 Wavelength (nm) (a) (b) Q = (1.34 ± 0.08) × 10 τ :1.12 ns 12 34 Time (ns) (c) Figure 1: Width-modulated, line-defect photonic crystal cavities. (a) Cavity design. The cavity has the theoretical Q. The hole shifts are typically 9 nm (red holes), 6 nm (green holes), and 3 nm (blue holes). (b) Spectral measurement of a nanocavity fabricated in a silicon hexagonal air-hole photonic slab with a = 420 nm and 2r = 216 nm. The transmission spectrum of a cavity with a second-stage hole-shift. The inner and outer hole-shifts are 8 and 4 nm, respectively. (c) Time-domain ring-down measurement. The time decay of the output light intensity from the same cavity as (b). Details can be found in the reference. In addition, resonator-based optical switches are well 2. ALL-OPTICAL BISTABLE SWITCHING BY known to exhibit optical bistability [10] and thus they can THERMO-OPTIC NONLINEARITY be used for optical memory and all-optical logic [11]. Such functionality is one of the most important functions missing As described above, photonic crystal nanocavities have a from existing photonic devices. Thus, we believe that all- promising potential for all-optical switching applications. optical bistable switches based on photonic crystal cavities To experimentally confirm this, we have investigated all- are important candidates for future optical integration. optical bistable switching operations employing the thermo- In this paper, we investigate all-optical switching and optic nonlinearity induced by two-photon absorption (TPA) memory action in silicon photonic crystal nanocavity in silicon [12]. For this study, we employed an end- devices. First, we study the switching action using thermo- hole shifted four-point Si photonic crystal cavity integrated optic nonlinearity. Next, we investigate similar switch- with input/output photonic crystal waveguides (shown in ing action using much faster carrier-plasma nonlinearity. Figure 2(a))[13, 14]. Figure 2(b) shows transmission spectra Thirdly, we analyze the effect of carrier relaxation process in with various input power at 1.5 μm wavelength region. the switching action and made an attempt to further decrease As clearly seen in the graph, the transmission spectrum the relaxation time by ion implantation. Furthermore, we is shifted to longer wavelength (red-shifted). This shift is demonstrate bistable memory action employing basically the due to thermo-optic nonlinearity induced by two-photon same nanocavity devices and present an example of design absorption in the cavity. At input power higher than for on-chip all-optical logic circuits consisting of two bistable 10 μW, there is an abrupt kink in the spectrum. This nanocavities. kink corresponds to bistable switching. To see this more Intensity Transmission Masaya Notomi et al. 3 Red shifted −1 −2 1567.5 1568 1568.5 1569 1569.5 Wavelength (nm) 400 μW(4 dB) 25 μW(16 dB) 250 μW(6 dB) 10 μW(20 dB) 160 μW(8 dB) 2.5 μW(26 dB) 100 μW(10 dB) 250 nW (36 dB) 63 μW(12 dB) (a) (b) δ: detuning Red shift −1 1 2 10 10 Input power P (μW) IN δ = 0pm 100 pm 20 pm 120 pm 40 pm 140 pm 60 pm 160 pm 80 pm 180 pm (c) Figure 2: All-optical bistable switching in a silicon hexagonal air-hole photonic crystal nanocavity (end-hole shifted four-point defect cavity) realized by the thermo-optic nonlinearity induced by two-photon absorption in silicon. (a) Schematic of the sample and a scanning electron micrograph of the sample. a = 420 nm, 2r = 0.55a. The radius of end-holes of the cavity is 0.125a. V = 0.102 μm . The radius of end-holes of the waveguide is 0.15a. (b) Intensity-dependent transmission spectra taken by a tunable laser in the upsweep condition. Q in the linear regime is 33400. (c) Output power versus input power for various detuning values. The nonlinear regime starts from 10 μW, and the bistable regime starts from 40 μW. directly, we measured the output power as a function of This value is remarkably smaller that of bulk-type thermo- the input power at various detuning conditions, as shown optic nonlinear etalons (a few to several tens mW) [15] in Figure 2(c). Now, it is clear that this device exhibits and also smaller than that of recent miniature-sized thermo- bistable switching. The most noteworthy point regarding this optic silicon microring resonator devices (∼0.8 mW) [16]. In switching is its switching power, which is as small as 40 μW. addition, it is important to note that TPA occurs only in the Output power P (μW) OUT Output power (μW) 4 Advances in Optical Technologies Relaxation time measurement mode A (CW probe) Switch-on time measurement mode B (ON→OFF) δ (pump): 0 (nm) OFF 0 300 δ (probe): 0.38 (nm) −7dBm −7.6dBm −8dBm −1 200 −8.6dBm −2 t ∼ 100 ns −3 0 200 400 600 800 600 800 1000 1200 Time (ns) Time (ns) Stored energy = 4pJ (a) (b) Switch-on time measurement Critical slowing down 0 50 100 150 200 Time (ns) Incident energy =∼ 11 pJ (c) Figure 3: Temporal response of thermo-optic switching. (a) Switch-off. Temporal response of the probe output. At t = 800 nanoseconds, the pump signal was switched off. The input instantaneous power for the pump is 64 μW. The pulse width and period are 400 nanoseconds and 40 microseconds. The exponential fit gives a decay time of approximately 100 nanoseconds. (b) Switch-on operation for various input power. (c) Incident energy required for the switch-on operation estimated from the product of the incident energy and the time required for switch-onin(b). cavity (the linear absorption of silicon at this wavelength is which is normally required for signal processing. Since negligible), and, therefore, we can easily integrate this device bistable switching for one resonant mode should influence with transparent waveguides in the same chip. the transmission intensity of the other resonant mode in Our cavity shown in Figure 2(a) was intentionally de- the same cavity, we can easily realize such operation. As signed to have two resonant modes, and, therefore, we we reported in [12], we observe basically similar bistable can perform all-optical switching using independent two switching behavior in the relation between the input power inputs with different wavelengths (signal and control), for the control mode and the output power for the signal Output (probe) (in scale) Input energy (pJ) Output power (a.u.) Masaya Notomi et al. 5 NOT type switching (ON to OFF) AND type switching (OFF to ON) 0.1 0.1 0.01 0 200 400 600 800 1000 0 1000 2000 3000 4000 5000 Time (ps) Time (ps) U (U ) in eff U (U ) in eff 1042 (38) fJ 450 (16) fJ 298 (11) fJ 47 (2) fJ 859 (31) fJ 291 (11) fJ 206 (8) fJ 413 (15) fJ 156 (6) fJ 369 (13) fJ 666 (24) fJ 112 (4) fJ (a) (b) Figure 4: All-optical switching in a silicon photonic crystal nanocavity (end-hole shifted four point cavity) realized by carrier-plasma nonlinearity induced by two-photon absorption in silicon. Q for the control mode is 11500, and Q for the signal mode is 23000. (a) AND- type switching at various control pulse energies with the detuning of −0.3 nm. (b) NOT-type switching at various control pulse energies with no detuning. Each line is shifted by 500 picoseconds. Model calculation Experimental result 1 S On 50 (ps) 293 (ps) 267 (ps) 54 (ps) τ = 50 ∼ 100 (ps) 0.1 0.1 S × 10 Off S × 10 τ = 80 (ps) 0.01 0.01 −200 0 200 400 600 −200 0 200 400 600 Time (ps) Time (ps) δ =−0.45 (nm) δ =−0.45 (nm) δ = 0(nm) δ = 0.01 (nm) (a) (b) Figure 5: Comparison between the rate-equation analysis and measurement result. We modeled the cavity resonance as a Lorentzian function whose center wavelength is shifting in proportion to the carrier density. (a) Calculation. (b) Experiment. mode. This operation is basically what we expect for the so- Although the bistable operation itself is similar to that called all-optical transistors, and will be basis for various of nonlinear etalon switches, these photonic crystal switches logic functions. The detail of this operation is described in can be clearly distinguished in terms of the operating power [12]. For example, we demonstrated that we can amplify an and capability for integration. The mode volume of this AC signal using this device. cavity is only approximately 0.1 μm . This small footprint Signal transmission (a.u.) Signal transmission (a.u.) 6 Advances in Optical Technologies itself is of course advantageous for integration, but it is parameter condition. In this calculation, we assumed the also beneficial for reducing the switching speed because carrier relaxation time of 80 picoseconds. This suggests that our device is limited by the thermal diffusion process. To the effective carrier relaxation time for this all-optical switch demonstrate these characteristics, we measured temporal is in the range between 50 to 100 picoseconds. This fast response of the operation for switch-off and switch-on carrier relaxation may be attributed to the short diffusion processes, as shown in Figures 3(a) and 3(b). The relaxation time for generated carriers. Note that the photon lifetime time of our switch is approximately 100 nanoseconds, which of our cavity is approximately 10 picoseconds, and thus is much shorter than that of conventional thermo-optic the operation speed of our device is limited by the carrier switches (∼milliseconds). This amazingly fast thermo-optic relaxation time. This carrier relaxation time is much shorter switching is primarily due to the smallness of our cavity. In than that in other silicon photonic microdevices [18]. That addition, we can estimate the required switching energy from is, the small footprint of the device is again effective in the switch-on measurement. The deduced smallest value is as improving the operating speed. smallas11 pJasshown in Figure 3(c). 4. EFFECT OF CARRIER RELAXATION PROCESS ON 3. ALL-OPTICAL SWITCHING BY SWITCHING OPERATION CARRIER-PLASMA NONLINEARITY In Section 3, we demonstrate that silicon all-optical switches These thermo-optic nonlinear bistable switches clearly based on carrier-plasma nonlinearity can operate at a demonstrate that large Q/V photonic crystal cavities are significantly fast speed, which is attributed to the fast carrier very effective in improving the operation power and speed. relaxation process. We regard that this fast carrier relaxation However, the speed itself is still not very fast, which is limited is possibly due to the fact that the diffusion process is an by the intrinsically slow thermo-optic effect. To realize much efficient relaxation channel for nanocavities. To verify this faster all-optical switches, here we employ another nonlinear explanation, we performed numerical simulations for the effect, namely, the carrier-plasma effect [17]. This process is carrier diffusion process in silicon photonic crystal cavities also based on the same TPA process in silicon. Thus most of [19]. In this simulation, we assumed an initial carrier dis- the arguments concerning their advantages are similar to that tribution determined from the optical intensity distribution for thermo-optic nonlinearity. For this experiment, we used of the cavity mode, and numerically solved two-dimensional similar photonic crystal cavity devices with a control pulse diffusion equations with assuming a realistic photonic input. If the duration of the control pulse is sufficiently short, crystal cavity structure which is the same as that used in we can avoid thermal heating and may be able to observe only the experiment. The side-wall nonradiative recombination carrier-plasma nonlinearity. In fact, we observed a clear blue process at the air-hole surface is incorporated in the equation shift in the resonance when we injected a 6-picosecond pulse as effective surface recombination rate (S), and the effect into this device, which is consistent with the expected shift of the top-surface nonradiative recombination process is induced by the carrier-plasma nonlinearity. Figure 4 shows incorporated as an effective carrier lifetime parameter which the time-resolved output intensity for the signal mode when is determined from another calculation for a simple slab. a 6-picosecond control pulse is input [17]. We observed clear We calculated the time-dependent resonance wavelength all-optical AND-type switching from OFF to ON for the shift using instantaneous carrier concentration in the cavity. detuning of 0.45 nm (Figure 4(a)) and NOT-type switching The calculated snapshots of the carrier distribution at t from ON to OFF for the detuning of 0.01 nm (Figure 4(b)). = 0, 8, and 24 picoseconds are shown in Figures 6(a), The required switching energy is only a few hundred fJ, 6(b),and 6(c). These snapshots clearly show that the initial which is much smaller than that of ring-cavity-based silicon distribution is rapidly spread as a result of diffusion. This all-optical switches [18]. If we take the coupling efficiency rapid diffusion results rapid switching recovery. Figure 6(d) between the cavity and waveguide into account, the actual shows the calculated shift of the resonance wavelength for the cavity. The initial wavelength shift caused by the carrier pulse energy used for the switching is less than 10 fJ. This extremely small switching energy is attributed to large Q/V plasma shift is recovered quickly. As shown in the figure, ratio in our cavity. the nonradiative recombination does not seriously affect the The switching time of our device is approximately initial recovery. Therefore, we believe that the fast operation from 50 picoseconds to 300 picoseconds depending on the of our optical switches is explained by the rapid carrier detuning and control pulse energy. Considering the fact diffusion process. that the carrier lifetime in silicon is normally very long If we wish to increase the operation speed further, (∼microseconds), this switching time is also surprisingly we have to somehow decrease the carrier relaxation time. fast. This apparently indicates that the switching time is Although there are several ways to do so, we have recently not limited by the carrier recombination time of bulk employed an Ar-ion implantation process in order to silicon. We analyzed the switching behavior employing introduce extremely fast nonradiative recombination centers simplified rate equations for the photon and carrier density into silicon. If the carrier recombination time becomes faster in a photonic-crystal nanocavity incorporating the effective than the diffusion time, we can expect an improvement in the carrier relaxation time. We found that this simple model operation speed. When we implanted silicon photonic crystal + 14 −2 can reproduce the experimental result fairly well. Figure 5 nanocavity switches with Ar dose of 2.0 × 10 cm and shows simulated and experimental results for the same an acceleration voltage of 100 keV, we observed a significant Masaya Notomi et al. 7 2 2 1 1 0 0 −1 −1 −1 0ps 8ps 24 ps −2 −2 −2 −2 −10 1 2 −2 −10 1 2 −2 −10 1 2 x (μm) x (μm) x (μm) 17 17 16 16 16 16 03.8 × 10 7.5 × 10 03.1 × 10 6.3 × 10 02 × 10 4 × 10 −3 −3 −3 Electron density (cm ) Electron density (cm ) Electron density (cm ) (a) (b) (c) 0.15 0.1 S = 0cm/s 0.05 S = 8 × 10 cm/s 0 50 100 150 200 Time (ps) (d) Figure 6: Numerical simulation of carrier diffusion process for a silicon end-hole-shifted photonic crystal cavity. (a), (b), (c) snapshots of the carrier distribution at t = 0, 8, 24 picoseconds. (c) Shift of the resonance wavelength for the cavity as a function of time with the sidewall nonradiative recombination rate S = 0and S = 8 × 10 cm/s. improvement in switching speed as shown in Figures 7(a), 5. ALL-OPTICAL MEMORY OPERATION 7(b). The implantation condition was carefully determined AND LOGIC CIRCUIT so as to keep almost the same cavity Q but to significantly decrease the carrier lifetime in the cavity. In the case of In the same way as thermo-optic switching, carrier-plasma detuning for an NOT gate (Figure 7(a),itwas reducedfrom switching also provides bistable operation. Figure 8 shows 110 picoseconds to 50 picoseconds. In the case of detuning bistable operations realized by employing a pair of set and for an AND gate, the switching time was reduced from reset pulses [21]. When a set pulse is fed into the input 220 picoseconds to 70 picoseconds (Figure 7(b))[20]. As waveguide, the output signal is switched from OFF to ON shown in Figure 7(c), the ON/OFF ratio is mostly the same and remains ON even after the set pulse exits (green curve). between two conditions. In addition, the required switching When a pair of set and reset pulses is applied (as shown in energy was almost the same as that without the implantation. Figure 8(a)), the output is switched from OFF to ON by the Although the reduction of the carrier lifetime may lead to set pulse and then ON to OFF by the reset pulse (blue curve). increase in the switching energy, this change is not significant This is simply a memory operation using optical bistability. as far as the carrier lifetime is longer than the photon lifetime The energy of the set pulse is less than 100 fJ, and the DC bias and the control pulse length (which was the case in our input for sustaining the ON/OFF states is only 0.4 mW. These experiment). These results clearly demonstrate the effect small values are primarily the results of the large Q/V ratio of of ion-implantation on the improvement in the switching the photonic crystal cavity. It is worth noting that the largest speed. Q/V should always result in the smallest switching power, y (μm) Wavelength shift (−nm) y (μm) y (μm) 8 Advances in Optical Technologies but the operation speed can be limited by Q. In the present Ion-implanted situation, the switching speed is still limited by the carrier 70 ps relaxation time, and thus a large Q/V is preferable. In the 220 ps case when the photon lifetime limits the operation speed, we have to choose appropriate loaded Q for the required speed. Even in such a case, it is better to have high unloaded Q because loaded Q can be controlled by changing the cavity- 0.1 waveguide coupling, and high unloaded Q means low loss of the device. The best design of out device would be a device with the smallest volume, the lowest transmission loss, and the designated loaded Q (depending on the operation speed). The lowest loss with the designated loaded Q can be Non-ion-implanted obtained only when we employs an ultrahigh unloaded Q 0.01 cavity. Compared with other types of all-optical memories, −200 0 200 400 600 800 this device has several advantages, such as small footprint, Time (ps) low-energy consumption, and the capability for integration. (a) The fact that all the light signals used for the operation are transparent in waveguides is important for the application, 0.5 which is fundamentally different from bistable-laser-based 0.4 Non-ion-implanted optical memories. 0.3 In the above, we showed that a single photonic crystal cavity coupled to waveguides functions as a bistable switch or a memory. If we couple two or more bistable cavities, 0.2 Ion-implanted 110 ps we can create much more complex logic functions [11], in 50 ps the same way as with transistor-based logic in electronics. As an example, here we show our numerical design for 0.1 an all-optical flip-flop consisting of two bistable cavities integrated in a photonic crystal. It has been proposed that all- optical flip-flops be realized by using two nonlinear etalons with appropriate cross-feedback [22], but this proposal is unsuitable for on-chip integration. Here, we propose a −200 0 200 400 600 800 different design using two photonic crystal nanocavities [23]. Time (ps) A typical example of flip-flop operation in the high- (b) speed information processing is a retiming circuit, which corrects the timing jitter of an information bitstream and synchronizes it with the clock pulses. This function is normally accomplished by high-speed electronic circuits, but 0.8 if it can be done all optically, it will be advantageous for future ultrahigh-speed data transmission. Here, we propose 0.6 a simple flip-flop design for realizing the retiming function. Figure 9(a) shows a design for the retiming circuit. The 0.4 coupled cavities (C1 and C2) have one common resonant mode (λ = 1548.48 nm, Q = 4500) extended to both 2 2 0.2 cavities and two modes (λ = 1493.73 nm, Q = 6100, 1 1 and λ = 1463.46 nm, Q = 4100) localized in each cavity. 3 3 Here, we use two bistable switching operations for C1 and −100 1000 C2. The cross-feedback is realized as follows. C1 is switched Input energy (fJ) ON only when λ and λ are both applied (P 1and P 2 1 2 IN IN are ON). C2 is ON only when λ are applied (P 3isON) 3 IN Non-ion-implanted and simultaneously λ is supplied from C1 (which means C1 Ion-implanted is ON). Thus the output signal of λ (P 3) becomes ON 3 OUT (c) only if P 3 is turned ON when C1 is already ON in advance. IN These results achieve retiming process. We set P 1and P 3 IN IN Figure 7: All-optical switching for samples with and without ion- as two different clock signals as shown in Figure 9(b),and implantation. (a) NOT-type switching. (b) AND-type switching. assume P 2 to be bit-stream NRZ (nonreturn-to-zero) data IN (c) Signal transmission at the time when the control pulses enters with finite timing jitter. The resultant P 3isprecisely OUT the cavity. The ON/OFF contrast of the signal is shown in relation synchronized to the clock signals and is actually an RZ to the input control pulse energy. The circles are the minimal (return-to-zero) data stream converted from P 2 with jitter transmission for the nonimplanted sample, and the squares are for IN the implanted sample. corrected. Transmittance (a.u.) Transmittance (a.u.) Modulation depth Masaya Notomi et al. 9 P 1 P 2 OUT OUT Control 0.1 Reset C1 Set 0.01 C2 −200 0 200 400 600 800 1000 1200 1400 Time (ps) (a) P P 3 D OUT (a) ON Data (λ2) OFF Clock (λ1) Clock (λ3) 0.1 0.6 0.4 0.2 0.01 0 200 400 600 −200 0 200 400 600 800 1000 1200 1400 Time (ps) Time (ps) (b) Signal input Set ON Figure 9: All-optical retiming circuit based on two bistable cavities. Set ON/OFF (a) Design based on a hexagonal air-hole 2D photonic crystal with (b) a = 400 nm and 2r = 0.55 a. Two waveguides in the upper area (P and P ) are W1 and the other two in the lower area (P and P )are C B D Figure 8: All-optical bistable memory operation in a silicon W0.8. (b) Simulated operation. photonic crystal nanocavity (end-hole shifted four-point defect cavity) realized by the carrier-plasma nonlinearity induced by two- photon absorption in silicon. Q for the control mode is 7640, and Q for the signal mode is 12400. (a) Injected control light consisting operation may be possible after the optimization since our of a pair of set and reset pulses. (b) Output signal intensity as a rough estimation shows that a single cavity switch can function of time for three different cases: with no set/reset pulses operate at sub-mW input power for the similar condition. In (red curve), with set pulse only (green curve), and with set and reset addition, if we manage to employ the carrier-plasma effect pulses (blue curve). for this operation (as was done in Figure 8), we can expect further decrease in terms of the input power. In addition to this work, we have reported another design of all-optical logic circuit which is mostly equivalent to an SR We designed this function in a photonic crystal slab flip-flop employing two bistable cavities [8]. system, and numerically simulated its operation using the FDTD method. The structural parameters are shown in the figure caption. We assumed realistic material parameters 6. SUMMARY (3) −19 2 2 (with a Kerr coefficient χ /ε = 4.1 × 10 (m /V ), a typical value for AlGaAs) and the instantaneous driving Recent rapid progress in photonic crystal nanocavities power is assumed to be 60 mW for all three inputs. is enabling low-power, all-optical switching and memory Figure 9(b) shows three input signals (a data stream with actions on a silicon chip. We have shown that our experimen- jitter, and two clock pulses), and the output from P (P 3). tal demonstration of all-optical switching operation using D OUT As seen in this plot, P 3 is the RZ signal of the input thermo-optic nonlinearity and carrier-plasma nonlinearity, OUT with the jitter corrected. We confirmed that the operation both based on two-photon absorption in silicon. For both speed corresponds to 50 GHz operation. Note that this work cases, we observed significant decrease in the switching was intended to demonstrate the operation principle and power (energy) and also significant increase in the switch- the structure has not yet been optimized. We expect ∼mW ing speed. In this article, we numerically investigated the Input power (a.u.) Output power (a.u.) Transmittance (P 3) OUT 10 Advances in Optical Technologies diffusion process concerning photonic-crystal nanocavities, photonic crystal slabs,” Optics Express, vol. 12, no. 8, pp. 1551– 1561, 2004. which is fundamentally different from that in conventional [15] G. R. Olbright,N.Peyghambarian,H.M.Gibbs,H. optical devices with much larger size. Moreover, we have A. MacLeod, and F. Van Milligen, “Microsecond room- demonstrated their potential for optical logic by a com- temperature optical bistability and crosstalk studies in ZnS bination of bistable elements. 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