## Abstract

We propose an optical flip-flop circuit composed of two-port resonant-tunneling filters based on a two-dimensional photonic crystal slab with a triangular air-hole lattice. This circuit can function as an optical digital circuit that synchronizes input data with a clock. In this report, we demonstrate that this circuit can achieve a fast operating speed with a response time of about 10 ps and a low operating power of 60 mW by employing a two-dimensional FDTD calculation.

©2006 Optical Society of America

## 1. Introduction

An all-optical flip-flop circuit will be needed in future all-optical high-speed signal circuits. A flip-flop circuit is a digital circuit that temporarily memorizes past input/output information, and processes it with present input signals. These functions are indispensable in terms of achieving all-optical regeneration functions. One of the most important functions is that the output pulses are synchronized with the system clock. Several successful all-optical circuits have already been proposed [1–4]. Since most of them are based on the optical analogue AND gate, the output pulse width is determined by the clock pulse width. Therefore, the output pulse widths decrease when there is timing jitter in the optical data. Although all-optical flip-flop circuit can solve this problem, their operation speed is not so fast due to long feed-back loop waveguide for bistable operation [3, 4].

Recently, photonic crystal (PhC) has attracted attention as a platform on which to construct devices with dimensions of a few wavelengths of light for future photonic integrated circuits. There have been many studies on suppressing the out-plane radiation loss of two dimensional (2D) PhC devices and the quality of PhCs has been rapidly improved [5, 6]. We have reported a PhC-waveguide with a very low loss of less than 2 dB/cm [7] and an ultrasmall resonator with a high quality factor of 800,000 [8], and measured the logic gate operation and hysteresis characteristics of resonant tunneling filters combining waveguides and resonators in 2D-PhCs [8–13]. These filters operate with very low power and at very high speed [10–16] and are expected to be essential elements in terms of achieving all-optical processing. In this report, we propose a novel flip-flop circuit that connects two resonant tunneling filters in a 2D-PhC to synchronize the input data with the system clock. We simulate that it acts with very low power of 60 mW and fast operation speed of about 10 ps by a two-dimensional FDTD calculation.

## 2. Design and discussion

Figure 1 shows the schematic structure of our flip-flop circuit based on a 2D-PhC with a triangular air-hole lattice. The lattice constant *a* is 400 nm, and the air-hole diameter is 0.55*a*. This circuit contains two different resonators (C1, C2) and two kinds of waveguide (P1 = P2, P3 = P4). The two resonators have one identical resonant wavelength (*λ*2) and two different resonant wavelengths (*λ*1 and *λ*3 for C1 and C2, respectively). The widths of the waveguides are tuned so that the *λ*1 and *λ*3 lights can propagate in all the waveguides and the *λ*2 light can propagate only in P1 and P2.

We input the *λ*1 and the *λ*2 lights from P1, and the *λ*3 light from P3, which means that this circuit can be regarded as a structure composed of three kinds of circuits (F1, F2 and F3) as shown in Fig. 2. We can tune C1 and C2 so that they can be in the ON state when two signals are inputted. Here, ON/OFF indicates a state where the input light is resonant/non-resonant with the resonator. For example, the combination of *λ*1 and *λ*2 lights can turn on F1 because both lights can enter C1. In this case, F2 can also be ON because the resonant frequencies of C1 and C2 in F2 have the same value as *λ*2. The combination of the *λ*1 and *λ*3 lights cannot turn F1 or F3 on because they do not have a common resonator. Moreover, the combination of the *λ*2 and *λ*3 lights cannot turn F2 or F3 ON because *λ*3 is forbidden from entering C1 and *λ*2 light cannot enter C2 before C1 turns ON.

When F2 and F3 are bistable as shown in Fig. 3(a), the above combinations enable us to achieve a complex function as described below. Here, we consider a sequence of input lights as shown in Fig. 3(b) by using the equivalent circuit shown in Fig. 4. (1) t = 0. *λ*3 light is inputted. C2 stays in the OFF state. (2) t = t1. *λ*2 light is added in the middle of the first period (0 < t < T), but C1 and C2 do not turn ON. (3) t = T. *λ*3 light is cut off and *λ*1 light is inputted. Since C1 turns ON, the *λ*2 light reaches C2. (4) t = 2T. *λ*1 light is cut off and *λ*3 is inputted. Since C1 stays in the ON state and *λ*2 and *λ*3 lights are inputted into C2, C2 turns ON and *λ*3 light is outputted. (5) t = t3. Since C2 stays in the ON state after the *λ*2 light is cut off, *λ*3 light is outputted. (6) t = 3T. *λ*3 light is cut off. C2 turns OFF. These results show that this circuit temporarily memorizes the input condition of the *λ*1 and *λ*2 lights in the previous period, and processes them with the present *λ*3 signal to determine the output condition so that the *λ*3 pulse passes the circuit when both *λ*1 and *λ*2 are inputted in the previous period. Here, it should be noted that the output *λ*3 pulse width remains the same as the clock pulse width, which is a very important characteristic when the systems are cascaded. This is the mechanism of our flip-flop circuit whose output condition depends on the sequence of the input signals.

We simulate our system with the 2D-FDTD method. The effective refractive index of the slab is 2.78. The estimated resonant wavelengths (*λ*1, *λ*2 and *λ*3) are 1493.73 1548.48 and 1463.36 nm, respectively, and their quality factors for *λ*1, *λ*2, and *λ*3 are 6100, 4500 and 4100, respectively. First, we check the memory operations of the system. Here we assume the PhC material to be AlGaAs and we choose a Kerr coefficient of *χ*
^{(3)}/*ε*
_{0} = 4.1×10^{-19}[m^{2}/V^{2}] , which corresponds to a nonlinear refractive index of *n*
_{2} = 1.5×10^{-17}[m^{2}/W] in our calculation method. These nonlinear parameters are achievable values in many nearly instantaneous nonlinear materials [14–16]. Figure 5 is a bistable characteristic of F2 and F3. The dotted line is an input signal, and the solid and dashed lines are the output signals of F2 and F3, respectively. Since F2 contains two resonators and so needs more power than F3 for bistable operation, we set the wavelength detuning (= operation wavelength – resonant wavelength) of F2 and F3 at +0.43 and +0.92 nm, respectively, so that their hysteresis curves overlap. These values correspond to the 2δ and 3δ, respectively. Here δ is the minimum detuning for bistable operation [14–16].

We consider the clock operation of our system using *λ*1 and *λ*3 lights as the internal system clock. The clock pulse (CLOCK) of *λ*3 light is inputted from P3. And the data signal (DATA) of *λ*2 light with a non-return-to-zero (NRZ) format in which the signal level is low for ‘0’ and high for ‘1’, but does not return to zero between successive bits, and the inversed CLOCK (CLOCK¯) of *λ*1 light is inputted from P1. Figure 6(a) shows the time charts of our system for clock pulse width of 40 ps, and Fig. 6(b) is a movie of the field profile in the shaded time region in Fig. 6(a) with the clock pulse width of 20 ps. Their duty ratios are 50%. Here, the detuning value of F1 is +0.43 nm, which corresponds to 2δ. And the powers of the *λ*1, *λ*2 and *λ*3 lights are all 60 mW. The input NRZ format DATA deviate slightly from an ideal signal synchronized with the clock (dotted line). These figures show that our system outputs the AND signal between the ideal DATA and the CLOCK. That is, this system can synchronize the DATA with the CLOCK and regenerate the ideal DATA with a return-to-zero (RZ) format in which the signal returns to a rest state during a portion of the bit period. These functions are advantageous for clock operating digital systems. The system response time is about 10 ps, which means our system can operate with a 50 GHz clock. To overcome the speed limitation and achieve a clock operation of over 100 GHz with a low input power, it is very important to design a small mode volume (V_{eff}) resonator and to use material with a large n_{2} because the switching speed and the bistable threshold power are proportional to 1/Q and
V_{eff}/(n_{2}Q^{2}), respectively.

## 3. Conclusion

We proposed a 2D-PhC based all-optical digital circuit in which two resonant tunneling filters operating as bistable switches are connected so that their resonators are directly coupled with each other. We demonstrated that this system can automatically synchronize NRZ format input data with its clock and regenerate RZ format data with an operating power of 60 mW and a response time of about 10 ps by using a 2D-FDTD calculation. This ultrasmall nonlinear device has the potential to provide various signal processing functions in photonic-crystal-based optical circuits.

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