Fig. 1. Structure of a flip-flop circuit based on a 2D-PhC with a triangular air-hole lattice. The lattice constant a is 400 nm, the air-hole diameter is 0.55a, and the effective refractive index of the slab is 2.78. The two resonators (C1 and C2) have one identical resonant frequency (wavelength λ2=1548.48 nm) and two different resonant frequencies (wavelength λ1= 1493.73 nm for C1 and wavelength λ3 = 1463.36 nm for C2). Their quality factors for λ1, λ2, and λ3 are Q1=6100, Q2=4500 and Q3 = 4100, respectively. The widths of P1 and P3 are W ₀ =a√3 and 0.8W₀, respectively. The widths are tuned so that the λ1 and λ3 lights can propagate in all the waveguides and the λ2 light can propagate only in P1 and P2.

Fig. 2. Equivalent circuits of the flip-flop circuit for each resonant frequency. F1, F2 and F3 are the equivalent two-port resonant tunneling filters for input lights of λ1 and λ2, and λ3, respectively.

Fig. 3. Mechanism of the flip-flop circuit composed of F1, F2 and F3. (a) Hysteresis characteristics of F2 and F3. (b) Time chart of input and output signals. (1) t = 0. λ3 light is inputted. C2 stays in the OFF state. (2) t = t1. λ2 light is added in the middle of the first period (0 < t < T), but C1 and C2 do not turn ON. (3) t = T. λ3 light is cut off and λ1 light is inputted. Since C1 turns ON, the λ2 light reaches C2. (4) t = 2T. λ1 light is cut off and λ3 is inputted. Since C1 stays in the ON state and λ2 and λ3 lights are inputted into C2, C2 turns ON and λ3 light is outputted. (5) t = t3. Since C2 stays in the ON state after the λ2 light is cut off, λ3 light is outputted. (6) t = 3T. λ3 light is cut off. C2 turns OFF.

Fig. 4. Equivalent circuit. The switch opens when two signals are inputted and stays in the ON state until both signals are cut off.

Fig. 5. Bistable characteristics of F2 and F3. The Kerr coefficient is χ/ε ₀ = 4.1×10^-19[m²/V²], which corresponds to a nonlinear refractive index of n ₂ =1.5×;10^-17[m²/W] in our calculation method. The dotted line is an input signal, and the solid and dashed lines are the output signals of F2 and F3, respectively. The wavelength detuning values of F2 and F3 are +0.43 and +0.92 nm, respectively.

Fig. 6. Clock operation of the flip-flop circuit. The λ3 clock pulse (CLOCK) is inputted from P3. And the data signal (DATA) of NRZ λ1 light and the λ2 inversed CLOCK (CLOCK¯) are inputted from P1. The detuning values of F1, F2 and F3 are +0.43, +0.43 and +0.92 nm, respectively, and the input powers of the λ1, λ2 and λ3 lights are all 61 mW. (a) Time chart of the circuit. This figure shows that this circuit automatically synchronizes the NRZ input DATA with the internal clock, and regenerates the ideal DATA with the RZ format. (b) (1.93 MB) Movie of the field profile in the shaded time region in Fig. 6(a). There are three CLOCK pulses, but only the second one is outputted. The system response time is about 10 ps. [Media 1]