Numerical modeling of soliton-dragging logic gates

Abstract

The soliton-dragging logic gate is based on the soliton-dragging effect, which occurs when pulses of opposite polarization states in a birefringent optical fiber collide. The central frequencies of the two pulses and hence their velocities are shifted. The soliton-dragging effect is studied here for two solitons of the same amplitude, two solitons of different amplitudes, and two pulses that are not solitons. The dependences of the effect on the initial pulse separation, the initial pulse amplitudes, and the initial pulse profiles are all determined. The pulse interaction is studied by means of several different methods: (1) a complete solution of the coupled nonlinear Schrodinger equation, (2) a solution of ordinary differential equations that includes the effect of frequency chirp, (3) a solution of ordinary differential equations that neglects the effect of frequency chirp, and (4) the Born approximation. We compare the last three approaches with the first. We find that the second approach accurately predicts the velocity and the time shifts for the larger amplitude pulse in all cases of practical interest that we studied. Thus the second approach is useful in the design of soliton logic-based networks. The third approach is significantly less accurate, while the fourth approach is the least accurate of all.