Digital response in an all optical AND gate using parametric (x^(2) solitons

The main problem with optical logic is that the operation of a logic gate that works on two inputs is essentially a nonlinear process, whereas electromagnetic waves in most media are solutions to the linear Maxwell equations; in most dielectrics light does not interact with itself. However, in recent years there has been considerable advances in the theory and manufacture of nonlinear optical media, which now opens a new and exciting range of possibilities for implementing all optical logic circuits. One such possibility is the implementation of an all-optical AND gate as proposed by Drummond et al. (1999). In this method the two optical inputs are collided noncollinearly in a dispersive parametric planar waveguide. Consider firstly type II interaction in which the pulses have orthogonal polarizations. If only one pulse at a time is injected into the waveguide then it simply disperses. Whereas if two pulses arrive simultaneously then when they collide a phase-matched second harmonic is generated that traps the original two fundamentals, forming a 2+1D spatiotemporal soliton, which propagates stably towards the logic true output. Finally, it is also apparent that when no pulse is present on either input then no output will be generated. In this fashion AND gate logic operation is achieved. For such 2+1D solitons to form the basic requirements are anomalous dispersion and (nearly) matched group velocities at the fundamental and second harmonic frequencies