Time-dependent behavior of photorefractive two- and four-wave mixing

Abstract

A theoretical and experimental study of the temporal response of photorefractive two- and four-wave mixing processes is given. We examine the buildup and the decay of the output signal and the gratings when the input signal beam is turned on and off. For two-wave mixing we have performed an analysis that includes the depleted-pump regime. The experiment was done with a BaTiO3 crystal. The buildup-and-decay behavior is strongly dependent on the coupling constant and the ratio of the signal and pump intensities. From these measurements we obtain the crystal time constant, which was found to have an intensity dependence with a power of −0.7. The coupling constant is extracted from the data of the whole dynamic process of buildup and erasure and not only from the steady-state point, as is usually done. This is the first analytic study, to the best of our knowledge, for the four-wave mixing decay and buildup. We find that the solution for time-dependent four-wave mixing processes (the phase-conjugate mirror and the double phase-conjugate mirror) with undepleted pumps is identical to that for two-wave mixing with unidirectional optical feedback circuits. This similarity provides a direct way to study the stability properties of the devices. We find, for example, that in the unstable regime of four-wave mixing a self-pulsation of the output corresponds to the frequency detuning of the unidirectional two-wave mixing oscillator.