Optimization of the gain in non-uniform gratings in a Bi$_{12}$SiO$_{20}$ crystal considering the variation of fringe period, optical activity and polarization angles in a strong non-linear regime

Abstract

We solved numerically the set of non-linear differential material rate differential equations, and using these solutions, we include the non-uniformity of the grating and of the magnitude and phase of light modulation along a sample thickness to calculate self-consistently the energy exchange in two-wave mixing. We optimize the gain, considering strong nonlinear conditions, variation of fringe period, optical activity, birefringence, absorption, polarization angle, applied fields and two crystal orientations: the grating vector parallel and perpendicular to the face [001] Under these conditions there is a complex relationship among all these parameters, and the prediction of the conditions for the optimum value of the gain is not simple We report the optimal sample thickness for different situations We obtained a maximum gain of 5.2.