Influence of the non-uniformity of the grating along sample thickness and of grating period variation, on the diffraction efficiency optimization in a sillenite crystal (Bi12SiO20) in a strong non-linear regime under an external dc field

We solved numerically the set of partial, non-linear, material rate differential equations for different values of grating period in a photorefractive, sillenite crystal (Bi12SiO20). These solutions were used to include the non-uniformity of the grating along sample thickness to calculate the energy exchange in two wave mixing. We employed a vectorial approach to calculate the beam energy exchange. This calculation was performed for each value of grating period. We included optical activity, light absorption, birefringence and polarization angle of the interacting beams. Two crystal orientations were considered: when the grating vector is parallel to the face [0 0 1] and when it is perpendicular to the same face. We found a large influence of the non-uniformity of the grating on the diffraction efficiency and on the optimal sample thickness.