Polarization properties of a photorefractive Bi12SiO20 crystal and their application in an optical correlator

The polarization properties of Bi₁₂SiO₂₀ (BSO) crystals are investigated in detail theoretically and experimentally, and the results are used to describe the operation of an optical correlator for a particle image velocimeter (PIV) using a BSO crystal as the nonlinear optical element. The work is based on an extension of the optical beam-propagation (OBP) method to include all the significant optical properties of the BSO crystal when used in a two-wave mixing configuration, i.e., optical activity, field-induced birefringence, and anisotropic diffraction. The model is able to handle multiple gratings where the input beams do not have to be symmetric about the axis of propagation. Using the numerical model the polarization properties of the BSO crystal are analyzed and the operation of the correlator is explained. The model is able to take into account self-diffraction effects, and it is shown that these effects can have a significant influence in the setup employed for the optical correlator even when the diffraction efficiency is low. The predictions of the numerical model are verified by extensive experiments on the polarization state of the output of the correlator as a function of operating conditions and of the polarization state of the input beams