Transverse instability threshold in counterpropagating light beams for a nonlinear medium with local photorefractive response

We derive the threshold conditions for the instability of counterpropagating waves in a nonlinear medium with local photorefractive response against the excitation of transverse small-angle structures. These conditions allow for all the important types of diffraction from refractive-index reflection gratings and are not limited to the case of strict frequency degeneracy of the waves. We study the dependence of the crystal-thickness threshold and the secondary wave emission angle on the crystal parameters and the pump conditions. We show that when the pump wave intensities differ considerably, excitation of standing light structures is replaced by excitation of traveling structures. Finally, we discuss the applications of the theory to experiments with the photorefractive crystals LiNbO3 and LiTaO3.