Threshold for pattern formation in a medium with a local photorefractive response

Threshold equations for the instability of counterpropagating waves against spontaneous initiation of small-angle light patterns are analyzed for a medium with a local photorefractive response and various boundary conditions. These equations take into account all actual contributions to the reflection phase gratings. The form of the threshold equation is directly related to the spatial symmetry of the problem. We study the dependence of the threshold thickness of the crystal and the angle of light emission on experimentally controllable parameters and discuss the prospects for experimental studies of pattern formation in LiNbO3 crystals.