Transversal parametric oscillation and its external stability in photorefractive sillenite crystals

We develop the nonlinear theory of transversal parametric oscillation in photorefractive sillenite crystals. The theory is nonlinear in the sense that the nonlinear feedback from the parametric space-charge field waves, above threshold of their excitation, is taken into account. In this manner, an analytical solution for the stationary state of the parametric waves is obtained. We analyze the stationary states' stability both against small perturbations in amplitude and phase (internal stability) and against excitation of new secondary waves (external stability). It is shown that the stationary state of transversal parametric oscillation is stable within certain regions of external and internal parameters. This is opposed to the degenerate case (K/2 subharmonic generation), which is unstable.