Fundamentals of the nonlinear theory of photorefractive subharmonics

We formulate the fundamentals of the nonlinear theory of low-frequency space-charge waves in semiinsulating photorefractive crystals. This includes an analysis of dispersion relations for the waves, and of their parametric excitation by a running light pattern, a description of various stationary states (split and unsplit subharmonics) beyond the threshold of the parametric instability, and a study of the stability of those nonlinear steady states against small perturbations. Nonlinear eigenfrequency and mutual frequency shifts for strong waves and renormalization of the coupling coefficients for weak waves are important elements of the theory. An investigation of the stability of the subharmonics also incorporates their phase relations as well as certain special features of space-charge waves. One of the consequences of the theory is the modulational instability of the main subharmonic, characterized by doubling of the period of the primary light pattern. Finally we discuss further development and applications of the theory.