Running transverse waves in optical phase conjugation

We investigate the dynamics of four-wave mixing processes in photorefractive crystals in paraxial approximation, assuming the phase-conjugation condition. By applying an external electric field to the crystal, we observe an onset of instabilities in the phase-conjugate beam, the generation of running transverse waves, their mutual collisions, and a continuous transition to a regime of spatiotemporal chaos. This state appears as irregularly oscillating defectlike patterns in one transverse dimension. Running transverse waves are identified as the basic modes of the system giving rise to a secondary instability. The observed regular and irregular spatiotemporal oscillations are characterized by means of a spatiotemporal cross-correlation function and singular value decomposition. In the extension to two transverse dimensions the possibility of an even greater variety of regular and irregular patterns is observed. \textcopyright{} 1996 The American Physical Society.