High-modulation-depth effects in photorefractive wave mixing : influence on pattern formation and physical foundations

Spatio-temporal pattern formation in contra-directional two-wave mixing in photorefractive crystals is investigated both numerically and analytically, taking high-modulation-depth effects into account. We use a modified two-wavemixing model that includes a correction function f ðmÞ, which is introduced as a phenomenological modification. Transverse instabilities arise only if the modulation depth at one side of the crystal is high (near unity). Therefore, highmodulation-depth effects are both relevant and important. In the near field, transverse running waves appear above the instability threshold. The gain of the signal beam then exhibits an unexpected saturation. Furthermore, the physical justifications of the correction function f ðmÞ are investigated by exactly integrating the nonlinear Kukhtarev equations. We do not neglect the phases of the counter-propagating beams. For static gratings we obtain real and superlinear correction functions, whereas for running gratings they change to complex correction functions. PACS: 42.65.)k; 42.65.Hw; 42.65.Sf