Transverse modulational instability in counterpropagating two-wave mixing with frequency-detuned pump beams

We report theoretical and experimental evidence for transverse modulational instability of two counterpropagating beams in a photorefractive medium wi th no external feedback. A frequency detuning is applied to one of the beam s in order to drive the system to instability. We perform a linear-stabilit y analysis that allows for detuning of the counterpropagating pump beams in addition to an additional frequency detuning of the generated sidebands re lative to the main beams. The threshold condition for the general case of a complex photorefractive coupling constant is found, and instability is pre dicted for diffusion-dominated, drift-dominated, and mixed charge transport . We show that for the specific case of diffusion-dominated charge transpor t, transverse instability is always accompanied by a frequency shift of the sidebands. For frequency-degenerate pump beams the instability threshold i s reached at a coupling-constant times interaction-length product of gammal = 5.25i. The threshold is lowered (raised) for small positive (negative) f requency shifts of one of the pump beams. The theoretical predictions were verified experimentally with a photorefractive crystal of KNbO3. A modulati onal instability resulting in a spatially periodic roll pattern was observe d for a certain range of positive frequency detunings. Measurements of the transverse scale of the structures and the relative sideband intensities we re in agreement with the theoretical analysis. (C) 2001 Optical Society of America.