We report theoretical and experimental evidence for transverse modulational instability of two counterpropagating beams in a photorefractive medium with no external feedback. A frequency detuning is applied to one of the beams in order to drive the system to instability. We perform a linear-stability analysis that allows for detuning of the counterpropagating pump beams in addition to an additional frequency detuning of the generated sidebands relative to the main beams. The threshold condition for the general case of a complex photorefractive coupling constant is found, and instability is predicted for diffusion-dominated, drift-dominated, and mixed charge transport. We show that for the specific case of diffusion-dominated charge transport, transverse instability is always accompanied by a frequency shift of the sidebands. For frequency-degenerate pump beams the instability threshold is reached at a coupling-constant times interaction-length product of The threshold is lowered (raised) for small positive (negative) frequency shifts of one of the pump beams. The theoretical predictions were verified experimentally with a photorefractive crystal of A modulational instability resulting in a spatially periodic roll pattern was observed for a certain range of positive frequency detunings. Measurements of the transverse scale of the structures and the relative sideband intensities were in agreement with the theoretical analysis.
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