Transverse instability of energy-exchanging counterpropagating waves in photorefractive media

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Abstract
The transverse instability of counterpropagating waves in photorefractive media that is due to the formation of reflection gratings is studied. We obtain new solutions for the instability threshold that account for the reflection-grating-mediated transfer of energy between the pump waves. We find that the instability threshold is minimized for equal-intensity pump beams inside the medium, corresponding to externally supplied beams of unequal intensity when there is energy coupling between the pump beams. A coupling-constant-times-interaction-length product of at least 1.1 when the coupling constant is purely real, or at least 6.3 when the coupling constant is purely imaginary, is sufficient for observation of transverse instabilities. Comparison with the physically available photorefractive coupling constant leads to the conclusion that a variety of commonly available materials should be suitable for the observation of transverse instabilities. In addition, new results for the instability threshold of a reflection-grating four-wave mixing oscillation are obtained that include the effects of direct coupling between the pump waves.