Abstract
Stationary energy exchange between four copropagating light beams in a medium with diagonal bipolar nonlinearity is studied. This type of nonlinearity is common in nematic liquid crystals. Solutions of underlying Hamilton’s equations are thoroughly analyzed with the phase-plane approach for different wave-vector mismatches. The existence of an unstable eigenmode is demonstrated geometrically. This mode results from the considerable difference between the temperature dependences of the ordinary and extraordinary refractive indexes. Exact analytic solutions related to various regions of the phase plane are presented. Optical switching is demonstrated to be feasible under the stated conditions. It is found that the energy exchange essentially depends on the input phase mismatch. Intensities required for observing the predicted effects are evaluated.
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