DEGENERATE FOUR-WAVE MIXING AND BEAM AMPLIFICATION IN A KERR MEDIUM.

According to the theory of wave mixing in a nematic liquid-crystal thin cell based on the first-order optical path method, energy exchange between the two incident beams can occur in a thin medium even in the case of zero phase shift. In this case, the direction of energy transfer is determined by the relative intensity between the two incident beams; i. e. , the weaker beam is always amplified. A detailed theory has shown that, as far as the energy exchange between the incident beams is concerned, the first-order optical path method is not a good approximation. To explain the experimentally observed probe beam amplifcation process, it is shown that it is important to include the effect of the diffracted beam. The pump beam and the diffracted beam form an index grating and contribute to the growth of the probe beam via the four-wave mixing process. An extra enhancement can be obtained if this index grating is appropriately shifted with respect to the intensity grating, e. g. , by introducing the frequency shift to the probe beam. Detailed conditions governing the generation of the diffracted beam and the probe amplification are also derived; major roles are played by the film thickness, beam intensities, magnitude of the nonlinearity, phase shift, and scattering loss.