Four-wave mixing with partially coherent waves in photorefractive media. I. Transmission grating approximation

We investigate the effect of beam temporal coherence on four-wave mixing vi a transmission gratings in photorefractive media. We take into account the propagation of mutual coherence and self-coherence in space and the evoluti on of mutual coherence and self-coherence with time. Analytical solutions f or nondepleted-pump cases and numerical results for general cases are obtai ned. We find that the mutual coherence of the signal beam and the pump beam can be enhanced or reduced, depending on the coupling constant and the bea m ratio of the signal beam and the pump beam. A decrease of the initial mut ual coherence can lead to a lower phase-conjugate reflectivity in the nonde pleted-pump case. Even with low initial mutual coherence, high phase-conjug ate reflectivity can still be obtained in the case with pump depletion. As a result of the shift of the grating profile, partial coherence can lead to an enhancement of the phase-conjugate reflectivity when the signal-pump-be am ratio is small. We also found that when the initial value of the phase-c onjugate beam is zero, the phase-conjugate beam and the pump beam are in ph ase during propagation. Results for beam intensity and mutual coherence are presented and discussed to provide an insight into four-wave mixing with p artially temporally coherent waves. (C) 1999 Optical Society of America [S0 740-3224(99)02107-4].