We study four-wave mixing with orthogonally polarized pumps (OPP-FWM) in photorefractive crystal for both transmission and reflection gratings, taking pump depletion into consideration. We simplify the coupled wave equations in an analytical way, which makes qualitative understanding of the performance of OPP-FWM easier. Then we solve the simplified equations numerically by a shooting method. Properties such as the coupling efficiency of the writing beams, the diffraction efficiency, and the diffracted beam reflectivity are calculated as functions of the beam angles, the probe ratio, and the pump ratio. Some of the calculated results are compared with the experimental results. Two principal concepts, i.e., how the diffraction efficiency and the reflectivity are affected by changes in the relative phase of the two grating components and by the feedback effect that is due to the coupling of writing waves, are clearly explained with experimental proof. We also show that, because it requires a different form of the coupled wave equations, OPP-FWM shows a different angular dependence and has a much higher efficiency at larger angles between probe and pumps, as compared with the usual geometry of four-wave mixing in which all four waves are either ordinary or extraordinary.
© 1999 Optical Society of America
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