Cross-polarized photorefractive four-wave mixing with extraordinary writing beams and an ordinary reading beam

In parallel-polarized photorefractive four-wave mixing the phase-matching condition can be achieved automatically if the pump beams are allowed to propagate in directions opposite to each other. However, in cross-polarized photorefractive four-wave mixing, the incident angles of the beams should be adjusted to maintain the phase-matching condition. We analyze the phase-matching properties of cross-polarized four-wave mixing with extraordinary writing beams and an ordinary reading beam and obtain the phase-conjugate reflectivity in consideration of phase mismatching. We also perform an experiment in which a phase-conjugate beam is generated in cross-polarized four-wave mixing and confirm the analyses.