Rapid communication Vector phase conjugation in Cr
4+ :YAG by four-wave mixing with linearly-polarized pump beams
We describe a theory of four-wave mixing in the saturable absorber
Cr4+:YAG and compare with experiments performed at 1.064 \ensuremath{\mu}m wavelength. We show that the strong polarization dependence of the saturable absorption along orthogonal crystallographic axes leads to unique polarization properties for wave mixing in
Cr4+:YAG. Also there are a range of conditions that lead to vector phase conjugation of the polarization state of a signal beam. Optimum reflectivity for vector phase conjugation occurs when the pump beams have either orthogonal circular polarizations or parallel linear polarizations at 45\ifmmode^\circ\else\textdegree\fi{} to the crystallographic axes. The latter case is unique to this type of nonlinearity.
We study theoretically the properties of transient degenerate four-wave mixing in an isotropic, homogeneously saturable gain medium with interacting beams of arbitrary strength and polarization state. In particular we investigate the ability of the interaction to exhibit vectorial phase conjugation when orthogonally circularly polarized pump beams are used. This mechanism allows the correction of both phase and polarization distortions introduced to an optical beam. Numerical simulations are compared with experiments that use a flashlamp-pumped Nd3+:YAG amplifier and demonstrate good vector phase-conjugate fidelity for both weak and strong probe beams of arbitrary polarization state.