Degenerate four-wave mixing in the presence of nonuniform pump wave fronts

We derive the set of coupled equations that describes the process of degenerate four-wave mixing in the presence of spatially nonuniform pump-beam wave fronts. We investigate the influence of phase mismatch between plane-wave pump beams on the efficiency and on the fidelity of the phase-conjugation process, and we furnish, in the near-collinear geometry, the expression of the spatial degree of coherence of the phase-conjugate wave in terms of those of the input signal and of the pump beams.