Exact theory of pump-wave propagation and its effect on degenerate four-wave mixing in saturable-absorbing media

TLDR: In this article, an analytic solution for the intensity distribution of two counterpropagating pump waves within a saturable absorber is derived from this distribution, the spatial variation of the nonlinear absorption and coupling constants that appear in the coupled-amplitude equations for the probe and the signal (i.e., conjugate) waves are determined.

Abstract: An analytic solution for the intensity distribution of two counterpropagating pump waves within a saturable absorber is derived. From this distribution, the spatial variation of the nonlinear absorption and coupling constants that appear in the coupled-amplitude equations for the probe and the signal (i.e., conjugate) waves are determined. These coupled-amplitude equations are solved numerically in a noniterative manner, leading to a prediction for the phase-conjugate reflectivity. The results of the exact theory are compared with those of previously published theories. It is found that at large values of the input-pump intensities, the predicted phase-conjugate reflectivity is larger when pump-absorption effects are included in the theory.