Phase Conjugation with Saturable Gain and Saturable Absorption,
ROCHESTER UNIV NY INST OF OPTICS
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We have investigated 2WM and 4WM processes in photorefractive crystals in the nonsaturated regime, i.e. when the coupling between beams and the absorption depend on the light Intensity. Different models of saturable absorption in 2WM via reflection grating are considered, and the corresponding wave equations are solved exactly. The solutions are written in terms of hypergeometric functions or in quadratures. From the solutions it was found that the energy transfer between the waves is less effective in the nonsaturated stage of the process. Further, a model of multigrating 4WM is investigated, with intensity dependent coupling coefficients. A system of four nonlinear differential equations for the steady-state energy transfer is solved in terms of quadratures, and a boundary-value fitting procedure devised in the parameter space. Stable and unstable solutions are found, depending on the strength of the coupling. For g negative only stable solutions exist. In this region our procedure rapidly and accurately converges to a unique solution satisfying given boundary conditions. As compared to standard shooting or other methods, our procedure is found superior, especially when multiple solutions occur in the system.