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Optics Letters

Simple theory for degenerate four-wave mixing in photorefractive media

Paul Michael Petersen, Per Michael Johansen

Published Jan 1, 1988• 4 citations
Publisher

Abstract

A simple analytic theory for degenerate four-wave mixing in photorefractive media is presented. The theory is valid when the backward pump-beam intensity is much smaller than the forward pump-beam and probe-beam intensities.
DOI
10.1364/ol.13.000045

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A theoretical description for a forward degenerate four-wave mixing process in homogeneously broadened two-level absorbers with arbitrary intensities of all four beams is presented. Assuming no pump absorption and depletion, we obtain an analytical solution of forward degenerate four-wave mixing signal intensity in the limit of the strong pumps and weak probe and signal. In the case of low absorption or large detuning, this solution is shown to become equivalent to that of the phase-conjugate degenerate four-wave mixing derived by Abrams and Lind [Opt. Lett.2, 94 (1978)]. For arbitrary beam intensities and absorption parameters, the signal intensity is numerically calculated by solution of the coupled equations of complex wave amplitudes. Comparing the results of the numerical calculation with those of the analytical solution, we discuss the validity of using the analytical solution in practical experiments and show the saturation behavior that is due to the strong probe beam. The line shapes under the various ratios among the input beams and absorption parameters are also obtained and discussed.
A method for exact solution of the stationary holographic degenerate four-wave mixing in reflection geometry in photorefractive media is presented. The effects of pump depletion and light absorption in the nonlinear dynamic medium are rigorously taken into account. Numerical steps in the procedure are reduced to the solution of one simple nonlinear first-order differential equation, or are absent altogether when the equation is linearized, or for the case of no absorption. The method of solution is applicable to other wave-mixing geometries as well.
The effect of biasing illumination on the degenerate four-wave mixing (DFWM) in absorbing photorefractive (PR) media has been investigated. The input beams are considered to be spatially uniform. The analysis has been made both for transmission and reflection geometry. Considering pump beam depletion and the slowly varying amplitude approximation, nonlinear coupled wave equations are obtained and have been solved numerically by a shooting method. The effect of different parameters such as input beam intensities ratio, thickness of the interacting medium on the phase conjugate reflectively (PCR) has been investigated. It has been observed that PCR can be controlled to a large extent by controlling the biasing intensity.