The double phase-conjugate mirror (DPCM) is a stimulated four-wave mixing effect, mediated by either a χ3 mechanism or a photorefractive effect. The type of grating that operates in the DPCM can be a transmission or reflection grating, depending on the wave-mixing configuration. Any combination of nonlinearity and grating geometry is possible, so that four general DPCM classes emerge. An analytic solution of the last unsolved class, the photorefractive reflection DPCM, is presented. With these results, general observations concerning the four categories of double phase conjugation are made. An important conclusion is that the type of grating geometry and its associated boundary conditions dictate many of the basic features of the DPCM, regardless of the nonlinearity involved.
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