Rigorous coupled-wave diffraction theory is used to analyze two- and multi-wave mixing in a diffusion-controlled photorefractive material which is modeled by the Kukhtarev equations. These equations are first decoupled to yield a nonlinear time-dependent differential equation for the induced refractive index profile. The transmitted and reflected field coupling coefficients are studied for the cases when the incident optical fields are coherent and partially coherent, for materials with different gain constants, and for different values of the linear refractive index mismatch. In each case, the exact longitudinal inhomogeneity in the photorefractive medium is analyzed using rigorous coupled-wave diffraction theory. Our computations predict a possible temporal instability resulting in self-pulsation and anisotropic diffraction contributing to a significant generation of higher orders when two plane waves are incident on photorefractive materials. Six-wave coupling in index mismatched barium titanate is studied.