Optical wave mixing of arbitrary-profile beams in model materials exhibiting different material responses are investigated by asymptotic methods. The coupled-wave equations of previous theories are shown to be special cases of the equations governing the evolution of the zeroth-order term of a classical asymptote in wavelength solution. The classical theory is then generalized by reformulating the problem as a nonlinear integral equation, which is solved by a combination of Picard’s iteration and the method of stationary phase. This permits more satisfactory handling of phase-mismatched waves and may be extended to take into account boundaries, discontinuous initial conditions, and foci. The convergence criteria for the iteration also establish the existence and the uniqueness of the solution. The method may be applied equally to other forms of nonlinear material response. The coupled-wave equations are solved numerically for the case of real-time correlation by degenerate four-wave mixing and are compared with experimental results by using photorefractive Bi12SiO20. The results obtained demonstrate the significant effect of the interaction-region geometry and the material response on the correlation fidelity.
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