Asymptotic wave-wave processes beyond cascading in quadratic nonlinear optical materials

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Abstract
The method of multiple scales is used to derive several different systems of evolution equations for multiple interacting waves propagating in a strongly dispersive, weakly quadratically nonlinear optical material. Several two- and three-wave signaling problems are discussed. Among the problems discussed are the interaction between a low frequency field and the optical frequency field and between the optical frequency field and its second-harmonic field. In the efficient phase-matching regime, three-wave-mixing equations are obtained where quadratic nonlinearities dominate. Here, methods are discussed for cascading second-order nonlinearities to obtain intensity-dependent effects. For the large-phase-mismatch regime, cross-phase-modulation equations, analogous to fiber optics, are obtained where cubic nonlinearities dominate, and intensity-dependent modulations beyond cascading are obtained. Finally, the three-interacting (sum frequency) wave problem is examined for small and large asymptotic phase mismatch regimes. Analytical solutions to the derived evolution equations are given.

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