Space-time evolution of nonlinear three-wave interactions. II. Interaction in an inhomogeneous medium

The effects of dephasing due to spatial inhomogenelty on the space-time evolution (two-dimensional steady state) of nonlinear three-wave interactions are described. After summarizing previous work on the inhomogeneous-medium three-wave equations, the authors describe an inverse scattering transform for these equations. They then use this transform along with numerical integration of the equations to determine the effects of inhomogeneity on the nonlinear evolution of decay, backscatter, and explosive interactions. The effects include modified threshold conditions for explosive instabilities and modified conditions for optimal energy transfer in two-pump interactions. Energy transfer in both absolute and convective decay interactions in an inhomogeneous medium is found to plateau and then decrease with increasing pump width, in striking contrast to homogeneous-medium interactions. A suppression of the nonlinear modulation in stimulated backscatter is described. A time-asymptotic solution for the spatial profiles of daughter waves is given for the absolute instability.