Transient energy exchange between two concurrent coherent waves in a nonlinear medium

An analysis is made of the interaction between two mutually coherent plane waves in a medium whose refractive index varies by an amount proportional to the local exposure up to a selected time. It is found that the parameters of the process depend on a single self-similar variable, the product of the depth and the input exposure: $z\int|E|^2\,dt$. Analytic and numerical studies are made of the properties of the self-similar solution for various ratios of the wave intensities at the entrance to the medium.