Theoretical study of spatial solitons in planar waveguides

We investigate some of the theoretical notions underlying the observation of spatial solitons in nonlinear planar waveguides. We find that, when the beam is confined in one dimension principally by the action of a linear refractive-index profile, the nonlinear behavior of the beam in the orthogonal dimension is governed by the usual nonlinear Schrödinger equation with parameters modified by the linear waveguide modal properties. When either the power or the nonlinearity of the material is high, nonlinearity affects both dimensions, and a form of three-dimensional self-trapping begins to occur. A simple variational approximation gives an accurate picture of what is happening in this regime.