Modal analysis of nonlinear propagation in dielectric slab waveguide

In this paper we present a study of nonlinear guided propagation based on the development of the actual electromagnetic field in terms of the modes of a linear dielectric guide. This approach permits in principle to consider propagation over finite lengths of waveguide of general nonuniform nonlinearity, with arbitrary excitation at a finite location and to retain the second derivative term that is neglected in the usual Schrodinger equation approximation to the wave equation.