Phase-plane approach to nonlinear propagation in dielectric slab waveguide

Nonlinear propagation in dielectric slab waveguides is discussed in the framework of a phase-plane approach. It is shown that qualitative aspects, such as integrals of motion in phase-plane, emerge from the analysis. Systematic consideration of these quantities narrows the range of possible solutions and provides a direct physical interpretation of them. Particularly suggestive, in this respect, are the interpretations of the appearance of higher order modes and of the energy/boundary conditions constraints typical of the nonlinear problem. Results for the TE and TM cases are presented