A multiple scales method of analysing nonlinear guided-wave propagation in waveguides containing nonlinear dispersive anisotropic lossless materials is described. The procedure leads to systems of coupled wave equations which are generally in explicit Hamiltonian form. A specific system of third-order nonresonant nonlinearity in gallium arsenide with cleaved facets along (1 1̄ 0) planes and waveguide propagation along [1 1 0] directions is illustrated. Nonlinear CW stationary waves occurring in the most general system of two orthogonally polarised linear modes with slightly different propagation coefficients interacting through a third-order nonlinearity are classified, and their stability analysed with respect to both time-independent and time-dependent perturbations. It is shown that there are in general six different stationary states that may exist for a given total intensity of the wave. The qualitative dynamics and stability of these states are analysed using a geometrical representation of the Hamiltonian dynamics in a three-dimensional real space called Stokes space. © 2001 Published by Elsevier Science B.V.
Arnold, J. M. (2001). Anisotropic effects in nonlinear optical waveguides. Wave Motion, 34(3), 339–352. https://doi.org/10.1016/S0165-2125(01)00094-4