Nonlinear refractive coupling and vector solitons in anisotropic cubic media

Equations of motion are derived for the nonlinear refractive coupling between two coherent optical beams in an anisotropic cubic medium, allowing for a phase mismatch between the beams. These equations contain orientation-dependent self-phase-modulation, cross-phase-modulation, and four-wave-mixing, terms plus additional anisotropic terms that, for example, can generate an orthogonal polarization component. Stationary solutions (eigenpolarizations) are identified in which the polarization state does not change, and these can be classified as stable or unstable. It is shown that TE and TM modes in the common semiconductor waveguide orientation for frequencies at the half band gap or below become unstable if the magnitude of the birefringence is sufficiently small. Diffraction is included, and the polarization-state evolution is obtained for mixed-mode (vector) spatial solitons. The polarization evolution dynamics of vector spatial solitons broadly follows the equivalent plane-wave examples.