Transverse-Magnetic Wave Propagation in a Plane Waveguide Filled with Anisotropic Kerr Medium: Essentially Nonlinear Guided Regime

Propagation of electromagnetic waves in a waveguide filled with anisotropic Kerr medium is considered. The nonlinearity involves two non-negative parameters. If both parameters are zeros, then one arrives at a linear problem that has a finite number of eigenwaves. If the first parameter is positive and the second one is nonnegative, then the nonlinear problem has infinitely many solutions; only a finite number of these solutions have linear counterparts. This predicts existence of an essentially nonlinear guided regime