Nonlinear coupled electromagnetic wave propagation: Saturable nonlinearities

•Phenomenon of nonlinear coupled electromagnetic wave propagation is considered.•The problem is formulated with physically realistic conditions.•An original analytic approach is used to study the problem.•It is proved the existence of a novel (nonlinear) guided regime.

Propagation of a sum of two monochromatic transverse electric (TE) waves in a plane dielectric layer filled with nonlinear medium is considered. Nonlinearity in the layer is described by a diagonal tensor with arbitrary functions w.r.t. squared module of the complex amplitudes of an electric field. We look for guided waves that propagate along the boundaries of the layer and decay when they move off from the boundaries. It is proved that a novel nonlinear propagation regime arises, called ‘coupled TE wave.’ It is shown that two TE waves–generating the coupled wave–propagate at different frequencies ω1ω1, ω2ω2 with different propagation constants γ1γ1, γ2γ2, respectively. The wave propagation problem is reduced to a nonlinear 2-parameter transmission eigenvalue problem for Maxwell’s equations. An original analytical method to study the problem is suggested. For a wide class of saturable nonlinearities, it is proved the existence of isolated coupled eigenvalues (that correspond to the coupled propagation modes) and intervals of its localisation are found, zeros of the eigenfunctions are also determined. Theoretical results are illustrated with numerical calculations.