Nonlinear surface waves propagating along an interface between the Kerr nonlinear and hyperbolic graded-index crystals

The new types of transverse electric nonlinear surface waves propagating along the interface separating the crystal characterized by a spatial dependence of the dielectric constant accordingly with a hyperbolic function and Kerr type nonlinear crystal are described theoretically. Exact analytical solutions to the wave equation describing nonlinear surface waves in the cases of self-focusing and defocusing nonlinearities are found. Features of the influence of the parameters of the dielectric constant hyperbolic profile on the wave localization near the interface are found using obtained explicit forms of exact solutions of nonlinear equations formulated. It is found that the influence of system parameters on the wave localization characteristics is significantly different in crystals with positive and negative nonlinearity. The light intensity increases significantly in the case of a positive nonlinear response but it decreases significantly in the case of a negative nonlinear response with an increase in the effective refractive index.