Surface waves propagating along the interface between a parabolic graded-index medium and a self-focusing nonlinear medium: exact analytical solution

Abstract

The waveguide properties of interface between a parabolic graded-index medium and a self-focusing nonlinear medium are described theoretically. The exact analytical solution to the wave equation with dielectric permittivity dependent on the distance from interface and on the electric field intensity is found. The obtained solution describes the new type of nonlinear surface wave. It is shown that the electric field is localized completely inside the parabolic graded-index layer. The dispersion equation determining explicit dependence of the effective refractive index on the thickness of the parabolic graded-index layer and the change in dielectric constant in it is found in a particular case corresponding to the exotic surface wave propagation. The influence of the optical parameters on the distribution profile of the electric field across is analyzed. The decrease in the field in surface waves with distance from the interface is non-exponential.