New surface waves in a hyperbolic graded-index crystal

The transverse electric surface waves propagating along the surface of the crystal characterized by a spatial dependence of the dielectric permittivity are theoretically described. A hyperbolic profile of the dielectric permittivity of the crystal is used to obtain an exact analytical solution to the wave equation, which is expressed by Whittaker function. The influence of the parameters of the hyperbolic profile of the dielectric constant on the localization of the electric field near the crystal surface is analyzed. The dependencies of the effective refractive index on the parameters of a hyperbolic profile of the dielectric permittivity are explored. The way to effectively control the localization and intensity of the surface waves by changing the values of the parameters of the hyperbolic profile using the obtained exact solution is found.