Surface waves in a medium with spatial monotonic attenuation of the refractive index

New surface wave described by exact analytical solution to the stationary wave equation with the inhomogeneous refractive index attenuating with a distance from the surface is found. The exact solution is expressed by the modified Bessel function of the second kind. A decreasing profile of the refractive index characterized by two parameters such as the refractive index at the surface and the characteristic distance from surface that allows finding an exact analytical solution is proposed. It is found that an increase in both index profile parameters leads to a decrease in the width of the localization of the electric field near the surface. A dispersion equation that determines the effective refractive index of the surface wave is obtained. It is found that the effective refractive index monotonically increases with increasing both index profile parameters. It is shown that the penetration of a surface wave into media and its dispersion and power properties can be effectively controlled by varying the refractive index profile parameters.