Energy transport in the near field of an electric dipole near a layer of material

Abstract

We consider an oscillating electric dipole, embedded in a uniform medium with relative permittivity and relative permeability . The dipole is located near an interface with a layer with uniform material parameters and , and the second interface borders a uniform medium with parameters and . We have obtained the solutions for the electric and magnetic fields in the various regions, without any restrictions on the parameters and for any state of oscillation of the dipole (elliptical, in general). The solution involves a set of auxiliary functions, which are given as integral representations containing the Fresnel coefficients for plane waves. With this solution, the field lines of energy flow can be obtained, and we have considered the flow pattern for the simple case of a dipole oscillating perpendicular to the interface. When the material of the layer is optically thicker than the embedding medium of the dipole, energy flows more or less along straight lines. At an interface, the field lines refract, similar to optical rays. When the layer material is optically thinner, the energy flow lines curve. A portion of the energy that propagates toward the interface bends away from it before reaching the interface. Other field lines of energy flow cross the interface, but then return to the area of the dipole by crossing the interface again. This leads to an oscillation of energy back and forth through the interface. In the neighborhood of this oscillation, a concentric set of vortex tori appears.