Vertical dipole above a dielectric or metallic half space: Energy-flow considerations

The emission pattern from a classical dipole located above and oriented perpendicular to a metallic or dielectric half space is calculated for a dipole driven at constant amplitude. Emphasis is placed on the fields in the metal or dielectric. It is shown that the radial Poynting vector in the metal points inwards when the frequency of the dipole is below the surface plasmon resonance frequency. In this case, energy actually flows out of the interface at small radii and the power entering the metal can actually oscillate as a function of radius. The Joule heating in the metal is also calculated for a cylindrical volume in the metal. When the metal is replaced by a dielectric having permittivity less than that of the medium in which the dipole is immersed, it is found that energy flows out of the interface for sufficiently large radii, a result reminiscent of the Goos-Hänchen effect.