Application of the mutual-interaction method to a class of two-scatterer systems: II. Scatterer near an interface

Abstract

This paper applies the methodology developed in Part I to the problem of a separable scatterer near a dielectric (penetrable) or perfectly conducting (impenetrable) interface. For a penetrable interface, the scatterer may be on either side of the interface (exposed or embedded). As in Part I, the scatterer may also be an active element. Thus, our solutions extend the classic treatments of dipoles radiating near a planar dielectric interface. The mutual-interaction method accommodates a uniform half-space as an equivalent scattering plate of zero thickness that preserves amplitudes and phases of the transmitted and reflected waves. Because this scattering function necessarily includes a Dirac delta function, exact analytic solutions are possible for the class of separable scatterers, which include isotropic scatterers and electric or magnetic dipoles. The results can be interpreted within the context of image theory. Integrals similar to those derived by Sommerfeld must be evaluated to calculate the spatial fields for dielectric media; however, for highly conducting media good approximations are readily obtained.