Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.