Hd. Ngo et Cl. Rino, APPLICATION OF THE MUTUAL-INTERACTION METHOD TO A CLASS OF 2-SCATTERER SYSTEMS .1. 2 DISCRETE SCATTERERS, Waves in random media, 5(1), 1995, pp. 89-105
In a recent paper we developed a formalism that fully accommodates the
mutual interactions among scatterers separable by parallel places. Th
e 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-amplitud
e plane wave scattered from the object in isolation. This function can
be derived completely from the scattered far field with the help of a
nalytic continuation. For a two-scatterer system the mutual-interactio
n equations reduce to a single Fredholm integral equation of the secon
d kind. It turns out that analytic solutions are tractable for those s
cattering functions that are Dirac deltas or a sum of products of sepa
rable 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 in this
two-part paper. The exact scattering functions agree with results obt
ained by analytic continuation. This paper consists of two parts. Pact
I derives analytic solutions for two discrete scatterers (isotropic s
catterers, electric dipoles, magnetic dipoles). Part II is devoted to
scattering from an object (isotropic or dipole scatterer) near an inte
rface separating two semi-infinite uniform 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 obj
ects that are both radiating and scattering.