WAVE SCATTERING FUNCTIONS AND THEIR APPLICATION TO MULTIPLE-SCATTERING PROBLEMS

Scattering functions arise naturally in standard treatments of the eff ects of a material object or surface embedded in a uniform field. The most commonly used scattering function describes the far-field modulat ion imparted at large distances to a spherical wavefront eminating fro m the scatterer. The purpose of this paper is to develop the propertie s of the spectrum of scattered plane waves as an exact generalized sca ttering function. The linearity of the wave equations guarantees that such a representation exists; moreover, it is possible to derive the g eneralized scattering function from the far-field scattering function by analytic continuation. Although these properties are known, recent theoretical developments have motivated us to reexplore the interrelat ions among the far-field scattering function, the Green's function and various forms of the generalized scattering function as well as the s ymmetry properties of the generalized scattering function imposed by r eciprocity. For multiple-scattering objects that can be separated by p arallel planes, a system of difference equations is developed that ful ly accommodates the mutual interaction among the scatters. The mutual interaction equations were developed earlier, but we show here that th ey can be transformed into the form that would be obtained by using th e Foldy-Lax-Twersky formalism. This reinforces the equivalence between wave-space and configuration space formulations of the scattering pro blems.