Wave scattering functions and their application to multiple scattering problems

Scattering functions arise naturally in standard treatments of the effects of a material object or surface embedded in a uniform field. The most commonly used scattering function describes the far-field modulation imparted at large distances to a spherical wavefront eminating from the scatterer. The purpose of this is to develop the properties of the spectrum of scattered plane waves as an exact generalized scattering function. The linearity of the wave equations guarantees that such a representation exists; moreover, it is possible to derive the generalized 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 interrelations among the far-field scattering function, the Green's function and various forms of the generalized scattering function as well as the symmetry properties of the generalized scattering function imposed by reciprocity. For multiple-scattering objects that can be separated by parallel planes, a system of difference equations is developed that fully accommodates the mutual interaction among the scatterers. The mutual interaction equations were developed earlier, but we show here that they can be transformed into the form that would be obtained by using the Foldy-Lax-Twersky formalism. This reinforces the equivalence between wave-space and configuration space formulations of the scattering problems.