The formalism described in Chapters 4 and 5 applies equally to a scatterer in the form of a single body and to a fixed multi-particle group. However, when the scattering object is a cluster consisting of touching and/or separated distinct components, then it is often convenient to use a modified formalism in which the total scattered field is explicitly represented as a vector superposition of the partial fields contributed by the cluster components. This approach is based on the system of integral so-called Foldy equations (FEs) which follow directly from the MMEs, automatically incorporate all boundary conditions and the radiation condition at infinity, and rigorously describe the scattered electric field at any point in space. In this chapter, we will derive both the exact form of the FEs and an approximate far-field version. The latter applies to a group of widely separated particles and offers significant simplifications essential for the development of microphysical theories of radiative transfer and WL.

Vector form of the Foldy equations

Consider electromagnetic scattering by a fixed group of N finite particles collectively occupying the interior region VINT, according to Eq. (4.1). As before, we assume that the particles are imbedded in an infinite, homogeneous, linear, isotropic, and nonabsorbing medium.