Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: A tutorial

Abstract

Although free space cannot generate electromagnetic waves, the majority of existing accounts of frequency-domain electromagnetic scattering by particles and particle groups are based on the postulate of existence of an impressed incident field, usually in the form of a plane wave. In this tutorial we discuss how to account for the actual existence of impressed source currents rather than impressed incident fields. Specifically, we outline a self-consistent theoretical formalism describing electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents, some of which can be far removed from the object and some can reside in its vicinity, including inside the object. To make the resulting formalism applicable to a wide range of scattering-object morphologies, we use the framework of the volume integral equation formulation of electromagnetic scattering, couple it with the notion of the transition operator, and exploit the fundamental symmetry property of this operator. Among novel results, this tutorial includes a streamlined proof of fundamental symmetry (reciprocity) relations, a simplified derivation of the Foldy equations, and an explicit analytical expression for the transition operator of a multi-component scattering object.

“Independent” and “dependent” scattering by particles in a multi-particle group

“…The state-of-the art of the VIE formulation of frequency-domain electromagnetic scattering by an arbitrary fixed object has recently been summarized in Refs. [39][40][41]. Therefore, we recapitulate here only the most essential results while using exactly the same terminology and notation.…”

“…In general, the scattering object is an arbitrary finite group of 1 N ≤ < ∞ non-overlapping components made of nonmagnetic isotropic materials, including those with edges, corners, and intersecting internal interfaces [40]. We assume that the object is subjected to an impressed incident electromagnetic field inc ( ) E r in the form of a sourcefree solution of the frequency-domain Maxwell equations for an unbounded homogeneous space [41], where the position vector r connects the origin O of the laboratory coordinate system and the observation point. The total field everywhere in the three-dimensional space 3  can be represented as the sum of the incident and so-called scattered fields:…”

“…A key corollary of the VIE formalism [39,41] then states that the transition operator of the entire N-particle group is expressed in terms of the individual-particle transition operators:…”

“…A well-known fundamental result of the theory of electromagnetic scattering by small particles [39,41,46,47] is that at a sufficiently large distance from the particle, the scattered field evolves into a transverse outgoing spherical wave:…”

An overview of methods for deriving the radiative transfer theory from the Maxwell equations. II: Approach based on the Dyson and Bethe–Salpeter equations

“…In this paper we analyze how the use of the far-field assumption in the derivation of the radiative transfer equation can we delayed as far as possible. We therefore use the exact integral Foldy equations of electromagnetic scattering [6][7][8] formulated in terms of the transition dyadic of an individual particle. For a discrete random medium with uncorrelated particle positions, these are employed in conjunction with the Twersky approxima- cally plane-parallel layer with non-scattering plane boundaries (see Fig.…”