A new theory of the generalized optical cross-section theorem for electromagnetic fields

Abstract

Our focus is a unification of the generalized optical theorem facilitating discussion, within a unified general theory, of important effects of radiation and scattering in general nonhomogeneous propagating media, arbitrary excitation fields, and general representational domains (Green function representation, plane wave expansion, multipole expansion, and so on), among other aspects. The derived techniques are conceptually simple and rely mostly on cross flux concepts and Green's function theory. Unlike the most familiar derivations of the optical theorem, the derived methods do not make use of the stationary phase method (Jones' lemma). Particular attention is given to the full vector and dyadic version of the theory, but some results pertinent to the scalar theory are also discussed to provide a broader context applicable to a variety of partial differential equations of interest in the wave disciplines.