Individual and aggregate scattering matrices and cross-sections: Conservation laws and reciprocity

Abstract

For systems of multiple spheres, we investigate in detail the ‘individual’ and aggregate electromagnetic scattering matrices, and their relations with conservation laws, reciprocity and the optical theorem. In order for these relations to adopt their simplest form, care is taken to completely extract both incoming and outgoing phase factors in the definitions. We illustrate that the ‘individual’ cross-sections in an aggregate are defined only in terms of part of the total field, and consequently do not individually obey conservation laws or reciprocity; these relations should be satisfied for the scattering by the entire aggregate. We demonstrate that for scatterer centred transfer matrices, the conservation laws and reciprocity are automatically satisfied regardless of whether or not sufficient multipolarities were retained in the description of individual scatterers. Derivations and results are worked out in a particularly compact and transparent formalism, including magnetic permeability contrast, and the possibility of complex polarizations.