Scattering and absorption cross sections of compounded spheres I Theory for external aggregation

Abstract

The cross section for total scattering by clusters of spheres is derived from an integration, over a closed spherical surface, of the scattered Poynting flux associated with the different pairs of spheres in the ensemble. With the use of the addition theorem for vector spherical harmonics the integral can be evaluated analytically. The pairwise cross sections can be rearranged into an expression for the scattering cross section of sphere aggregates that is analogous to that obtained from Lorenz–Mie theory for a single sphere. The latter formulation, however, is more difficult to treat numerically than is the summation over pairwise cross sections.