Electromagnetic scattering by an aggregate of spheres

TLDR

The study develops a comprehensive solution for electromagnetic scattering by aggregates of arbitrarily sized and composed spheres, proposing an asymptotic iteration technique to compute interaction coefficients. The method extends Mie theory using spherical vector wave addition theorems to formulate coupled linear equations for interaction coefficients and reconstructs the total scattered field via a second translational addition theorem. The authors derive rigorous analytical expressions for cross sections and amplitude‑scattering matrix elements, and validate the approach with preliminary numerical results that agree with laboratory measurements.

Abstract

We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.