Multiple Scattering of Electromagnetic Waves by Arbitrary Configurations

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Abstract
This paper extends to three‐dimensional vector electromagnetic scattering problems our previous development of the scalar problems. We introduce a vector‐dyadic formalism that facilitates exploiting the previous results, and derive analogous integral equations which specify the multiple‐scattering amplitudes for many objects in terms of the corresponding functions for isolated scatterers. One representation is in terms of the dyadic analog of Beltrami's operator. For arbitrary configurations, the multi‐scattered amplitudes are developed as series in inverse powers of the separations of scatterers (with coefficients in terms of isolated scatterer amplitudes and their derivatives); for two scatterers, we derive a corresponding closed form in terms of a differential operator. Another representation is a system of algebraic equations for the many‐body multipole coefficients in terms of the isolated scatterer values. Explicit closed forms are derived for two arbitrarily spaced elementary scatterers (electric dipoles, magnetic dipoles, etc.) both by separations of variables, and by working with elementary dyadic fields.