Vector spherical harmonics and their application to classical electrodynamics

Abstract

A set of vector spherical harmonics which was earlier introduced and shown to be applicable to magnetostatics problems, is employed to decompose and solve Maxwell equations. Expressions for the radiation fields for the transverse electric and magnetic modes, the angular distribution of multipole radiation, and the total power radiated in terms of the set of vector spherical harmonics are also derived. The interesting and important Rayleigh scattering problem of electromagnetic plane waves scattering by a conducting sphere is discussed in some detail within the approach. Numerous other problems particularly well adapted for the vector spherical harmonic approach advocated in the paper are suggested.