General vector basis function solution of Maxwell’s equations

Abstract

A general method for solving Maxwell's equations exactly, based on expansion of the solution in a complete set of vector basis functions, is developed. These vector eigenfunctions are derived from the complete set of separable solutions to the scalar Helmholtz equation and are shown to form a complete set. The method is applicable to a variety of problems, including the study of near and far field electromagnetic scattering from particles with arbitrary shapes, for particles whose characteristic length scale $d$ $\ensuremath{\approx}\ensuremath{\lambda}$, the wavelength of the incident electromagnetic wave.