Closed form formula for Mie scattering of nonparaxial analogues of Gaussian beams

Nicole J. Moore & Miguel A. Alonso
A closed form formula is found for the Mie scattering coefficents of incident complex focus beams (which are a nonparaxial generalization of Gaussian beams) with any numerical aperture. This formula takes the compact form of multipoles evaluated at a single complex point. Included are the cases of incident scalar fields as well as electromagnetic fields with many polarizations, such as linear, circular, azimuthal and radial. Examples of incident radially and azimuthally polarized beams are presented.