Mie scattering of high numerical aperture fields

Recently, we proposed several complete orthonormal bases to increase the efficiency of modeling directional, high numerical aperture fields for both the scalar and electromagnetic cases, based on the idea of imaginary focus displacements. Their elements, which can be thought of as nonparaxial analogs of Laguerre-Gauss beams, are analytic solutions to the wave equation in free space and can be optimized for the particular angular spread (NA) using a single parameter corresponding to the imaginary displacement. The scattering of these basis elements off spherical particles can be calculated analytically, as can also the resulting forces and torques exerted on the particle by any linear combination of these fields. Applications involving both fully coherent and partially coherent fields are discussed.