Formulation of the beam shape coefficients based on spherical expansion of the scalar function

Abstract

In solving spherical particle scattering in generalized Lorenz-Mie theory, two sets of beam shape coefficients (BSCs) are calculated, one is for the transverse electric field and another is for the transverse magnetic field. The current work presents an indirect method which introduces the spherical expansion of a scalar potential function. In this way, the BSCs of the beam fields are obtained as combinations of the expansion coefficients of the scalar function, which allows formulating the BSCs more easily and speeding up the numerical calculation. The method is rigorous and is flexible to different shaped beams.