Radial quadrature method for evaluating the beam shape coefficients in spherical coordinates

Abstract

In this paper, we present a new quadrature method which uses the azimuthal and radial integrals for determining the beam shape coefficients (BSCs) for shaped beams. To outline the method and to validate it, the tilted plane wave and the Gaussian beam are taken as examples for beams whose descriptions strictly satisfy or not Maxwell equations respectively. Numerical results are discussed and it is concluded that the proposed method may offer a powerful alternative tool for rigorous and fast calculation of the BSCs in spherical particle scattering, in the case when the quadrature cannot be solved analytically in closed form and has to be evaluated numerically.