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

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. (c) 2023 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, a new quadrature method for determining the beam shape coefficients (BSCs) of shaped beams using azimuthal and radial integrals is presented. The method is outlined and validated using the tilted plane wave and Gaussian beam as examples. Numerical results show that the proposed method can be a powerful alternative tool for fast and rigorous calculations of BSCs in spherical particle scattering scenarios where analytical solutions are not feasible and numerical evaluations are necessary.