Abstract

The radial quadrature method was recently proposed for formulating the beam shape coefficients (BSCs) for shaped beams. A new deduction of BSCs using the R-quadrature method is presented in this paper, using the integral of the spherical Bessel functions in the interval ranging from zero to infinity. Based on the scalar description of the Bessel beam, the equivalence between the R-quadrature and the finite series (FS) method is confirmed. The spherical wave expansion of the scalar function allows us to simplify the formulation of the BSCs in the R-quadrature and the FS and to speed up the numerical BSC calculation. As a by-product, FS expansions of the associated Legendre functions are established, which we do not find in the literature.

© 2023 Optica Publishing Group

Calculation of light scattering of an elliptical Gaussian beam by a spherical particle

Jianqi Shen, Xiang Liu, Wei Wang, and Haitao Yu
J. Opt. Soc. Am. A 35(8) 1288-1298 (2018)

Evaluation of beam shape coefficients in T-matrix methods using a finite series technique: on blow-ups using hypergeometric functions and generalized Bessel polynomials

Gérard Gouesbet, Luiz F. M. Votto, and Leonardo A. Ambrosio
J. Opt. Soc. Am. B 40(12) 3174-3181 (2023)

Expansion of an arbitrarily oriented, located, and shaped beam in spheroidal coordinates

Feng Xu, Kuanfang Ren, and Xiaoshu Cai
J. Opt. Soc. Am. A 24(1) 109-118 (2007)

Compact formulation of the beam shape coefficients for elliptical Gaussian beam based on localized approximation

Jianqi Shen, Xiaowei Jia, and Haitao Yu
J. Opt. Soc. Am. A 33(11) 2256-2263 (2016)

Beam shape coefficient calculation for a Gaussian beam: localized approximation, quadrature and angular spectrum decomposition methods

Juncheng Qiu and Jianqi Shen
Appl. Opt. 57(2) 302-313 (2018)