Radial quadrature method for evaluating the beam shape coefficients of the Laguerre–Gaussian beam

Abstract

Calculation of the beam shape coefficients (BSCs) is crucial in analyzing the interaction between the shaped beam and spherical particle. In this paper, the radial quadrature method is used to formulate the BSCs of the Laguerre–Gaussian beam. The expressions of the BSCs for the Laguerre–Gaussian beam are obtained in terms of integrals, infinite series, and FS. It is proved that the FS expressions of the BSCs are the same as those achieved in the FS technique. The validity of the BSCs is numerically checked in the BSC calculation and the beam’s reconstruction. It is concluded that the infinite series expressions of the radial quadrature BSCs are efficient and reliable.