Scattering of Laguerre-Gauss light beam by a sphere: the angular spectrum decomposition method and a comparison with the localized approximation method

Abstract

Evaluation of the beam shape coefficients (BSC) in the spherical wave expansion of the incident beam is vital in analyzing light scattering by spherical particles. Different methods have been developed for this purpose. In this work, the formulas of the BSCs for the Laguerre-Gauss beam (LGB) are derived in the angular spectrum decomposition (ASD) method. Under the paraxial condition, these ASD-BSCs are approximated to the expressions in either series or single integrals. Besides, the BSCs for the LGB are also obtained in the localized approximation (LA) method. It is found that the approximate ASD-BSCs are same as those LA-BSCs. Numerical calculation is implemented for verifying the BSC calculations. The validity of the approximate BSC calculation is discussed, together with the distribution of the angular spectrum of the beam. The work offers another example of the shaped beams for mathematically justifying the LA method and suggests another way to discuss the validity of the LA method.