Finite series expressions to evaluate the beam shape coefficients of a Laguerre–Gauss beam freely propagating.

Abstract

When using some analytical and semi-analytical scattering theories such as Generalized Lorenz–Mie Theories (GLMTs) and Extended Boundary Condition Method (EBCM) for structured beams, electromagnetic fields, expanded over a set of vector wave functions, may be encoded in some coefficients known as Beam Shape Coefficients (BSCs). In the case of Laguerre–Gauss beams freely propagating, the evaluation of BSCs by using numerical quadratures is time-consuming while localized approximations have been shown to be of limited validity. The present paper therefore establishes finite series expressions to evaluate the BSCs of Laguerre–Gauss beams freely propagating in a rigorous framework, which has the known advantage of speeding up computations with respect to the use of a numerical quadrature technique.