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

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. (C) 2019 Elsevier Ltd. All rights reserved.