Evaluation of beam shape coefficients of paraxial Laguerre-Gauss beam freely propagating by using three remodeling methods

In the framework of a series of papers devoted to warnings concerning the evaluation of beam shape coefficients (BSCs) of electromagnetic beams by using a localized approximation, a recent paper provided finite series explicit expressions to evaluate BSCs of paraxial Laguerre-Gauss freely propagating beam. In the present paper, these expressions are numerically implemented and finite series numerical results are compared with results obtained by using quadratures and a localized approximation. These three methods provide a remodeling of the beam, changing the non-Maxwellian paraxial Laguerre-Gauss beam to a beam which perfectly satisfies Maxwell's equations. Comparisons between the three methods are discussed in terms of accuracy and computational time efficiency. (C) 2019 Elsevier Ltd. All rights reserved.