Evaluation of beam shape coefficients of paraxial Laguerre-Gauss 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.