title: Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.
abstract: A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.
authors.affiliation: Centre de recherche sur les Ions, les Matériaux et la Photonique, Unité Mixte de Recherche 6252, Commissariat à l'Energie Atomique, Centre National de la Recherche Scientifique, Ecole Nationale Supérieure d'Ingénieurs de Caen, Université de Caen, 6 Bd Maréchal Juin, F-14050 Caen, France. Emmanuel.Cagniot@ensicaen.fr
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Cagniot
authors.forename: Michael
authors.initials: M
authors.lastname: Fromager
authors.forename: Kamel
authors.initials: K
authors.lastname: Ait-Ameur