Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method

A variant of the Gaussian beam expansion method consists in expanding the Bessel function 10 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 J(0) 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. (C) 2009 Optical Society of America