Abstract

A variant of the Gaussian beam expansion method consists in expanding the Bessel function $J_0$ 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.

© 2009 Optical Society of America

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