The generalized beam propagation factor of truncated standard and elegant Laguerre–Gaussian beams

Abstract

On the basis of the truncated second-order moments method in the cylindrical coordinate systems and the expansion of the hard-edged aperture function into a finite sum of complex Gaussian functions, an approximate method for calculating the generalized beam propagation factor (M2 factor) is proposed. Closed-form expressions for the generalized M2 factor of truncated standard and elegant Laguerre–Gaussian beams are respectively derived; it is shown that they depend on the orders p and m of the Laguerre polynomial and the beam truncation parameter δ. Some typical numerical examples are given and compared by using the obtained analytical method and the numerical integration method.