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 used to calculate the generalized beam propagation factor (M² factor) is proposed. The approximate analytical expressions of the generalized M² factor for rotationally symmetric hard-edged diffracted flattened Gaussian beams defined by Gori [Opt. Commun. 107, 335 (1994)] and Li [Opt. Lett. 27, 1007 (2002)] are derived, respectively; we show that it depends on the beam order N and the beam truncation parameter delta. Some typical numerical examples are given to illustrate its applications that we compare by using the obtained analytical method and the numerical integration method.
© 2005 Optical Society of America
Zhangrong Mei and Daomu Zhao, "Approximate method for the generalized M² factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams," Appl. Opt. 44, 1381-1386 (2005)