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 δ. 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
Original Manuscript: April 28, 2004
Revised Manuscript: September 17, 2004
Manuscript Accepted: September 27, 2004
Published: March 10, 2005
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)