Analytical expressions of generalized M2 factor of hard-edged diffracted Laguerre-Gaussian beams

On the basis of the truncated second-order moments method in the cylindrical coordinate systems, exact analytical expressions of the generalized beam propagation factor (M-G(2) factor) of hard-edged diffracted standard and elegant Laguerre-Gaussian beams are derived and illustrated numerically. It is shown that the M-G(2) factor of truncated standard and elegant Laguerre-Gaussian beams is dependent on the beam orders m and p and the beam truncation parameter delta. The result can also be reduced to that for the non-truncated case as the truncation parameter approaches to be infinite, and to that for truncated Gaussian beams if the mode order of Laguerre polynomial is zero. (c) 2005 Elsevier GmbH. All rights reserved.