A new superposition scheme for representing flattened Gaussian (FG) beams is proposed. Such a representation, unlike the original proposed by Gori [Opt. Commun. 107, 335 (1994)], is based on an expansion in terms of the so-called elegant Laguerre-Gaussian beams. This new representation allows us to obtain the closed-form expression of a FG beam of any order propagating through a paraxial ABCD optical system by means of a simple recurrence rule, which turns out to be particularly stable even when it is applied to FG beams of very high orders (>10(4)). (C) 2001 Optical Society of America.
Borghi R (2001). Elegant Laguerre-Gauss beams as a new tool for describing axisymmetric flattened Gaussian beams. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION, 18(7), 1627-1633 [10.1364/JOSAA.18.001627].