A new superposition scheme for representing flattened Gaussian (FG) beams is proposed. Such a representation, unlike the original proposed by Gori [Opt. Commun. <b>107</b>, 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<sup>4</sup>).
© 2001 Optical Society of America
Riccardo Borghi, "Elegant Laguerre-Gauss beams as a new tool for describing axisymmetric flattened Gaussian beams," J. Opt. Soc. Am. A 18, 1627-1633 (2001)