Abstract

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 $\mathit{ABCD}$ 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 $(>{10}^4).$

© 2001 Optical Society of America

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