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Lorentz beams as a basis for a new class of rectangularly symmetric optical fields

El Gawhary, O; Severini, S; (2007) Lorentz beams as a basis for a new class of rectangularly symmetric optical fields. OPT COMMUN , 269 (2) 274 - 284. 10.1016/j.optcom.2006.08.007.

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Abstract

In this work we present a new and wide class of scalar, rectangular symmetrical optical fields, the free-space propagation of which can be given in a closed-form in the paraxial approximation. In particular it is shown how such fields can be expressed as a finite linear combination of the recently introduced Lorentz beams [O. El Gawhary, S. Severini, J. Opt. A: Pure Appl. Opt., 8 (2006) 409.] that, in this way, act as a basis for the newly introduced class. Because of their mathematical form, we call such fields super-Lorentzian beams. Some common features of the class are pointed out and the concept of order of the beam introduced. Moreover, by using these results, we demonstrate the existence of a new family of mutually orthogonal paraxial fields with a related new class of orthogonal polynomials. (c) 2006 Elsevier B.V. All rights reserved.

Type:Article
Title:Lorentz beams as a basis for a new class of rectangularly symmetric optical fields
DOI:10.1016/j.optcom.2006.08.007
Keywords:beam propagation, orthogonal polynomials, FLATTENED GAUSSIAN BEAMS, LASER-BEAMS

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