Open AccessFractionalization of optical beams: II. Elegant Laguerre–Gaussian modes
Author(s) -
Julio C. Gutiérrez-Vega
Publication year - 2007
Publication title -
optics express
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.15.006300
Subject(s) - paraxial approximation , laguerre polynomials , physics , angular momentum , light beam , gaussian , optics , gaussian beam , beam (structure) , function (biology) , classical mechanics , mathematical analysis , quantum mechanics , mathematics , evolutionary biology , biology
We apply the tools of fractional calculus to introduce new fractional-order solutions of the paraxial wave equation that smoothly connect the elegant Laguerre-Gaussian beams of integral-order. The solutions are characterized in general by two fractional indices and are obtained by fractionalizing the creation operators used to create elegant Laguerre-Gauss beams from the fundamental Gaussian beam. The physical and mathematical properties of the circular fractional beams are discussed in detail. The orbital angular momentum carried by the fractional beam is a continuous function of the angular mode index and it is not restricted to take only discrete values.