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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 10 — May. 14, 2007
  • pp: 6300–6313

Fractionalization of optical beams: II. Elegant Laguerre-Gaussian modes

Julio C. Gutiérrez-Vega  »View Author Affiliations

Optics Express, Vol. 15, Issue 10, pp. 6300-6313 (2007)

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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.

© 2007 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(140.3300) Lasers and laser optics : Laser beam shaping
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

Original Manuscript: March 19, 2007
Revised Manuscript: May 3, 2007
Manuscript Accepted: May 3, 2007
Published: May 7, 2007

Julio C. Gutiérrez-Vega, "Fractionalization of optical beams: II. Elegant Laguerre–Gaussian modes," Opt. Express 15, 6300-6313 (2007)

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