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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 22, Iss. 7 — Jul. 1, 2005
  • pp: 1274–1287

One-dimensional description of cylindrically symmetric laser beams: application to Bessel-type nondiffracting beams

Guy Rousseau, David Gay, and Michel Piché  »View Author Affiliations


JOSA A, Vol. 22, Issue 7, pp. 1274-1287 (2005)
http://dx.doi.org/10.1364/JOSAA.22.001274


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Abstract

We introduce a new representation of coherent laser beams that are usually described in circular cylindrical coordinates. This representation is based on the decomposition of a laser beam of a given azimuthal order into beams exhibiting Cartesian symmetry. These beams, which we call constituent waves, diffract along only one of their transverse dimensions and propagate noncollinearly with the propagation axis. A cylindrically symmetric laser beam is then considered a coherent superposition of constituent waves and is represented by an integral over an angular variable. Such a representation allows for the introduction of the propagation factor M 2 , defined in terms of one-dimensional root-mean-square (rms) quantities, in the treatment of two-dimensional beams. The representation naturally leads to the definition of a new rms parameter that we call the quality factor Q. It is shown that the quality factor defines in quantitative terms the nondiffracting character of a laser beam. The representation is first applied to characterize Laguerre–Gauss beams in terms of these one-dimensional rms parameters. This analysis reveals an asymptotic link between Laguerre–Gauss beams and one-dimensional Hermite–Gauss beams in the limit of high azimuthal orders. The representation is also applied to Bessel–Gauss beams and demonstrates the geometrical and one-dimensional characters of the Bessel–Gauss beams that propagate in a nondiffracting regime. By using two separate rms parameters, Q and M 2 , our approach gives an alternative way to describe laser beam propagation that is especially well suited to characterize Bessel-type nondiffracting beams.

© 2005 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(140.3300) Lasers and laser optics : Laser beam shaping

History
Original Manuscript: October 21, 2004
Manuscript Accepted: January 14, 2005
Published: July 1, 2005

Citation
Guy Rousseau, David Gay, and Michel Piché, "One-dimensional description of cylindrically symmetric laser beams: application to Bessel-type nondiffracting beams," J. Opt. Soc. Am. A 22, 1274-1287 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-7-1274


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