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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

  • Editor: Franco Gori
  • Vol. 28, Iss. 10 — Oct. 1, 2011
  • pp: 2100–2107

Bessel–Gauss beams as rigorous solutions of the Helmholtz equation

Alexandre April  »View Author Affiliations


JOSA A, Vol. 28, Issue 10, pp. 2100-2107 (2011)
http://dx.doi.org/10.1364/JOSAA.28.002100


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Abstract

The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel–Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre–Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

© 2011 Optical Society of America

OCIS Codes
(010.3310) Atmospheric and oceanic optics : Laser beam transmission
(030.4070) Coherence and statistical optics : Modes
(260.1960) Physical optics : Diffraction theory
(260.3160) Physical optics : Interference
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

History
Original Manuscript: July 11, 2011
Revised Manuscript: August 17, 2011
Manuscript Accepted: August 18, 2011
Published: September 20, 2011

Citation
Alexandre April, "Bessel–Gauss beams as rigorous solutions of the Helmholtz equation," J. Opt. Soc. Am. A 28, 2100-2107 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-10-2100


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