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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 25 — Dec. 8, 2008
  • pp: 21087–21092

Elliptical beams

Miguel A. Bandres and Julio C. Gutiérrez-Vega  »View Author Affiliations


Optics Express, Vol. 16, Issue 25, pp. 21087-21092 (2008)
http://dx.doi.org/10.1364/OE.16.021087


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Abstract

A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the EB are the standard, elegant, and generalized Ince-Gauss beams, Mathieu-Gauss beams, among others.

© 2008 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

History
Original Manuscript: October 29, 2008
Revised Manuscript: November 27, 2008
Manuscript Accepted: December 2, 2008
Published: December 4, 2008

Citation
Miguel A. Bandres and Julio C. Gutiérrez-Vega, "Elliptical beams," Opt. Express 16, 21087-21092 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-21087


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References

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  2. M. A. Bandres and J. C. Gutiérrez-Vega, "Ince-Gaussian modes of the paraxial wave equation and stable resonators," J. Opt. Soc. Am. A 21, 873-880 (2004). [CrossRef]
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