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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)

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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

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

Miguel A. Bandres and Julio C. Gutiérrez-Vega, "Elliptical beams," Opt. Express 16, 21087-21092 (2008)

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  1. M. A. Bandres and J. C. Gutiėrrez-Vega, "Ince-Gaussian beams," Opt. Lett. 29, 144-146 (2004). [CrossRef] [PubMed]
  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]
  3. M. A. Bandres, "Elegant Ince-Gaussian beams," Opt. Lett. 29, 1724-1726 (2004). [CrossRef] [PubMed]
  4. M. A. Bandres and J. C. Gutiérrez-Vega, "Generalized Ince Gaussian beams," Proc. SPIE 6290, 6290-0S (2006).
  5. U. T. Schwarz, M. A. Bandres and J. C. Gutiérrez-Vega, "Observation of Ince-Gaussian modes in stable resonators," Opt. Lett. 29, 1870-1872 (2004). [CrossRef] [PubMed]
  6. T. Ohtomo, K. Kamikariya, K. Otsuka, and S. Chu, "Single-frequency Ince-Gaussian mode operations of laserdiode-pumped microchip solid-state lasers," Opt. Express 15, 10705-10717 (2007). [CrossRef] [PubMed]
  7. S. Chu and K. Otsuka, "Stable donutlike vortex beam generation from lasers with controlled Ince-Gaussian modes," Appl. Opt. 46, 7709-7719 (2007). [CrossRef] [PubMed]
  8. T. Ohtomo, S. Chu, and K. Otsuka, "Generation of vortex beams from lasers with controlled Hermite- and Ince-Gaussian modes," Opt. Express 16, 5082-5094 (2008). [CrossRef] [PubMed]
  9. J. B. Bentley, J. A. Davis, M. A. Bandres, and J. C. Gutiérrez-Vega, "Generation of helical Ince-Gaussian beams with a liquid-crystal display," Opt. Lett. 31, 649-651 (2006). [CrossRef] [PubMed]
  10. J. C. Gutiérrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (2005). [CrossRef]
  11. C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng. 45, 068001 (2006). [CrossRef]
  12. M. Guizar-Sicairos and J. C. Gutiérrez-Vega, "Generalized Helmholtz-Gauss beams and its transformation by paraxial optical systems," Opt. Lett. 31, 2912-2914 (2006). [CrossRef] [PubMed]
  13. M. A. Bandres and J. C. Gutiérrez-Vega, "Cartesian beams," Opt. Lett. 32, 3459-3461 (2007). [CrossRef] [PubMed]
  14. A. Torre, "A note on the general solution of the paraxial wave equation a Lie algebra view," J. Opt. A: Pure Appl. Opt. 10, 55006 (2008). [CrossRef]
  15. M. A. Bandres and J. C. Gutiérrez-Vega, "Circular beams," Opt. Lett. 33, 177-179 (2008). [CrossRef] [PubMed]
  16. A. E. Siegman, Lasers (University Science, 1986).
  17. K. M. Urwin and F. M. Arscott, "Theory of the Whittaker-Hill equation," Proc. R. Soc. Edinb. [Biol],  69, 28-44 (1970).
  18. M. A. Bandres and M. Guizar-Sicairos, "The paraxial group," doc. ID 101079 (posted 16 October 2008, in press).
  19. M. R. Dennis, "Rows of optical vortices from elliptically perturbing a high-order beam," Opt. Lett. 31, 1325-1327 (2006). [CrossRef] [PubMed]
  20. E. G. Abramochkin and V. G. Volostnikov, "Generalized Gaussian beams," J. Opt. A: Pure Appl. Opt. 6, S157- S161 (2004). [CrossRef]

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