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Optics Letters

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  • Editor: Anthony J. Campillo
  • Vol. 32, Iss. 23 — Dec. 1, 2007
  • pp: 3459–3461

Cartesian beams

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


Optics Letters, Vol. 32, Issue 23, pp. 3459-3461 (2007)
http://dx.doi.org/10.1364/OL.32.003459


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Abstract

A new and very general beam solution of the paraxial wave equation in Cartesian coordinates is presented. We call such a field a Cartesian beam. The complex amplitude of the Cartesian beams is described by either the parabolic cylinder functions or the confluent hypergeometric functions, and the beams are characterized by three parameters that are complex in the most general situation. The propagation through complex A B C D optical systems and the conditions for square integrability are studied in detail. Applying the general expression of the Cartesian beams, we also derive two new and meaningful beam structures that, to our knowledge, have not yet been reported in the literature. Special cases of the Cartesian beams are the standard, elegant, and generalized Hermite–Gauss beams, the cosine-Gauss beams, the Lorentz beams, and the fractional order beams.

© 2007 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: September 12, 2007
Revised Manuscript: October 8, 2007
Manuscript Accepted: October 17, 2007
Published: November 29, 2007

Citation
Miguel A. Bandres and Julio C. Gutiérrez-Vega, "Cartesian beams," Opt. Lett. 32, 3459-3461 (2007)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-23-3459


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References

  1. A. E. Siegman, Lasers (University Science, 1986).
  2. M. A. Bandres and J. C. Gutiérrez-Vega, Opt. Lett. 29, 144 (2004). [CrossRef] [PubMed]
  3. J. C. Gutiérrez-Vega and M. A. Bandres, J. Opt. Soc. Am. A 22, 289 (2005). [CrossRef]
  4. C. P. Boyer, E. G. Kalnins, and W. Miller, Jr., J. Math. Phys. 16, 499 (1975). [CrossRef]
  5. A. Wunsche, J. Opt. Soc. Am. A 6, 1320 (1989). [CrossRef]
  6. M. A. Bandres and J. C. Gutiérrez-Vega, Proc. SPIE 6290, 6290-0S (2006).
  7. O. El Gawhary and S. Severini, J. Opt. A, Pure Appl. Opt. 8, 409 (2006). [CrossRef]
  8. J. C. Gutiérrez-Vega, Opt. Lett. 32, 1521 (2007). [CrossRef] [PubMed]
  9. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1964).

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