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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 25 — Dec. 10, 2007
  • pp: 16719–16728

Airy-Gauss beams and their transformation by paraxial optical systems

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

Optics Express, Vol. 15, Issue 25, pp. 16719-16728 (2007)

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We introduce the generalized Airy-Gauss (AiG) beams and analyze their propagation through optical systems described by ABCD matrices with complex elements in general. The transverse mathematical structure of the AiG beams is form-invariant under paraxial transformations. The conditions for square integrability of the beams are studied in detail. The AiG beam describes in a more realistic way the propagation of the Airy wave packets because AiG beams carry finite power, retain the nondiffracting propagation properties within a finite propagation distance, and can be realized experimentally to a very good approximation.

© 2007 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(070.2590) Fourier optics and signal processing : ABCD transforms
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

Original Manuscript: November 14, 2007
Revised Manuscript: November 23, 2007
Manuscript Accepted: November 24, 2007
Published: December 3, 2007

Miguel A. Bandres and Julio C. Gutiérrez-Vega, "Airy-Gauss beams and their transformation by paraxial optical systems," Opt. Express 15, 16719-16728 (2007)

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  1. H. Kogelnik and T. Li, "Laser beams and resonators," Proc. IEEE,  54, 1312-1329 (1966). [CrossRef]
  2. A. E. Siegman, Lasers (University Science, Mill Valley CA, 1986).
  3. E. G. Kalnins and W. MillerJr., "Lie theory and separation of variables. 5. The equations iUt +Uxx = 0 and iUt +Uxx-c/x2 U = 0," J. Math. Phys. 15, 1728-1737 (1974). [CrossRef]
  4. M. V. Berry and N. L. Balazs, "Nonspreading wave packets," Am. J. Phys. 47, 264-267 (1979). [CrossRef]
  5. I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, "Nondispersive accelerating wave packets," Am. J. Phys. 62, 519-521 (1994). [CrossRef]
  6. K. Unnikrishnan and A. R. P. Rau, "Uniqueness of the Airy Packet in quantum mechanics, " Am. J. Phys. 64, 1034-1036 (1996). [CrossRef]
  7. G. A. Siviloglou and D. N. Christodoulides, "Accelerating finite energy Airy beams," Opt. Lett. 32, 979-981 (2007). [CrossRef] [PubMed]
  8. I. M. Besieris and A. M. Shaarawi, "A note on an accelerating finite energy Airy beam," Opt. Lett. 32, 2447-2449 (2007). [CrossRef] [PubMed]
  9. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Phys. Rev. Lett. 99, 213901 (2007). [CrossRef]
  10. H. M. Osaktas, Z. Zalevski, and M. A. Kutay, The Fractional Fourier Transform with applications in Optics and Signal processing (Wiley, London, 2001).
  11. M. Abramowitz and I.A. Stegun, Handbook of mathematical functions (Dover, New York, 1964).
  12. O. Vallée and M Soares, Airy functions and applications to physics (Imperial College Press, London, 2004).

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