OSA's Digital Library

Optics Letters

Optics Letters


  • Editor: Anthony J. Campillo
  • Vol. 32, Iss. 8 — Apr. 15, 2007
  • pp: 927–929

Limits of the paraxial approximation in laser beams

Pablo Vaveliuk, Beatriz Ruiz, and Alberto Lencina  »View Author Affiliations

Optics Letters, Vol. 32, Issue 8, pp. 927-929 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (174 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The validity of the paraxial approximation for laser beams in free space is studied via an integral criterion based on the propagation invariants of Helmholtz and paraxial wave equations. This approach allows one to determine the paraxial limit for beams with nondefined spot size and for beams described by more parameters in addition to typical longitudinal wavelength and transverse waist. As examples, the paraxiality of higher-order Hermite, Laguerre, and Bessel–Gaussian beams was completely determined. This method could be extended to nonlinear optics and Bose condensates.

© 2007 Optical Society of America

OCIS Codes
(140.3300) Lasers and laser optics : Laser beam shaping
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation

ToC Category:
Lasers and Laser Optics

Original Manuscript: October 19, 2006
Revised Manuscript: January 2, 2007
Manuscript Accepted: January 8, 2007
Published: March 19, 2007

Pablo Vaveliuk, Beatriz Ruiz, and Alberto Lencina, "Limits of the paraxial approximation in laser beams," Opt. Lett. 32, 927-929 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Yariv, Quantum Elecronics (Wiley, 1989).
  2. J. T. Verdeyen, Laser Electronics (Prentice-Hall, 1981).
  3. A. E. Siegman, Lasers (University Science, 1986).
  4. E. V. Goldstein, K. Plättner, and P. Meystre, J. Res. Natl. Inst. Stand. Technol. 101, 583 (1996).
  5. M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975). [CrossRef]
  6. F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987). [CrossRef]
  7. R. Borghi, M. Santarsiero, and M. A. Porras, J. Opt. Soc. Am. A 18, 1618 (2001). [CrossRef]
  8. M. A. Bandres and J. C. Gutiérrez-Vega, Opt. Lett. 29, 144 (2004). [CrossRef] [PubMed]
  9. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Opt. Lett. 18, 411 (1993). [CrossRef] [PubMed]
  10. A. P. Sheppard and M. Haelterman, Opt. Lett. 23, 1820 (1998). [CrossRef]
  11. A. Lencina and P. Vaveliuk, Phys. Rev. E 71, 056614 (2005). [CrossRef]
  12. A. Lencina, P. Vaveliuk, B. Ruiz, M. Tebaldi, and N. Bolognini, Phys. Rev. E 74, 056614 (2006). [CrossRef]
  13. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1980).
  14. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited