OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 31, Iss. 30 — Oct. 20, 1992
  • pp: 6389–6402

Complex beam parameter and ABCD law for non-Gaussian and nonspherical light beams

Miguel A. Porras, Javier Alda, and Eusebio Bernabeu  »View Author Affiliations


Applied Optics, Vol. 31, Issue 30, pp. 6389-6402 (1992)
http://dx.doi.org/10.1364/AO.31.006389


View Full Text Article

Enhanced HTML    Acrobat PDF (1675 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We define the width, divergence, and curvature radius for non-Gaussian and nonspherical light beams. A complex beam parameter is also defined as a function of the three previous ones. We then prove that the ABCD law remains valid for transforming the new complex beam parameter when a non-Gaussian and nonspherical, orthogonal, or cylindrical symmetric laser beam passes through a real ABCD optical system. The product of the minimum width multiplied by the divergence of the beam is invariant under ABCD transformations. Some examples are given.

© 1992 Optical Society of America

History
Original Manuscript: July 26, 1991
Published: October 20, 1992

Citation
Miguel A. Porras, Javier Alda, and Eusebio Bernabeu, "Complex beam parameter and ABCD law for non-Gaussian and nonspherical light beams," Appl. Opt. 31, 6389-6402 (1992)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-31-30-6389


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. Kogelnik, “Imaging of optical mode-resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
  2. H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966). [CrossRef]
  3. J. P. Taché, “Derivation of the ABCD law for Laguerre–Gaussian beams,” Appl. Opt. 26, 2698–2700 (1987). [CrossRef] [PubMed]
  4. S. G. Roper, “Beam divergence of a highly multimode CO2 laser,” J. Phys. E 11, 1102–1103 (1978). [CrossRef]
  5. J. T. Hunt, P. A. Renard, W. W. Simmons, “Improved performance of fusion lasers using the imaging properties of multiple spatial filters,” Appl. Opt. 16, 779–782 (1977). [PubMed]
  6. C. B. Hogge, R. R. Butts, M. Burlakoff, “Characteristics of phase-aberrated nondiffraction-limited laser beams,” Appl. Opt. 13, 1065–1070 (1974). [CrossRef] [PubMed]
  7. J. T. Hunt, P. A. Renard, R. G. Nelson, “Focusing properties of an aberrated laser beam,” Appl. Opt. 15, 1458–1464 (1976). [CrossRef] [PubMed]
  8. J. P. Campbell, L. G. DeShazer, “Near fields of truncated-Gaussian apertures,” J. Opt. Soc. Am. 59, 1427–1429 (1969). [CrossRef]
  9. P. Belland, J. P. Crenn, “Changes in the characteristics of a Gaussian beam weakly diffracted by a circular aperture,” Appl. Opt. 21, 522–527 (1982). [CrossRef] [PubMed]
  10. W. H. Carter, “Spot size and divergence for Hermite–Gaussian beams of any order,” Appl. Opt. 19, 1027 (1980). [CrossRef] [PubMed]
  11. R. L. Phillips, L. C. Andrews, “Spot size and divergence for Laguerre Gaussian beams of any order,” Appl. Opt. 22, 643–644 (1983). [CrossRef] [PubMed]
  12. F. Gori, M. Santarsiero, A. Sona, “The change of the width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991). [CrossRef]
  13. J. Alda, S. Wang, E. Bernabeu, “Analytical expression for the complex radius of curvature tensor Q for generalized Gaussian beams,” Opt. Commun. 80, 350–352 (1991). [CrossRef]
  14. The most usual definition of the Fourier transform is with the minus in the exponential (see Ref. 18 below). In addition, in paraxial wave optics the most usual definition of the plane wave traveling toward positive x is with the minus in the exponential (see Ref. 17 below). The consequence of these choices is the minus in this expression.
  15. P. A. Bélanger, P. Mathieu, “On an extremum property of Gaussian beams and Gaussian pulses,” Opt. Commun. 67, 396–398 (1988). [CrossRef]
  16. A. E. Siegman, E. A. Sziklas, “Mode calculations in unstable resonators with flowing saturable gain. 1: Hermite–Gaussian expansion,” Appl. Opt. 13, 2775–2791 (1974). [CrossRef] [PubMed]
  17. A. E. Siegman, Lasers, (Oxford U. Press, Mill Valley, Calif., 1986), pp. 777–782.
  18. J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), pp. 323–330.
  19. S. M. Selby, ed., Standard Mathematical Tables (CRC, Boca Raton, Fla., 1972), p. 449.

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited