OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 44, Iss. 8 — Mar. 10, 2005
  • pp: 1381–1386

Approximate method for the generalized M² factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams

Zhangrong Mei and Daomu Zhao  »View Author Affiliations


Applied Optics, Vol. 44, Issue 8, pp. 1381-1386 (2005)
http://dx.doi.org/10.1364/AO.44.001381


View Full Text Article

Acrobat PDF (114 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

On the basis of the truncated second-order moments method in the cylindrical coordinate systems and the expansion of the hard-edged aperture function into a finite sum of complex Gaussian functions, an approximate method used to calculate the generalized beam propagation factor (M² factor) is proposed. The approximate analytical expressions of the generalized M² factor for rotationally symmetric hard-edged diffracted flattened Gaussian beams defined by Gori [Opt. Commun. 107, 335 (1994)] and Li [Opt. Lett. 27, 1007 (2002)] are derived, respectively; we show that it depends on the beam order N and the beam truncation parameter delta. Some typical numerical examples are given to illustrate its applications that we compare by using the obtained analytical method and the numerical integration method.

© 2005 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(110.1220) Imaging systems : Apertures
(350.5500) Other areas of optics : Propagation

Citation
Zhangrong Mei and Daomu Zhao, "Approximate method for the generalized M² factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams," Appl. Opt. 44, 1381-1386 (2005)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-44-8-1381


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. A. E. Siegman, "New developments in laser resonators," in Optical Resonators, D. A. Holmes, ed., Proc. SPIE 1224, 2-14 (1990).
  2. A. E. Siegman, "How to (maybe) measure laser beam quality," in DPSS Lasers: Application and Issues, M. W. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 184-199.
  3. R. Martinez-Herrero and P. M. Mejias, "Second-order spatial characterization of hard-edge diffracted beams," Opt. Lett. 18, 1669-1671 (1993).
  4. R. Martinez-Herrero, P. M. Mejias, and M. Arias, "Parametric characterization of coherent, lowest-order Gaussian beams propagating through hard-edged apertures," Opt. Lett. 20, 124-126 (1995).
  5. C. Pare and P.-A. Belanger, "Propagation law and quasi-invariance properties of the truncated second-order moment of a diffracted laser beam," Opt. Commun. 123, 679-693 (1996).
  6. P.-A. Belanger, Y. Champagne, and C. Pare, "Beam propagation factor of diffracted laser beams," Opt. Commun. 105, 233-242 (1994).
  7. M. Scholl, S. Müffer, and O. Post, "Description of diffracted beams by weighted moments," in Third International Workshop on Laser Beam and Optics Characterization, M. Morin and A. Giesen, eds., Proc. SPIE 2870, 112-122 (1996).
  8. F. Gori, "Flattened Gaussian beams," Opt. Commun. 107, 335-341 (1994).
  9. B. Lü and S. Luo, "Generalized M2 factor of hard-edged diffracted flattened Gaussian beams," J. Opt. Soc. Am. A 18, 2098-2102 (2001).
  10. Y. Li, "Light beams with flat-toped profiles," Opt. Lett. 27, 1007-1009 (2002).
  11. J. J. Wen and M. A. Breazeale, "A diffraction beam field expressed as the superposition of Gaussian beams," J. Acoust. Soc. Am. 83, 1752-1756 (1988).
  12. D. Zhao, H. Mao, W. Zhang, and S. Wang, "Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system," Opt. Commun. 224, 5-12 (2003).
  13. D. Zhao, H. Mao, and H. Liu, "Propagation of off-axial Hermite-cosh-Gaussian beams," J. Opt. 6, 77-83 (2004).
  14. A. Erdelyi, W. Magnus, and F. Oberhettinger, Tables of Integral Transforms (McGraw-Hill, New York, 1954).

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited