OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 6 — Jun. 1, 2013
  • pp: 1099–1106

Uniform approximation of paraxial flat-topped beams

Riccardo Borghi  »View Author Affiliations


JOSA A, Vol. 30, Issue 6, pp. 1099-1106 (2013)
http://dx.doi.org/10.1364/JOSAA.30.001099


View Full Text Article

Enhanced HTML    Acrobat PDF (397 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A uniform asymptotic theory of the free-space paraxial propagation of coherent flattened Gaussian beams is proposed in the limit of nonsmall Fresnel numbers. The pivotal role played by the error function in the mathematical description of the related wavefield is stressed.

© 2013 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Propagation

History
Original Manuscript: April 16, 2013
Manuscript Accepted: April 18, 2013
Published: May 13, 2013

Citation
Riccardo Borghi, "Uniform approximation of paraxial flat-topped beams," J. Opt. Soc. Am. A 30, 1099-1106 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-6-1099


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994). [CrossRef]
  2. V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, D. Ambrosini, and G. Schirripa Spagnolo, “Propagation of axially symmetric flattened Gaussian beams,” J. Opt. Soc. Am. A 13, 1385–1394 (1996). [CrossRef]
  3. R. Borghi, “Elegant Laguerre–Gauss beams as a new tool for describing axisymmetric flattened Gaussian beams,” J. Opt. Soc. Am. A 18, 1627–1633 (2001). [CrossRef]
  4. M. Santarsiero and R. Borghi, “On the correspondence between super-Gaussian and flattened Gaussian beams,” J. Opt. Soc. Am. A 16, 188–190 (1999). [CrossRef]
  5. Y. Li, “Light beams with flat-topped profiles,” Opt. Lett. 27, 1007–1009 (2002). [CrossRef]
  6. This can be easily verified by using common scientific databases such as, for instance, http://scholar.google.com .
  7. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  8. J. Stamnes, “Uniform asymptotic theory of diffraction by apertures,” J. Opt. Soc. Am. 73, 96–109 (1983). [CrossRef]
  9. K. Schwarzschild, “Die Beugungsfigure im Fernrohr weit ausserhalb des Focus,” Sitzb. München Akad. Wiss. Math.-Phys. Kl. 28, 271–294 (1898). [CrossRef]
  10. K. D. Mielenz, “Algorithms for Fresnel diffraction at rectangular and circular apertures,” J. Res. Natl. Inst. Stand. Technol. 103, 497 (1998). [CrossRef]
  11. NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/ . DLMF Update, Version 1.0.6, May6, 2013.
  12. E. Zauderer, “Complex argument Hermite–Gaussian and Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 3, 465–469 (1986). [CrossRef]
  13. G. Szegö, Orthogonal Polynomials (American Mathematical Society, 1939).
  14. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series (Gordon and Breach, 1986), Vol. I.
  15. N. M. Temme, “Uniform asymptotic expansions of integrals: a selection of problems,” J. Comput. Appl. Math. 65, 395–417 (1995). [CrossRef]
  16. R. B. Dingle, Asymptotic Expansions: Their Derivation and Interpretation (Academic, 1973).
  17. M. Eichhorn, G. Stöppler, M. Schellhorn, K. T. Zawilski, and P. G. Schunemann, “Gaussian-versus flat-top-pumping of a mid-IR ZGP RISTRA OPO,” Appl. Phys. B 108, 109–115 (2012). [CrossRef]
  18. H. Malik and A. Malik, “Strong and collimated terahertz radiation by super-Gaussian lasers,” Europhys. Lett. 100, 45001 (2012). [CrossRef]
  19. M. Gong, Y. Qiu, Q. Liu, L. Huang, P. Yan, and H. Zhang, “Beam quality improvement by amplitude gain control in power amplifier system,” Laser Phys. Lett. 9, 838 (2012). [CrossRef]
  20. H. Ma, Z. Liu, X. Xu, and J. Chen, “Simultaneous adaptive control of dual deformable mirrors for full-field beam shaping with the improved stochastic parallel gradient descent algorithm,” Opt. Lett. 38, 326–328 (2013). [CrossRef]
  21. E. Mironov, A. Voitovich, and O. Palashov, “Apodizing diaphragm based on the Faraday effect,” Opt. Commun. 295, 170–175 (2013). [CrossRef]
  22. Y. A. Brichkov, Handbook of Special Functions (CRC Press, 2008).

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