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

  • Vol. 18, Iss. 7 — Jul. 1, 2001
  • pp: 1627–1633

Elegant Laguerre–Gauss beams as a new tool for describing axisymmetric flattened Gaussian beams

Riccardo Borghi  »View Author Affiliations


JOSA A, Vol. 18, Issue 7, pp. 1627-1633 (2001)
http://dx.doi.org/10.1364/JOSAA.18.001627


View Full Text Article

Enhanced HTML    Acrobat PDF (147 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A new superposition scheme for representing flattened Gaussian (FG) beams is proposed. Such a representation, unlike the original proposed by Gori [Opt. Commun. 107, 335 (1994)], is based on an expansion in terms of the so-called elegant Laguerre–Gaussian beams. This new representation allows us to obtain the closed-form expression of a FG beam of any order propagating through a paraxial ABCD optical system by means of a simple recurrence rule, which turns out to be particularly stable even when it is applied to FG beams of very high orders (>104).

© 2001 Optical Society of America

OCIS Codes
(140.3300) Lasers and laser optics : Laser beam shaping
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

History
Original Manuscript: September 12, 2000
Revised Manuscript: January 23, 2001
Manuscript Accepted: January 23, 2001
Published: July 1, 2001

Citation
Riccardo Borghi, "Elegant Laguerre–Gauss beams as a new tool for describing axisymmetric flattened Gaussian beams," J. Opt. Soc. Am. A 18, 1627-1633 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-7-1627


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994). [CrossRef]
  2. C. Palma, V. Bagini, “Expansions of general beams in Gaussian beams,” Opt. Commun. 116, 1–7 (1995). [CrossRef]
  3. V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, D. Ambrosini, G. Schirripa Spagnolo, “Propagation features of axially symmetric flattened Gaussian beams,” J. Opt. Soc. Am. A 13, 1385–1394 (1996). [CrossRef]
  4. S.-A. Amarande, “Beam propagation factor and the kurtosis parameter of flattened Gaussian beams,” Opt. Commun. 129, 311–317 (1996). [CrossRef]
  5. B. Lü, B. Zhang, S. Luo, “Far-field intensity distribution, M2 factor, and propagation of flattened Gaussian beams,” Appl. Opt. 38, 4581–4584 (1999). [CrossRef]
  6. M. Santarsiero, D. Aiello, R. Borghi, S. Vicalvi, “Focusing of axially symmetric flattened Gaussian beams,” J. Mod. Opt. 44, 633–650 (1997). [CrossRef]
  7. X. Deng, Y. Li, D. Fan, Y. Qiu, “Propagation of paraxial circular symmetric beams in a general optical system,” Opt. Commun. 140, 226–230 (1997). [CrossRef]
  8. D. Aiello, R. Borghi, M. Santarsiero, S. Vicalvi, “The integrated intensity of focused flattened Gaussian beams,” Optik 109, 97–103 (1998).
  9. R. Borghi, M. Santarsiero, S. Vicalvi, “Focal shift of focused flat-topped beams,” Opt. Commun. 154, 243–248 (1998). [CrossRef]
  10. B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999). [CrossRef]
  11. B. Lü, S. Luo, “General propagation equation of flattened Gaussian beams,” J. Opt. Soc. Am. A 17, 2001–2004 (2000). [CrossRef]
  12. R. Borghi, M. Santarsiero, “Modal decomposition of flat-topped beams produced by multimode stable-cavity lasers,” Opt. Lett. 23, 313–315 (1998). [CrossRef]
  13. R. Borghi, M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron. 35, 745–750 (1999). [CrossRef]
  14. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  15. C. J. R. Sheppard, S. Saghafi, “Flattened light beams,” Opt. Commun. 132, 144–152 (1996). [CrossRef]
  16. R. M. Potvliege, “Waveletlike basis function approach to the propagation of paraxial beams,” J. Opt. Soc. Am. A 17, 1043–1047 (2000). [CrossRef]
  17. S. De Silvestri, P. Laporta, V. Magni, O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: the super-Gaussian approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988). [CrossRef]
  18. A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24, 1071–1079 (1992). [CrossRef]
  19. B. Lü, B. Zhang, X. Wang, “Three-dimensional intensity distribution of focused super-Gaussian beams,” Opt. Commun. 126, 1–6 (1996). [CrossRef]
  20. S.-A. Amarande, “Approximation of super-Gaussian beams by generalized flattened Gaussian beams,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 345–348 (1997). [CrossRef]
  21. M. Santarsiero, R. Borghi, “On the correspondence between super-Gaussian and flattened Gaussian beams,” J. Opt. Soc. Am. A 16, 188–190 (1999). [CrossRef]
  22. B. Lü, S. Luo, B. Zhang, “A comparison between the flattened Gaussian beam and super-Gaussian beam,” Optik 110, 285–288 (1999).
  23. A. E. Siegman, “Hermite–Gaussian functions of complex argument as optical-beam eigenfunctions,” J. Opt. Soc. Am. 63, 1093–1094 (1973). [CrossRef]
  24. T. Takenaka, M. Yokota, O. Fukumitsu, “Propagation for light beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 2, 826–829 (1985). [CrossRef]
  25. E. Zauderer, “Complex argument Hermite–Gaussian and Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 3, 465–469 (1986). [CrossRef]
  26. M. Abramowitz, I. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1972).
  27. For brevity we limit ourselves to the three-dimensional axisymmetric case, but the extension to the rectangular case is immediate.
  28. As usual, circ(r)is defined as 1 if r≤1and 0 elsewhere, rbeing the radial coordinate in R2.
  29. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. I, Chap. 6, p. 785.
  30. Note that Eq. (3) differs from the formula quoted in Ref. 29by a factor of n! as the result of the different normalization for the Laguerre polynomial used here, i.e., Ln(0)=1.
  31. A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integrals and Series (Gordon, New York, 1986), Vol. 1.
  32. H. Ma, B. Lü, “The propagation of complex-argument Laguerre-Gaussian beams,” Optik 111, 273–279 (2000).
  33. A. Siegman, Lasers (University Science, Mill Valley, 1986).
  34. Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981). [CrossRef]
  35. I. S. Gradshtein, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).
  36. A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integrals and Series (Gordon, New York, 1986), Vol. 2.
  37. M. Born, E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge U. Press, Cambridge, UK, 1999).
  38. M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]

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
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited