OSA's Digital Library

Optics Letters

Optics Letters


  • Editor: Anthony J. Campillo
  • Vol. 31, Iss. 10 — May. 15, 2006
  • pp: 1447–1449

Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes

Scott M. Sepke and Donald P. Umstadter  »View Author Affiliations

Optics Letters, Vol. 31, Issue 10, pp. 1447-1449 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (75 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer’s finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell equations exactly in the form of quickly converging Fourier–Gegenbauer series.

© 2006 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: December 14, 2005
Revised Manuscript: February 9, 2006
Manuscript Accepted: February 10, 2006

Scott M. Sepke and Donald P. Umstadter, "Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes," Opt. Lett. 31, 1447-1449 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975). [CrossRef]
  2. H. Hora, Physics of Laser Driven Plasmas (Wiley, 1981).
  3. L. W. Davis, Phys. Rev. A 19, 1177 (1979). [CrossRef]
  4. J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989). [CrossRef]
  5. L. Cicchitelli, H. Hora, and R. Postle, Phys. Rev. A 41, 3727 (1990). [CrossRef] [PubMed]
  6. H. Hora, Laser Plasma Physics: Forces and the Nonlinearity Principle (SPIE, 2000).
  7. H. Hora, M. Hoelss, W. Scheid, J. W. Wang, Y. K. Ho, F. Osman, and R. Castillo, in Proc. SPIE, 3886, 145 (2000).
  8. S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, Phys. Rev. Lett. 95, 035004 (2005). [CrossRef] [PubMed]
  9. B. W. Boreham and H. Hora, Phys. Rev. Lett. 42, 776 (1979). [CrossRef]
  10. B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998). [CrossRef]
  11. A. Maltsev and T. Ditmire, Phys. Rev. Lett. 90, 053002 (2003). [CrossRef] [PubMed]
  12. H. Hora, W. Scheid, T. Hauser, Y. Kato, Y. Kitagawa, K. Mima, and T. Yamanaka, in Proceedings of the 13th International Conference on Laser Interactions and Related Plasma Phenomena, G.Miley and E.M.Campbell, eds., AIP Proc. No. 406 (AIP, 1997), p. 495. [CrossRef]
  13. S. Masuda, M. Kando, H. Kotaki, and K. Nakajima, Phys. Plasmas 12, 013102 (2005). [CrossRef]
  14. S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004). [CrossRef]
  15. P. Varga and P. Török, Opt. Commun. 152, 108 (1998). [CrossRef]
  16. S. DeSilestri, P. Laporta, V. Magni, and O. Svelto, IEEE J. Quantum Electron. QE-24, 1172 (1988). [CrossRef]
  17. Y. Li, Opt. Lett. 27, 1007 (2002). [CrossRef]
  18. R. Borghi, J. Opt. Soc. Am. A 18, 1627 (2001). [CrossRef]
  19. H. Mao and D. Zhao, J. Opt. Soc. Am. A 22, 647 (2005). [CrossRef]
  20. Y. Li, Opt. Commun. 206, 225 (2002). [CrossRef]
  21. F. Gori, Opt. Commun. 107, 335 (1994). [CrossRef]
  22. R. Potvliege, J. Opt. Soc. Am. A 17, 1043 (2000). [CrossRef]
  23. M. Santarsiero and R. Borghi, J. Opt. Soc. Am. A 16, 188 (1999). [CrossRef]
  24. V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, D. Ambrosini, and G. S. Spagnolo, J. Opt. Soc. Am. A 13, 1385 (1996). [CrossRef]
  25. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, 1980).
  26. R. Kant, J. Mod. Opt. 40, 337 (1993). [CrossRef]
  27. M.Abramowitz and I.A.Stegun, eds., Handbook of Mathematical Functions, 12th ed. (Dover, 1972).

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