OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: G. I. Stegeman
  • Vol. 23, Iss. 10 — Oct. 1, 2006
  • pp: 2166–2173

Analytical solutions for the electromagnetic fields of flattened and annular Gaussian laser modes. II. Large F-number laser focusing

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

JOSA B, Vol. 23, Issue 10, pp. 2166-2173 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (965 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A spherical Hankel function series solution for the vector components of a general flattened Gaussian laser field is derived, based on the angular spectrum of plane waves. This perturbative series is valid for spot sizes greater than ten wavelengths, creating a complete vector solution for a general flattened Gaussian laser profile for all focusing conditions when coupled to the model developed in Part I of this investigation [ J. Opt. Soc. Am. B 23, 2157 (2006) ]. The focusing and propagation properties of these fields are then explored numerically. Finally, the exact solution is compared to the perturbative Hermite–Gaussian (0,0) laser mode by comparing the focal plane boundary conditions imposed in each and is found to be a separate and distinct solution under tight focusing conditions.

© 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:
Physical Optics

Original Manuscript: March 14, 2006
Manuscript Accepted: June 2, 2006

Scott M. Sepke and Donald P. Umstadter, "Analytical solutions for the electromagnetic fields of flattened and annular Gaussian laser modes. II. Large F-number laser focusing," J. Opt. Soc. Am. B 23, 2166-2173 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. Sepke and D. Umstadter, "Analytical solutions for the electromagnetic fields of flattened and annular Gaussian laser modes. I. Small F-number laser focusing," J. Opt. Soc. Am. B 23, 2157-2165 (2006). [CrossRef]
  2. L. Cicchitelli, H. Hora, and R. Postle, "Longitudinal field components for laser beams in vacuum," Phys. Rev. A 41, 3727-3732 (1990). [CrossRef] [PubMed]
  3. B. W. Boreham and B. Luther-Davies, "High-energy electron acceleration by ponderomotive forces in tenuous plasmas," J. Appl. Phys. 50, 2533-2538 (1979). [CrossRef]
  4. S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, "Optical deflection and temporal characterization of ultrafast laser-produced electron beams," Phys. Rev. Lett. 95, 035004 (2005). [CrossRef] [PubMed]
  5. B. W. Boreham and H. Hora, "Debye length discrimination of nonlinear laser forces acting on electrons in tenuous plasmas," Phys. Rev. Lett. 42, 776-779 (1979). [CrossRef]
  6. B. Quesnel and P. Mora, "Theory and simulation of the interaction of ultraintense laser pulses with electrons in vacuum," Phys. Rev. E 58, 3719-3732 (1998). [CrossRef]
  7. A. Maltsev and T. Ditmire, "Above threshold ionization and in tightly focused, strongly relativistic laser fields," Phys. Rev. Lett. 90, 053002 (2003). [CrossRef] [PubMed]
  8. H. Hora, W. Scheid, T. Hauser, Y. Kato, Y. Kitagawa, K. Mima, and T. Yamanaka, "Free wave laser acceleration of electrons and consequences for the Umstadter experiment," in Proceedings of the 13th International Conference on Laser Interaction and Related Plasma Phenomena, AIP Conf. Proc. No. 406 (AIP, 1997), p. 495. [CrossRef]
  9. S. Masuda, M. Kando, H. Kotaki, and K. Nakajima, "Suppression of electron scattering by the longitudinal components of tightly focused laser fields," Phys. Plasmas 12, 013102 (2005). [CrossRef]
  10. H. Hora, Physics of Laser Driven Plasmas (Wiley, 1981).
  11. H. Hora, M. Hoelss, W. Scheid, J. W. Wang, Y. K. Ho, F. Osman, and R. Castillo, "Acceleration of electrons in vacuum by lasers and the accuracy principle of nonlinearity," in High-Power Lasers in Energy Engineering, K.Mima, G.L.Kulcinski, and W.Hogan, eds., Proc. SPIE 3886, 145-156 (2000).
  12. H. Hora, Laser Plasma Physics (SPIE, 2000).
  13. M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975). [CrossRef]
  14. L. W. Davis, "Theory of electromagnetic beams," Phys. Rev. A 19, 1177-1179 (1979). [CrossRef]
  15. J. P. Barton and D. R. Alexander, "Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800-2802 (1989). [CrossRef]
  16. J. X. Wang, W. Sheid, M. Hoelss, and Y. K. Ho, "Fifth-order corrected field descriptions of the Hermite-Gaussian (0,0) and (0,1) mode laser beam," Phys. Rev. E 64, 066612 (2001). [CrossRef]
  17. Y. I. Salamin and C. H. Keitel, "Electron acceleration by a tightly focused laser beam," Phys. Rev. Lett. 88, 095005 (2002). [CrossRef] [PubMed]
  18. R. Borghi, A. Ciattoni, and M. Santarisiero, "Exact axial electromagnetic field for vectorial Gaussian and flattened Gaussian boundary distributions," J. Opt. Soc. Am. A 19, 1207-1211 (2002). [CrossRef]
  19. P. Varga and P. Török, "The Gaussian wave solution of Maxwell's equations and the validity of scalar wave approximation," Opt. Commun. 152, 108-118 (1998). [CrossRef]
  20. S. Sepke and D. Umstadter, "Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes," Opt. Lett. 31, 1447-1449 (2006). [CrossRef] [PubMed]

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