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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: 2157–2165

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

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

JOSA B, Vol. 23, Issue 10, pp. 2157-2165 (2006)

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Many laser interaction models assume that incident focused laser fields are Gaussian and use either the approximate TEM 00 series model or the exact integral Gaussian angular-spectrum solution. Many practical laser systems, however, produce flat-top transverse intensity profiles, and indeed, such profiles are often desired. Here, an exact, integral solution is derived for all of the vector components having a general flattened Gaussian profile using the angular-spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The resulting integrals are solved for tight focusing conditions exactly by making use of a Fourier–Gegenbauer expansion. This technique follows closely that of Sepke and Umstadter [ Opt. Lett. 31, 1447 (2006)] but, by redefining the expansion coefficients, the simplicity of the model is greatly enhanced and the computation time reduced by roughly a factor of 2 beyond the 2 orders of magnitude improvement obtained previously. This series solution is stable at all points and converges after S 20 w 0 terms, where w 0 is the 1 e waist normalized to the laser wavelength.

© 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. I. Small F-number laser focusing," J. Opt. Soc. Am. B 23, 2157-2165 (2006)

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