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

Scott M. Sepke, Donald P. Umstadter

Research output: Contribution to journalArticle

6 Scopus citations


Many laser interaction models assume that incident focused laser fields are Gaussian and use either the approximate TEM00 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 ∼ 20w0 terms, where w0 is the 1/e waist normalized to the laser wavelength.

Original languageEnglish (US)
Pages (from-to)2157-2165
Number of pages9
JournalJournal of the Optical Society of America B: Optical Physics
Issue number10
Publication statusPublished - Oct 2006


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Atomic and Molecular Physics, and Optics

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