Many laser interaction models assume that incident focused laser fields are Gaussian and use either the approximate TEM<sub>00</sub> 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∼20w<sub>0</sub> terms, where w<sub>0</sub> is the 1/e waist normalized to the laser wavelength.
© 2006 Optical Society of America
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)