Many laser interaction models assume that incident focused laser fields are Gaussian and use either the approximate 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 terms, where is the waist normalized to the laser wavelength.
© 2006 Optical Society of AmericaFull Article | PDF Article
Y. Chen and H. A. Haus
Opt. Lett. 16(23) 1841-1843 (1991)
D. T. Gavel, R. G. Vernon, and J. R. Morris
J. Opt. Soc. Am. A 30(12) 2482-2501 (2013)
Vincent Ricardo Daria and Caesar Saloma
Appl. Opt. 40(11) 1767-1775 (2001)