The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer’s finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell equations exactly in the form of quickly converging Fourier–Gegenbauer series.
© 2006 Optical Society of America
Lasers and Laser Optics
Original Manuscript: December 14, 2005
Revised Manuscript: February 9, 2006
Manuscript Accepted: February 10, 2006
Scott M. Sepke and Donald P. Umstadter, "Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes," Opt. Lett. 31, 1447-1449 (2006)