Abstract

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

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
J. Opt. Soc. Am. B 23(10) 2157-2165 (2006)

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

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J. Opt. Soc. Am. B 23(10) 2166-2173 (2006)

Analytical solutions for the electromagnetic fields of flattened and annular Gaussian laser modes. III. Arbitrary length pulses and spot sizes

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J. Opt. Soc. Am. B 23(11) 2295-2302 (2006)

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