Gaussian, Hermite-Gaussian, and Laguerre-Gaussian beams: A primer

Details Gaussian, Hermite-Gaussian, and Laguerre-Gaussian beams: A primer Gaussian, Hermite-Gaussian, and Laguerre-Gaussian beams: A primer

2004-10-04

arxiv.org/abs/physics/0410021v1

Physics

Optics

29 pages, 4 figures. Submitted to Am. J. Phys

Scientific paper

The paper aims at presenting a didactic and self-contained overview of Gauss-Hermite and Gauss-Laguerre laser beam modes. The usual textbook approach for deriving these modes is to solve the Helmoltz electromagnetic wave equation within the paraxial approximation. Here, a different technique is presented: Using the plane wave representation of the fundamental Gaussian mode as seed function, all higher-order beam modes are derived by acting with differential operators on this fundamental solution. Even special beam modes as the recently introduced Bessel beams are easily described within that framework.

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