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

Abstract

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.

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

References in corpus (1)

• Optical alignment and spinning of laser-trapped microscopic particles

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