Gaussian Laser Beams via Oblate Spheroidal Waves
Kirk T. McDonald
TL;DR
This paper derives a new set of Gaussian laser beam modes using oblate spheroidal coordinates, connecting them to the well-known Gaussian-Laguerre modes through coordinate transformation.
Contribution
It introduces a novel derivation of Gaussian laser beam modes via oblate spheroidal wave solutions, expanding the mathematical framework for beam analysis.
Findings
Derived circularly polarized Gaussian beam modes in oblate spheroidal coordinates.
Connected these modes to Gaussian-Laguerre modes through coordinate transformation.
Provides a new mathematical approach to analyze laser beam profiles.
Abstract
We deduce a set of circularly polarized Gaussian laser beam modes via a separation-of-variables solution to the Helmholtz wave equation in oblate spheriodal coordinates. On transforming to cylindrical coordinates these become the well-known Gaussian-Laguerre modes.
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Taxonomy
TopicsOrbital Angular Momentum in Optics · Advanced Fiber Laser Technologies · Laser-Matter Interactions and Applications