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Updated: Dec 6, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Modal Majorana Sphere and Hidden Symmetries of Structured-Gaussian Beams
R Gutiérrez-Cuevas1,2,3, S A Wadood1,2, A N Vamivakas1,2,4,5
1The Institute of Optics, University of Rochester, Rochester, New York 14627, USA.
Abstract:
Structured-Gaussian beams are shown to be fully and uniquely represented by a collection of points (or a constellation) on the surface of the modal Majorana sphere, providing a complete generalization of the modal Poincaré sphere to higher-order modes. The symmetries of this Majorana constellation translate into invariances to astigmatic transformations, giving way to continuous or quantized geometric phases. The experimental amenability of this system is shown by verifying the existence of both these symmetries and geometric phases.
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