Modal Majorana Sphere and Hidden Symmetries of Structured-Gaussian Beams
Rodrigo Gutiérrez–Cuevas, S. A. Wadood, A. N. Vamivakas, Miguel A. Alonso
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.
Topics & Concepts
MAJORANAHomogeneous spaceGeneralizationPhysicsModalGaussianTheoretical physicsCelestial spherePure mathematicsQuantum mechanicsMathematicsMathematical analysisGeometryFermionPolymer chemistryAstrophysicsChemistryOrbital Angular Momentum in OpticsDigital Holography and MicroscopyPlanetary Science and Exploration