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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.
Physical Review Letters
|October 5, 2020
Summary
Structured-Gaussian beams are uniquely represented on the modal Majorana sphere, generalizing the Poincaré sphere. This representation reveals symmetries leading to geometric phases, experimentally verified for higher-order modes.
Area of Science:
- Optical physics
- Quantum optics
- Beam propagation
Background:
- Structured-Gaussian beams are crucial in optical physics.
- The modal Poincaré sphere represents lower-order beams.
- A generalized representation for higher-order modes is needed.
Purpose of the Study:
- To introduce a novel representation for structured-Gaussian beams.
- To generalize the modal Poincaré sphere concept.
- To explore symmetries and geometric phases in higher-order beams.
Main Methods:
- Utilizing the modal Majorana sphere for beam representation.
- Analyzing symmetries of the Majorana constellation.
- Investigating invariance under astigmatic transformations.
Main Results:
- Structured-Gaussian beams are uniquely mapped to points on the modal Majorana sphere.
- Symmetries of the Majorana constellation correspond to invariances in astigmatic transformations.
- Continuous and quantized geometric phases were observed.
Conclusions:
- The modal Majorana sphere offers a complete representation for structured-Gaussian beams.
- This framework reveals fundamental symmetries and geometric phases.
- The system demonstrates experimental feasibility for studying these phenomena.
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