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SU(2) Poincaré Sphere: A generalized representation for multi-dimensional structured light

SU(2) Poincaré Sphere: A generalized representation for multi-dimensional structured light
SU(2) Poincaré Sphere: A generalized representation for multi-dimensional structured light
Structured light, as a general term for arbitrary states of amplitude, phase, and polarization in optical fields, is highly topical because of a myriad of applications it has fostered. A geometric description to graphically group classes of structured light has obvious benefits, with some notable advances in analogous Poincaré sphere (PS) mapping for both spin and orbital angular momentum (OAM), as well as ray-optical PS approaches for propagation-invariant fields, but all limited in dimensionality they can describe. Here we propose a generalizedSU(2) PS for arbitrary dimensional structured light. The states on it represent extended families of beams with multidimensional ray-wave structures, accurately described by SU(2) symmetry groups. We outline how to construct this mapping theoretically, revealing insights into mode transformations involving OAM and geometric phase, and fully verify its efficacy experimentally. The generality of our approach is evident by the reduction to prior PS representations as special cases. We also demonstrate an extension of our approach to explain amore general high-dimensional vector beam. This construction naturally accounts for the salient topology of the classical PSs while bringing to more new degrees of freedom and dimensions for tailoring a larger variety of quantum-to-classical structured beams for a variety of applications.
1536-6065
Shen, Yijie
42410cf7-8adb-4de6-9175-a1332245c368
Wang, Zhaoyang
90bcc7c2-e3c5-4881-9be1-3d2e13271e14
Fu, Xing
b93bc44e-4b8c-4e94-9b40-ad53938c59d6
Naidoo, Darryl
66678f54-6fa9-4e6f-93b6-13d45fba5dbf
Forbes, Andrew
e745cc06-a297-4fe8-9597-edf694c50c81
Shen, Yijie
42410cf7-8adb-4de6-9175-a1332245c368
Wang, Zhaoyang
90bcc7c2-e3c5-4881-9be1-3d2e13271e14
Fu, Xing
b93bc44e-4b8c-4e94-9b40-ad53938c59d6
Naidoo, Darryl
66678f54-6fa9-4e6f-93b6-13d45fba5dbf
Forbes, Andrew
e745cc06-a297-4fe8-9597-edf694c50c81

Shen, Yijie, Wang, Zhaoyang, Fu, Xing, Naidoo, Darryl and Forbes, Andrew (2020) SU(2) Poincaré Sphere: A generalized representation for multi-dimensional structured light. Physical Review.

Record type: Article

Abstract

Structured light, as a general term for arbitrary states of amplitude, phase, and polarization in optical fields, is highly topical because of a myriad of applications it has fostered. A geometric description to graphically group classes of structured light has obvious benefits, with some notable advances in analogous Poincaré sphere (PS) mapping for both spin and orbital angular momentum (OAM), as well as ray-optical PS approaches for propagation-invariant fields, but all limited in dimensionality they can describe. Here we propose a generalizedSU(2) PS for arbitrary dimensional structured light. The states on it represent extended families of beams with multidimensional ray-wave structures, accurately described by SU(2) symmetry groups. We outline how to construct this mapping theoretically, revealing insights into mode transformations involving OAM and geometric phase, and fully verify its efficacy experimentally. The generality of our approach is evident by the reduction to prior PS representations as special cases. We also demonstrate an extension of our approach to explain amore general high-dimensional vector beam. This construction naturally accounts for the salient topology of the classical PSs while bringing to more new degrees of freedom and dimensions for tailoring a larger variety of quantum-to-classical structured beams for a variety of applications.

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1a-2020-SU(2)PS-PhysRevA.102.031501 - Version of Record
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Accepted/In Press date: 17 August 0202
Published date: 9 September 2020

Identifiers

Local EPrints ID: 449748
URI: http://eprints.soton.ac.uk/id/eprint/449748
ISSN: 1536-6065
PURE UUID: 5d23302b-a34c-4e61-83ce-72c004464899

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Date deposited: 15 Jun 2021 16:32
Last modified: 15 Jun 2021 16:32

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Contributors

Author: Yijie Shen
Author: Zhaoyang Wang
Author: Xing Fu
Author: Darryl Naidoo
Author: Andrew Forbes

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