SU(2) polarization evolution on higher-order Poincaré sphere by using general $q$-plate
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913912072437760 |
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| author | Umar, Mohammad Senthilkumaran, P. |
| author_facet | Umar, Mohammad Senthilkumaran, P. |
| contents | This paper investigates the rotational dynamics on the higher-order Poincaré sphere with the use of $q$-plate by exploring three key aspects: the topological condition, the global-local rotation, and the SU(2) polarization evolution on the sphere. The polarized light beam corresponding to this sphere and $q$-plates shares analogous topological features, characterized by azimuthal variation. We have formulated the topological condition that establishes a connection between the $q$-plate and the higher-order Poincaré sphere, enabling the SU(2) polarization evolution on the same higher-order Poincaré sphere. Leveraging this correspondence, we have shown that a single \textit{global} SO(3) rotation on the higher-order Poincaré sphere is a collection of multiple \textit{local} SO(3) rotations on the standard Poincaré sphere. SO(3) is related to SU(2) through a two-to-one surjective homomorphism, with SU(2) serving as its double cover. Moreover, we demonstrate that a general $q$-plate, defined by a continuously tunable retardance ranging from $0$ to $2π$ and an offset angle ranging from $0$ to $π/2$, provides the complete coverage on the higher-order Poincaré sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SU(2) polarization evolution on higher-order Poincaré sphere by using general $q$-plate Umar, Mohammad Senthilkumaran, P. Optics This paper investigates the rotational dynamics on the higher-order Poincaré sphere with the use of $q$-plate by exploring three key aspects: the topological condition, the global-local rotation, and the SU(2) polarization evolution on the sphere. The polarized light beam corresponding to this sphere and $q$-plates shares analogous topological features, characterized by azimuthal variation. We have formulated the topological condition that establishes a connection between the $q$-plate and the higher-order Poincaré sphere, enabling the SU(2) polarization evolution on the same higher-order Poincaré sphere. Leveraging this correspondence, we have shown that a single \textit{global} SO(3) rotation on the higher-order Poincaré sphere is a collection of multiple \textit{local} SO(3) rotations on the standard Poincaré sphere. SO(3) is related to SU(2) through a two-to-one surjective homomorphism, with SU(2) serving as its double cover. Moreover, we demonstrate that a general $q$-plate, defined by a continuously tunable retardance ranging from $0$ to $2π$ and an offset angle ranging from $0$ to $π/2$, provides the complete coverage on the higher-order Poincaré sphere. |
| title | SU(2) polarization evolution on higher-order Poincaré sphere by using general $q$-plate |
| topic | Optics |
| url | https://arxiv.org/abs/2506.20286 |