2025/06/25 by Mohammad Umar, Umar, Mohammad, P. Senthilkumaran +1 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Black Holes and Theoretical Physics #FOS: Physical sciences #Nonlinear Waves and Solitons #Optics (physics.optics)
paper · pdf · doi:10.48550/arxiv.2506.20286
openalex publication_date 2025/06/25 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28
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 global SO(3) rotation on the higher-order Poincaré sphere is a collection of multiple 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.