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    Vector vortex optical beams acquire discrete topological phases of 0 or π under specific transformations. This finding, demonstrated experimentally, relates to spin-orbit mode separability and generalizes prior research.

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    Area of Science:

    • Optics and Photonics
    • Quantum Information
    • Topological Physics

    Background:

    • Vector vortex optical beams possess unique polarization and spatial characteristics.
    • Topological phases in optical systems are crucial for quantum information processing and novel optical phenomena.
    • Previous studies explored topological phases using only polarization transformations.

    Purpose of the Study:

    • To investigate the topological phase acquired by vector vortex optical beams.
    • To explore the role of local unitary operations on polarization and transverse degrees of freedom.
    • To demonstrate the discrete nature of geometric phases in these optical systems.

    Main Methods:

    • Theoretical simulations of vector vortex beam transformations.
    • Experimental implementation using birefringent wave plates and astigmatic mode converters.
    • Interferometric measurements to detect acquired topological phases and analyze visibility.

    Main Results:

    • Vector vortices acquire discrete geometric phase values of 0 or π.
    • These phases correspond to distinct homotopy classes on the SO(3) manifold.
    • Interference pattern visibility is linked to spin-orbit mode separability.

    Conclusions:

    • Local unitary operations on vector vortices lead to discrete topological phases.
    • The study generalizes previous findings by including transverse mode transformations.
    • Experimental results validate theoretical predictions, confirming the discrete phase acquisition.