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Updated: Feb 16, 2026

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Hilbert's Hotel in polarization singularities.

Yangyundou Wang, Greg Gbur

    Optics Letters
    |December 15, 2017
    PubMed
    Summary

    We theoretically show how polarization singularities form using fractional optical elements, involving complex mathematics akin to Hilbert's Hotel. The optical element's structure determines two unique topological processes.

    Area of Science:

    • Optics and Photonics
    • Mathematical Physics

    Background:

    • Polarization singularities are crucial in optics.
    • Fractional optical elements offer novel light manipulation.
    • Understanding their formation requires advanced mathematical frameworks.

    Purpose of the Study:

    • To theoretically investigate the creation of polarization singularities.
    • To explore the role of fractional nonuniform polarization optical elements.
    • To connect optical phenomena with the mathematics of infinite sets.

    Main Methods:

    • Theoretical modeling of light propagation.
    • Analysis of fractional optical element structures.
    • Application of countably infinite set mathematics, specifically Hilbert's Hotel.

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    Main Results:

    • Demonstration of polarization singularity creation.
    • Identification of two distinct topological processes.
    • Correlation between element structure and observed topological behavior.

    Conclusions:

    • The evolution of fractional optical elements leads to polarization singularities.
    • Hilbert's Hotel mathematics provides a framework for understanding this process.
    • The topological outcomes are contingent on the specific fractional optical element design.