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Optical centroid ellipses beyond polarization ellipses.

Jia Cheng, Liang Fang, Jinman Chen

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    We introduce centroid ellipses, a novel geometric mapping for optical orbital angular momentum (OAM) superpositions. These ellipses are directly observable and enable quantification of OAM states for advanced optical metrology.

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    Area of Science:

    • Optics and Photonics
    • Quantum Information Science

    Background:

    • Polarization ellipses arise from photonic spin state superposition.
    • Optical orbital angular momentum (OAM) states are crucial in various photonic applications.

    Purpose of the Study:

    • To introduce centroid ellipses as a geometric representation for OAM superpositions.
    • To demonstrate direct observation and quantification of OAM states using centroid ellipses.

    Main Methods:

    • Coaxial interference to map OAM superpositions onto a modal Poincaré sphere (PS).
    • Analysis of dynamical interferograms with broken rotational symmetry to observe centroid ellipses.
    • Inference of modal Stokes parameters from centroid ellipses for OAM quantification.

    Main Results:

    • Centroid ellipses were successfully introduced and observed experimentally.
    • Arbitrary OAM superpositions on first- and second-order modal PSs were completely quantified.
    • A unified geometric perspective for optical angular momenta was established.

    Conclusions:

    • Centroid ellipses offer a directly observable alternative to polarization ellipses for OAM analysis.
    • This method provides a powerful tool for high-dimensional optical metrology.
    • The findings unify geometric perspectives on optical angular momenta.