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    This study defines the cross-spectral density orbital angular momentum (CSD-OAM) matrix for optical fields. It reveals two distinct types of polarization within general random fields, linked to single or paired OAM modes.

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    Area of Science:

    • Quantum Optics
    • Electromagnetism
    • Wave Physics

    Background:

    • Orbital Angular Momentum (OAM) is a fundamental property of light, crucial for optical communications and microscopy.
    • Characterizing the polarization of light with OAM requires advanced mathematical frameworks.
    • Stationary optical fields exhibit complex statistical properties that influence their OAM and polarization.

    Purpose of the Study:

    • To establish the properties of the cross-spectral density orbital angular momentum (CSD-OAM) matrix for stationary optical fields.
    • To introduce and define OAM-resolved polarization properties based on the CSD-OAM matrix.
    • To investigate the nature of polarization within general random optical fields concerning OAM.

    Main Methods:

    • Mathematical formulation of the CSD-OAM matrix for beam-like optical fields.
    • Analysis of the CSD-OAM matrix to derive polarization characteristics.
    • Theoretical investigation of polarization states in general random fields.

    Main Results:

    • The properties of the CSD-OAM matrix for stationary optical fields are established.
    • OAM-resolved polarization properties are introduced, directly linked to the CSD-OAM matrix.
    • Two fundamental types of polarization are identified in general random fields: single-mode and dual-mode OAM-related polarization.

    Conclusions:

    • The CSD-OAM matrix provides a powerful tool for analyzing OAM-dependent polarization.
    • General random fields exhibit a rich polarization structure that can be decomposed based on OAM.
    • The findings offer new insights into the polarization dynamics of light carrying orbital angular momentum.