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    This study introduces a matrix method to describe how orbital angular momentum (OAM) changes in light beams using linear systems. It reveals new types of OAM transformation systems and generalizes optical transfer functions.

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    Area of Science:

    • Physics
    • Optics
    • Photonics

    Background:

    • Orbital angular momentum (OAM) is a key property of light.
    • Understanding OAM transformations in optical systems is crucial for applications.
    • Existing models often simplify system interactions.

    Purpose of the Study:

    • To develop a matrix description for OAM transformations in scalar optical beams.
    • To generalize the amplitude transfer function (ATF) to include mode-to-mode OAM coupling.
    • To explore new types of OAM transforming systems and extend the analysis to random scenarios.

    Main Methods:

    • Introduced a matrix description for OAM transformations.
    • Generalized the amplitude transfer function (ATF) to account for OAM coupling.
    • Analyzed radially independent systems.
    • Extended the framework to random beams and non-local systems.

    Main Results:

    • Developed a generalized ATF that incorporates mode-to-mode OAM coupling.
    • Identified potential for novel OAM transforming systems in radially independent scenarios.
    • Generalized the optical transfer function (OTF) to the OAM space for random beams and systems.

    Conclusions:

    • The matrix description provides a comprehensive framework for analyzing OAM transformations.
    • The generalized ATF and OTF offer new tools for understanding light-matter interactions.
    • The findings open avenues for designing advanced optical systems with tailored OAM manipulation.