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    Area of Science:

    • Optics and Photonics
    • Quantum Optics
    • Optical Engineering

    Background:

    • The geometric structure of light beam oscillations in Orbital Angular Momentum (OAM) space is defined by the orbitalization ellipse.
    • Understanding this ellipse is crucial for applications utilizing OAM-carrying beams.

    Purpose of the Study:

    • To introduce a numerical framework for identifying the orbitalization ellipse's shape and orientation.
    • To leverage singular value decomposition (SVD) for analyzing OAM beam properties.

    Main Methods:

    • Constructing a matrix from the beam's OAM components.
    • Applying singular value decomposition (SVD) to this matrix.
    • Analyzing the singular values and vectors to determine ellipse parameters.

    Main Results:

    • Demonstrated that SVD provides an effective numerical method for characterizing the orbitalization ellipse.
    • Successfully determined the shape and orientation of the ellipse from OAM components.
    • The framework offers insights into the geometric structure of OAM beams.

    Conclusions:

    • Singular value decomposition offers a powerful tool for analyzing the orbitalization ellipse in OAM space.
    • This method facilitates the optimization of optical systems employing high-dimensional OAM beams.
    • The findings contribute to a deeper understanding of light beam structures and their manipulation.