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    We present a new analytical method to create optical beams with controllable orbital angular momentum (OAM) and tailored intensity profiles. This technique allows precise OAM manipulation while maintaining flexibility in beam shaping.

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    Area of Science:

    • Optics and Photonics
    • Quantum Information Science

    Background:

    • Orbital angular momentum (OAM) is a fundamental property of light.
    • Controlling OAM and beam intensity independently is crucial for advanced optical applications.

    Purpose of the Study:

    • To develop an analytical procedure for constructing optical beams with arbitrary OAM.
    • To enable flexible shaping of transverse intensity distributions without altering OAM.

    Main Methods:

    • Application of fractional differential operators in the Fourier domain.
    • Derivation of general expressions for OAM content in optical beams.
    • Identification of parameters governing OAM value and those allowing free modification.

    Main Results:

    • An analytical procedure for generating optical beams with desired OAM values.
    • Demonstration of independent control over OAM and beam intensity profiles.
    • Identification of key parameters for OAM control and beam shaping.

    Conclusions:

    • The proposed method offers precise control over optical beam properties.
    • This technique advances the development of OAM-based optical technologies.
    • Enables new possibilities in optical communication and microscopy.