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Twisted vortex Gaussian Schell-model beams, generalized ABCD systems, and multidimensional Hermite polynomials.

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    Summary
    This summary is machine-generated.

    This study introduces multidimensional Hermite polynomials (MDHPs) for a more efficient representation of the cross-spectral density (CSD) of twisted vortex partially coherent beams. Experimental validation confirms the accuracy of this new theoretical approach in optical systems.

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    Area of Science:

    • Optics
    • Mathematical Physics

    Background:

    • Partially coherent beams, specifically twisted vortex beams, are crucial in optical systems.
    • Existing methods for describing the cross-spectral density (CSD) of these beams can be computationally intensive.
    • The need for efficient and accurate mathematical representations is vital for theoretical and experimental optical studies.

    Purpose of the Study:

    • To derive a novel theoretical framework for the cross-spectral density (CSD) function of a twisted vortex partially coherent beam.
    • To introduce and utilize multidimensional Hermite polynomials (MDHPs) for representing the CSD function.
    • To provide a computational method and experimental validation for the proposed theoretical model.

    Main Methods:

    • Derivation of the cross-spectral density (CSD) function using multidimensional Hermite polynomials (MDHPs).
    • Development of a recurrence relation for computing MDHPs.
    • Implementation of MATLAB code for generating MDHPs of arbitrary order.
    • Experimental measurement of the spectral density of a twisted vortex beam propagating through an asymmetric optical system.

    Main Results:

    • A new formulation for the CSD function of twisted vortex partially coherent beams is established using MDHPs.
    • MDHPs demonstrate significant notational and computational advantages over traditional one-dimensional Hermite polynomials.
    • MATLAB code for generating MDHPs is provided, facilitating practical application.
    • Experimental results align with the predictions of the derived theoretical CSD function, confirming its validity.

    Conclusions:

    • The use of MDHPs provides an effective and computationally advantageous method for characterizing the CSD of twisted vortex partially coherent beams.
    • The derived theoretical model is experimentally validated, offering a reliable tool for optical system analysis.
    • This work advances the understanding and mathematical description of partially coherent beam propagation in optical systems.