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    Area of Science:

    • Optics and Photonics
    • Mathematical Physics

    Background:

    • Paraxial beam propagation in linear media possesses rotational symmetry described by the su(2) Lie algebra.
    • Laguerre-Gaussian beams (LGBs) and Hermite-Gaussian beams (HGBs) are fundamental beam families in optics.

    Purpose of the Study:

    • To explore a family of paraxial beams that leverage the su(2) symmetry.
    • To create optical analogs of generalized SU(2) Lie group coherent states.
    • To achieve controllable transitions between LGBs and HGBs.

    Main Methods:

    • Constructing beams as linear superpositions of Laguerre-Gaussian beams.
    • Utilizing a single complex parameter to tune beam characteristics.
    • Employing digital holography for experimental validation.

    Main Results:

    • A novel family of paraxial beams was generated, smoothly transitioning between LGB and HGB characteristics.
    • These beams exhibit propagation-invariant properties, with only a scaling factor change.
    • Experimental validation confirmed the practical feasibility of generating and controlling these beams.

    Conclusions:

    • The developed beams offer a versatile tool for optical applications requiring propagation invariance.
    • This work provides optical analogs for generalized SU(2) Lie group coherent states.
    • The findings demonstrate a practical method for creating hybrid Laguerre-Gaussian and Hermite-Gaussian beams.