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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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Filamentation with nonlinear Bessel vortices.

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    Area of Science:

    • Nonlinear optics
    • Laser physics
    • Plasma physics

    Background:

    • Laser beam propagation in nonlinear media is complex.
    • High-order Bessel beams offer unique propagation characteristics.
    • Nonlinear effects like Kerr nonlinearity and multiphoton absorption significantly alter beam behavior.

    Purpose of the Study:

    • To investigate the formation and dynamics of ring-shaped filaments in nonlinear media.
    • To identify and characterize stationary nonlinear high-order Bessel solutions.
    • To explore the potential applications of these structures in laser-induced material modification.

    Main Methods:

    • Direct numerical simulations of nonlinear beam propagation.
    • Analysis of axicon-focused Gaussian beams with helicity in a Kerr medium with multiphoton absorption.
    • Semi-analytical determination of the existence region for nonlinear Bessel vortices.

    Main Results:

    • Identification of two propagation regimes: stable and unstable.
    • Stable regime characterized by beam reshaping into nonlinear Bessel vortices.
    • Unstable regime leads to filament breakup into helical or irregular patterns.
    • Nonlinear Bessel vortices create intense, ring-shaped ionized channels.

    Conclusions:

    • Nonlinear Bessel vortices act as attractors in stable propagation regimes.
    • The existence of these vortices is dependent on input power and cone angle.
    • The generated ionized channels offer potential for novel applications in laser material processing of transparent dielectrics.