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    This study introduces a novel time-domain method for solving the nonlinear Schrödinger equation, avoiding spurious effects. The research analyzes pulse fission and identifies key dispersion coefficients impacting ultrashort pulses.

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    Area of Science:

    • Nonlinear optics
    • Computational physics
    • Ultrafast science

    Background:

    • The nonlinear Schrödinger equation (NLSE) models phenomena like pulse propagation in optical fibers.
    • Traditional methods like split-step Fourier transform require careful step-size control to avoid errors.
    • Understanding pulse fission is crucial for managing ultrashort pulse dynamics.

    Purpose of the Study:

    • To present a direct time-domain solution for the NLSE using the Green function method.
    • To analyze pulse fission without introducing spurious effects common in other numerical methods.
    • To establish relationships between pulse width and higher-order dispersion coefficients.

    Main Methods:

    • Direct time-domain solution of the nonlinear Schrödinger equation via the Green function method.
    • Simultaneous calculation of dispersion and nonlinear effects.
    • Analysis of pulse fission and its dependence on dispersion parameters (β₂, β₃, β₄).

    Main Results:

    • A novel numerical method for solving the NLSE directly in the time domain is demonstrated.
    • The method avoids spurious effects by simultaneously calculating dispersion and nonlinearities.
    • The relationship between minimum pulse width (T₀) and dispersion coefficients (β₂, β₃, β₄) is determined.
    • Pulse fission is shown to occur in both normal and anomalous dispersion regimes.

    Conclusions:

    • The Green function method offers a robust alternative for simulating ultrashort pulse propagation.
    • Higher-order dispersion coefficients significantly influence pulse fission dynamics.
    • Accurate dispersion values are critical for predicting and controlling ultrashort pulse behavior in femtosecond and attosecond regimes.