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Probability density function estimation for filament creation in lossy, turbulent, nonlinear media.

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    This study introduces two engineering models to predict the probability distribution of the Filamentation Onset Distance (FOD) in turbulent atmospheres. These models, using log-normal and gamma probability density functions (PDFs), show good agreement with simulation results for long-range laser propagation.

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    Area of Science:

    • Nonlinear Optics
    • Atmospheric Optics
    • Laser Physics

    Background:

    • Optical Kerr effects from high peak-power lasers in atmospheres are well-studied.
    • Previous research estimated Filamentation Onset Distance (FOD) but not its statistical variance.
    • Understanding FOD variance is crucial for predicting laser beam behavior in real-world atmospheric conditions.

    Purpose of the Study:

    • To develop and compare two engineering models for predicting the FOD Probability Density Function (PDF) in lossy, turbulent, nonlinear media.
    • To characterize how atmospheric turbulence affects the FOD variation.
    • To validate these models against existing computer simulation data.

    Main Methods:

    • Developed two ad hoc engineering models for FOD PDF prediction.
    • One model utilizes a log-normal PDF, with mean and variance linked to the Rytov Variance.
    • The second model employs a gamma PDF, using identical mean and variance equations.
    • Compared model predictions with results from prior computer simulations.

    Main Results:

    • Both the log-normal and gamma PDF models demonstrated reasonable agreement with computer simulation results for long-range filamentation.
    • The two proposed PDF models yielded similar prediction outcomes.
    • No significant preference was found for either model based on the provided data comparisons.

    Conclusions:

    • The developed engineering models provide a viable method for predicting the statistical distribution of Filamentation Onset Distance (FOD) in turbulent atmospheres.
    • Both log-normal and gamma PDFs offer comparable accuracy for long-range filamentation predictions.
    • These models contribute to a better understanding of laser beam propagation dynamics in realistic atmospheric conditions.