Background A deep understanding of the initial filamentation dynamics of high-power femtosecond lasers in turbulent atmospheres can provide crucial mechanistic support for applications such as long-distance atmospheric remote sensing and laser-guided mines.

Purpose To reveal the perturbation mechanisms and statistical laws of atmospheric turbulence and laser parameters on the filamentation onset distance along a 40-meter transmission path,

Methods this paper establishes a numerical simulation model based on the modified two-dimensional nonlinear Schrödinger equation (NLSE), which comprehensively accounts for linear diffraction, Kerbel self-focusing, multiphoton absorption (MPA), and turbulent phase perturbations conforming to the von Kármán spectrum; The split-step Fourier method was employed to solve the equation. By applying turbulent phase perturbations layer by layer and performing cyclic diffraction-nonlinearity calculations, large-scale Monte Carlo simulations were conducted for varying laser powers, initial beam waist sizes, and turbulence intensities. The robustness of various FOD criteria—including the gradient method, relative growth rate method, and minimum beam size method—was compared under strong turbulent conditions.

Results The results indicate that traditional absolute intensity threshold methods tend to underestimate the FOD under strong turbulence, while composite criteria based on second derivatives and relative growth rates more accurately capture the onset of self-focusing collapse; Statistical analysis revealed that increasing laser power or reducing initial waist size significantly shortens the average FOD. As turbulence intensity increases, the probability distribution of the FOD exhibits pronounced broadening and non-Gaussian long-tail characteristics; Furthermore, this distribution was accurately fitted by the Gamma distribution function, with the average FOD under weak turbulent conditions being slightly shorter than the theoretical value predicted by Marburger.

Conclusions The FOD dataset constructed herein not only advances the understanding of nonlinear collapse dynamics in turbulent media but also enables data-driven predictions of FOD statistics via deep learning approaches.