Probability distribution of irradiance fluctuations at arbitrary positions on a long-distance propagating Gaussian beam cross-section

This is the authors' abstract. We don't add key points for this paper.

Using a four-dimensional numerical simulation program for laser atmospheric propagation, we investigate the intensity fluctuations and their probability density function (PDF) characteristics of Gaussian beams under long-range atmospheric transmission. The results indicate that under different atmospheric turbulence conditions, the scintillation index on the beam cross-section is relatively low near the center and increases with the distance from the center. When the single-point scintillation index exceeds 2.0, the scintillation index primarily determines the PDF of single-point intensity fluctuations, and intensity fluctuations at locations with the same scintillation index exhibit nearly identical PDFs. Furthermore, the exponential-Weibull distribution provides a good fit for the single-point intensity fluctuation PDFs. Based on this, we establish quantitative expressions relating the parameters of the exponential-Weibull distribution to the scintillation index. For scintillation indices greater than 2.0, the fitting is nearly perfect, demonstrating the universality of these expressions.