A high-power laser beam propagating through a dielectric in the presence of fluctuations is subject to diffraction, dissipation, and optical Kerr nonlinearity. A method of moments was applied to a stochastic, nonlinear enveloped wave equation to analyze the evolution of the long-term spot radius. For propagation in atmospheric turbulence described by a Kolmogorov-von Kármán spectral density, the analysis was benchmarked against field experiments in the low-power limit and compared with simulation results in the high-power regime. Dissipation reduced the effect of self-focusing and led to chromatic aberration.
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