Theoretical and numerical investigation of filament onset distance in atmospheric turbulence

We analyze and simulate the propagation of laser beams with powers larger than the nonlinear self-focusing power through atmospheric turbulence. Turbulence-induced filamentation is theoretically described in terms of whole-beam self-focusing and transverse modulational instability. We describe a numerical simulation method to model nonlinear focusing in turbulence. We find good agreement between our simulation and a previously published laboratory-scale experiment. Simulations are then performed to calculate probability distributions for filament onset and wander over kilometer distances, and are compared with theory. The theoretical model can be made to agree with the simulations for physically meaningful choices of a few fitting parameters. We also examine the use of focusing optics to control filamentation range of modulationally unstable beams.