Engineering equation for filamentation self-focusing collapse distance in atmospheric turbulence

The propagation of high peak-power laser beams in real atmospheres will be affected by both linear and nonlinear effects contained therein. Atmospheric turbulence usually will induce decreases in the filamentation self-focusing collapse distance for refractive index structure parameter increases. This paper provided the first validated analytical equation for predicting the nonlinear self-focusing collapse distance based on a modification of Petrishchev’s and Marburger’s theories. It shows that the estimate of the peak power to critical power at range in turbulence is modified to be the product of the transmitted peak power to critical power ratio times a multiplicative factor derived from Petrishchev’s turbulence equations. This estimate is used in the Marburger distance equation to yield a predicted self-focusing collapse distance. This approach was compared to previous NRL’s HELCAP computer simulation results and showed good agreement. The HELCAP simulations capability has shown good agreement between its results and a previously published laboratory-scale experiment. The analytical approach in this paper may provide a guide for further numerical simulations, more formal theoretical developments and field experiments.