We have simulated optical propagation through atmospheric turbulence in which the spectrum near the inner scale follows that of Hill and Clifford [J. Opt. Soc. Am. <b>68</b>, 892 (1978)] and the turbulence strength puts the propagation into the asymptotic strong-fluctuation regime. Analytic predictions for this regime have the form of power laws as a function of β<sub>0</sub><sup>2</sup>, the irradiance variance predicted by weak-fluctuation (Rytov) theory, and l<sub>0</sub>, the inner scale. The simulations indeed show power laws for both spherical-wave and plane-wave initial conditions, but the power-law indices are dramatically different from the analytic predictions. Let σ<sub>I</sub><sup>2</sup>−1=a(β<sub>0</sub><sup>2</sup>/β<sub>c</sub><sup>2</sup>)<sup>−b</sup>(l<sub>0</sub>/R<sub>f</sub>)<sup>c</sup>, where we take the reference value of β<sub>0</sub><sup>2</sup> to be β<sub>c</sub><sup>2</sup>=60.6, because this is the center of our simulation region. For zero inner scale (for which c=0), the analytic prediction is b=0.4 and a=0.17 (0.37) for a plane (spherical) wave. Our simulations for a plane wave give a=0.234±0.007 and b=0.50±0.07, and for a spherical wave they give a=0.58±0.01 and b=0.65±0.05. For finite inner scale the analytic prediction is b=1/6, c=7/18 and a=0.76 (2.07) for a plane (spherical) wave. We find that to a reasonable approximation the behavior with β<sub>0</sub><sup>2</sup> and l<sub>0</sub> indeed factorizes as predicted, and each part behaves like a power law. However, our simulations for a plane wave give a=0.57±0.03, b=0.33±0.03, and c=0.45±0.06. For spherical waves we find a=3.3±0.3, b=0.45±0.05, and c=0.8±0.1.
© 2000 Optical Society of America
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(030.6600) Coherence and statistical optics : Statistical optics
Stanley M. Flatté and James S. Gerber, "Irradiance-variance behavior by numerical simulation for plane-wave and spherical-wave optical propagation through strong turbulence," J. Opt. Soc. Am. A 17, 1092-1097 (2000)