## Abstract

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. **68**, 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 ${\beta}_{0}^{2},$ the irradiance variance predicted by weak-fluctuation (Rytov) theory, and ${l}_{0},$ 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 ${\sigma}_{I}^{2}-1=a({\beta}_{0}^{2}/{\beta}_{c}^{2}{)}^{-b}({l}_{0}/{R}_{f}{)}^{c},$ where we take the reference value of ${\beta}_{0}^{2}$ to be ${\beta}_{c}^{2}=60.6,$ 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 $a=0.234\pm 0.007$ and $b=0.50\pm 0.07,$ and for a spherical wave they give $a=0.58\pm 0.01$ and $b=0.65\pm 0.05.$ 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 ${\beta}_{0}^{2}$ and ${l}_{0}$ indeed factorizes as predicted, and each part behaves like a power law. However, our simulations for a plane wave give $a=0.57\pm 0.03,$
$b=0.33\pm 0.03,$ and $c=0.45\pm 0.06.$ For spherical waves we find $a=3.3\pm 0.3,$
$b=0.45\pm 0.05,$ and $c=0.8\pm 0.1.$

© 2000 Optical Society of America

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