Irradiance-variance behavior by numerical simulation for plane-wave and spherical-wave optical propagation through strong turbulence

We have simulated optical propagation through atmospheric turbulence in whi ch 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 propagat ion 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 i rradiance 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 drama tically different from the analytic predictions. Let sigma(1)(2) - 1 = a(be ta(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 simu lation region. For zero inner scale (for which c = 0), the analytic predict ion is b = 0.4 and a = 0.17 (0.37) for a plane (spherical) wave. Our simula tions 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 approx imation the behavior with beta(0)(2) and l(0) indeed factorizes as predicte d, and each part behaves like a power law. However, our simulations for a p lane 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 +/- 0.06, and c = 0.8 +/ - 0.1. (C) 2000 Optical Society of America [S0740-3232(00)02006-8].