Analytical expressions for the log-amplitude correlation function of a plane wave through anisotropic atmospheric refractive turbulence

Abstract

The effect of anisotropic Kolmogorov turbulence on the log-amplitude correlation function for plane-wave fields is investigated using analysis, numerical integration, and simulation. A new analytical expression for the log-amplitude correlation function is derived for anisotropic Kolmogorov turbulence. The analytic results, based on the Rytov approximation, agree well with a more general wave-optics simulation based on the Fresnel approximation as well as with numerical evaluations, for low and moderate strengths of turbulence. The new expression reduces correctly to previously published analytic expressions for isotropic turbulence. The final results indicate that, as asymmetry becomes greater, the Rytov variance deviates from that given by the standard formula. This deviation becomes greater with stronger turbulence, up to moderate turbulence strengths. The anisotropic effects on the log-amplitude correlation function are dominant when the separation of the points is within the Fresnel length. In the direction of stronger turbulence, there is an enhanced dip in the correlation function at a separation close to the Fresnel length. The dip is diminished in the weak-turbulence axis, suggesting that energy redistribution via focusing and defocusing is dominated by the strong-turbulence axis. The new analytical expression is useful when anisotropy is observed in relevant experiments.

Analytical expressions for the log-amplitude correlation function for spherical wave propagation through anisotropic non-Kolmogorov atmosphere

“…Using the approach of Mellin transforms pioneered by Sasiela [9], our development follows that of our previous two papers on plane waves in the same context [7,8]. We present only key steps in the analysis, leaving a large but routine amount of algebra for the reader.…”

“…However, results from laser wave propagation experiments in the past along horizontal paths near the ground, and more recently over very long paths as well as vertical paths, show that the atmospheric turbulence can deviate from the standard isotropic Kolmogorov spectrum [5,6]. In our previous papers on this subject [7,8], we developed analytical expressions for the log-amplitude correlation of a plane wave that is valid in the low to moderate regimes of integrated path turbulence, for fixed turbulence strength along the path. In this paper, we develop a similar general expression for the log-amplitude correlation of a spherical wave propagating through anisotropic non-Kolmogorov turbulent atmosphere.…”

“…The new expression is useful for estimating the effects of deviations from the standard isotropic Kolmogorov spectrum, especially in field-site experiments. It is noted that many references included in our earlier papers [7,8] are omitted in order keep this paper concise.…”

Average Polarization of Electromagnetic Gaussian Schell-Model Beams through Anisotropic Non-Kolmogorov Turbulence

“…In this paper we employ the anisotropic non-Kolmogorov power spectrum reported in [10], [11] for marine/terrene-atmosphere by using generalized von Karman model [10], [12], marine/terrene-atmosphere model [18], [20]. According to the discussion in [9], we apply the approximation of the anisotropy existing along the direction of propagation (z axis) of the beam, and by the discussions in [21] for the spectral model of non-Kolmogorov atmospheric turbulence [20], the power spectrum of refractiveindex fluctuations of non-Kolmogorov turbulence can be expressed as [18] …”

“…Toselli et al proposed power spectrum models of non-Kolmogorov turbulence to theoretically investigate the effect of anisotropy [9] and analyzed the impact of the spectral index variations on the long-term beam spread and scintillation index of the plane wave and spherical wave for several anisotropic coefficient values ζ [10] in the weak turbulence condition. The effect of anisotropic Kolmogorov turbulence on the log-amplitude correlation function for plane wave and spherical wave fields is investigated in [11], [12]. Yao et al explored the effects of the anisotropic parameter on the spectral density, the spectral degree of coherence and on the spectral degree of polarization of the GSM beam [13].…”