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

Abstract

An analytical expression for the log-amplitude correlation function based on the Rytov approximation is derived for spherical wave propagation through an anisotropic non-Kolmogorov refractive turbulent atmosphere. The expression reduces correctly to the previously published analytic expressions for the case of spherical wave propagation through isotropic Kolmogorov turbulence. These results agree well with a wave-optics simulation based on the more general Fresnel approximation, as well as with numerical evaluations, for low-to-moderate strengths of turbulence. These results are useful for understanding the potential impact of deviations from the standard isotropic Kolmogorov spectrum.

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].…”

Analysis of temporal power spectra for optical waves propagating through weak anisotropic non-Kolmogorov turbulence

“…Theoretical expressions for the temporal power spectra of optical waves have been derived for weak and moderate to strong isotropic nonKolmogorov turbulence [7,8]. However, both experimental and theoretical results have shown that the atmospheric turbulence can also be anisotropic [3,[9][10][11][12][13][14][15][16][17][18][19][20][21]. Grechko et al [11] reported a strong anisotropy in the middle atmosphere from experimental observations of star scintillation.…”

“…Experimental measurements [10] have shown that the outer scale of turbulence in the horizontal direction can be many times larger than in the vertical direction. The horizontal size of these eddies (or cells) is typically tens of meters across or, in some cases, kilometers across [20]. Anisotropy is usually present at high altitude, above the atmospheric boundary layer, which extends to about 2 km in altitude and it is more evident for large turbulence cells or eddies [20].…”

“…The horizontal size of these eddies (or cells) is typically tens of meters across or, in some cases, kilometers across [20]. Anisotropy is usually present at high altitude, above the atmospheric boundary layer, which extends to about 2 km in altitude and it is more evident for large turbulence cells or eddies [20]. Anisotropy also can be present at a few meters above the ground [9].…”