Analysis of angle of arrival fluctuations for optical waves’ propagation through weak anisotropic non-Kolmogorov turbulence

Abstract

Analytical expressions for the variance of angle of arrival (AOA) fluctuations based on the Rytov approximation theory are derived for plane and spherical waves' propagation through weak anisotropic non-Kolmogorov turbulence atmosphere. The anisotropic spectrum model based on the assumption of circular symmetry in the orthogonal plane throughout the path is adopted and it includes the same degree of anisotropy along the direction of propagation for all the turbulence cells size in the inertial sub-range. The derived expressions consider a single anisotropic coefficient describing the turbulence anisotropic property and a general spectral power law value in the range 3 to 4. They reduce correctly to the previously published analytic expressions for the cases of plane and spherical waves' propagation through weak isotropic non-Kolmogorov turbulence for the special case of anisotropic factor equaling one. To reduce the complexity of the analytical results, the asymptotic-fit expressions are also derived and they fit well with the close-form ones. These results are useful for understanding the potential impact of deviations from the standard isotropic non-Kolmogorov turbulence atmosphere.

Two-frequency mutual coherence function for Gaussian-beam pulses propagating along a horizontal path in weak anisotropic atmospheric turbulence

“…(8), (21), and (26) leads to a closed-form expression for the near-field two-frequency MCF of Gaussian-beam pulses propagating along a horizontal line-ofsight path in anisotropic atmospheric turbulence, Similarly, its far-field counterpart is given by the combination of Eqs. (8), (22), and (26).…”

“…As a result, numerous efforts have been made to understand the effects of anisotropy of turbulence on various aspects of optical-wave propagation including beam wander, beam broadening, angleof-arrival fluctuations, scintillations, log-amplitude correlation function, and so on [15][16][17][18][19][20][21]. Also, the impact of anisotropy on temporal broadening of narrowband optical pulses has recently been investigated in the strong-turbulence limit [10].…”

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.…”

“…For weak anisotropic non-Kolmogorov turbulence, the researchers have derived theoretically a series of turbulence effects models, including the long-term beam spread, variance of irradiance fluctuations, log-amplitude correlation function (it equals one fourth of the spatial covariance function of irradiance fluctuations), variance of AOA fluctuations, and modulation transfer function [18][19][20][21][22]. When turbulence strength increases beyond the weak turbulence regime, Andrews et al [23] developed several mathematical turbulence effect models (longterm spot size, spatial coherence radius, and variance of irradiance fluctuations) for Gaussian beam propagating through moderate to strong anisotropic non-Kolmogorov turbulence.…”

“…When turbulence strength increases beyond the weak turbulence regime, Andrews et al [23] developed several mathematical turbulence effect models (longterm spot size, spatial coherence radius, and variance of irradiance fluctuations) for Gaussian beam propagating through moderate to strong anisotropic non-Kolmogorov turbulence. References [18,[21][22][23] adopt the assumption of circular symmetry of turbulence cells in the orthogonal xy-plane throughout the path and the same degree of anisotropy along the propagation direction for all the turbulence cells. The closed-form expressions (composed of specific mathematical functions) were obtained eventually.…”