Anisotropic non-Kolmogorov Turbulence Research Articles

Superimposed orbital angular momentum mode of multiple Hankel–Bessel beam propagation in anisotropic non-Kolmogorov turbulence

Mathematical models for the superimposed orbital angular momentum (OAM) mode of multiple Hankel–Bessel (HB) beams in anisotropic non-Kolmogorov turbulence are developed. The effects of anisotropic turbulence and source parameters on the mode detection spectrum of the superimposed OAM mode are analyzed. Anisotropic characteristics of the turbulence in the free atmosphere can enhance the performance of OAM-based communication. The HB beam is a good source for mitigating the turbulence effects due to its nondiffraction and self-focusing properties. Turbulence effects on the superimposed OAM mode can be effectively reduced by the appropriate allocation of OAM modes at the transmitter based on the reciprocal features of the mode cross talk.

Generalized anisotropic turbulence spectra and applications in the optical waves' propagation through anisotropic turbulence.

Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. In this work, two theoretical atmosphere refractive-index fluctuations spectral models are derived for optical waves propagating through anisotropic non-Kolmogorov atmospheric turbulence. They consider simultaneously the finite turbulence inner and outer scales and the asymmetric property of turbulence eddies in the orthogonal xy-plane throughout the path. Two anisotropy factors which parameterize the asymmetry of turbulence eddies in both horizontal and vertical directions are introduced in the orthogonal xy-plane, so that the circular symmetry assumption of turbulence eddies in the xy-plane is no longer required. Deviations from the classic 11/3 power law behavior in the spectrum model are also allowed by assuming power law value variations between 3 and 4. Based on the derived anisotropic spectral model and the Rytov approximation theory, expressions for the variance of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov turbulence. Calculations are performed to analyze the derived spectral models and the variance of AOA fluctuations.

Temporal frequency spread of optical wave propagation through anisotropic non-Kolmogorov turbulence

In this paper, we derive new analytic expressions for the atmospheric-induced frequency spread of optical plane and spherical waves propagating in a horizontal path and experiencing anisotropic non-Kolmogorov turbulence. The anisotropic spectrum model is based on the assumption that circular symmetry is maintained in the orthogonal xy-plane throughout the path and that it includes the same degree of anisotropy along the direction of propagation for all the turbulence cell sizes. These expressions are developed in the weak fluctuation region using the Rytov approximation method and are independent of the knowledge of the temporal mutual coherence function for the optical waves. We perform our analysis based on a generalized von Karman power spectrum of the index of refraction. The spectrum considers the effect of finite inner and outer scales of turbulence, together with a non-Kolmogorov spectral power exponent α that varies between 3–4. The simulation results show that the anisotropic parameter impacts on the frequency spread by a factor . Moreover the frequency spread is most significant for α values around 3.1.

Influence of asymmetry turbulence cells on the angle of arrival fluctuations of optical waves in anisotropic non-Kolmogorov turbulence.

Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. Very recent analyses of angle of arrival (AOA) fluctuations of an optical wave in anisotropic non-Kolmogorov turbulence have adopted the assumption that the propagation path was in the z-direction with circular symmetry of turbulence cells maintained in the orthogonal xy-plane throughout the path, and one single anisotropy factor was adopted in the orthogonal xy-plane to parameterize the asymmetry of turbulence cells or eddies in both horizontal and vertical directions. In this work, the circular symmetry assumption of turbulence cells or eddies in the orthogonal xy-plane is no longer required, and two anisotropy parameters are introduced in the orthogonal xy-plane to investigate the AOA fluctuations. In addition, deviations from the classic 11/3 spectral power law behavior for Kolmogorov turbulence are allowed by assuming spectral power law value variations between 3 and 4. With the Rytov approximation theory, new theoretical models for the variance of AOA fluctuations are developed for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. When the two anisotropic parameters are equal to each other, they reduce correctly to the recently published results (the circular symmetry assumption of turbulence cells or eddies in the orthogonal xy-plane was adopted). Furthermore, when these two anisotropic parameters equal one, they reduce correctly to the previously published analytic expressions for the cases of optical wave propagation through weak isotropic non-Kolmogorov turbulence.

Influence of anisotropic turbulence on the long-range imaging system by the MTF model

Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. In this paper, new analytic expressions for the anisotropic non-Kolmogorov turbulence modulation transfer function (MTF) based on Rytov approximation theory have been derived for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. Compared with the previously published results where the turbulence inner and outer scales were set separately to zero and infinite for calculation convenience, the concept of anisotropy at different turbulence cell scales and finite turbulence inner and outer scales are introduced to study the MTF models. Also, deviations from the classic 11/3 spectral power law behavior for Kolmogorov turbulence are allowed by assuming spectral power law value variations between 3 and 4. To reduce the complexity and calculation time of the analytic results, the asymptotic-fit expressions are also derived and they fit well with the closed-form ones. Calculations are performed to analyze the anisotropic non-Kolmogorov turbulence’s influence on the long-range imaging system.

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

Analytic expressions for the temporal power spectra of irradiance fluctuations and angle of arrival (AOA) fluctuations are derived for optical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. In the derivation, the anisotropic non-Kolmogorov spectrum is adopted, which adopts the assumption of circular symmetry in the orthogonal plane throughout the path and the same degree of anisotropy along the propagation direction for all the turbulence cells. The final expressions consider simultaneously the anisotropic factor and general spectral power law values. When the anisotropic factor equals one (corresponding to the isotropic turbulence), the derived temporal power spectral models have good consistency with the known results for the isotropic turbulence. Numerical calculations show that the increased anisotropic factor alleviates the atmospheric turbulence's influence on the final expressions.

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

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.

Atmospheric turbulence MTF for optical waves׳ propagation through anisotropic non-Kolmogorov atmospheric turbulence

Abstract The conventional investigations for atmospheric turbulence have assumed that the refractive-index fluctuations of atmosphere are statistically homogeneous and isotropic. Developments of experimental and theoretical investigations have shown that the isotropic turbulence generally exists near the ground, and in the free atmosphere layer above the ground the anisotropic turbulence appears. Hence, deviations from the previously published results obtained with the isotropic turbulence assumption are possible. In this study, new analytic expressions for the anisotropic atmospheric turbulence modulation transfer function (MTF) are derived for optical plane and spherical waves propagating through anisotropic non-Kolmogorov turbulence. They consider both an anisotropic coefficient and a general spectral power law value in the range 3 to 4. When the anisotropic coefficient equals one (corresponding to the isotropic turbulence), the new results obtained in this work can reduce correctly to the previously published analytic expressions under isotropic non-Kolmogorov turbulence. The derived MTF models physically describe the turbulence anisotropic property of high atmospheric layer. Numerical calculations show that with the increase of anisotropic factor which is proportional to the atmospheric layer altitude, the atmospheric turbulence produces less effect on the imaging system.