non-Kolmogorov Atmospheric Turbulence Research Articles

Influence of non-Kolmogorov atmospheric turbulence on the beam quality of vortex beams.

Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function (WDF), the analytical expressions for the propagation factors (M2-factors) and Strehl ratio SR of the Gaussian Schell-model (GSM) vortex beams and GSM non-vortex beams propagation through non-Kolmogorov atmospheric turbulence are derived, and used to study the influence of non-Kolmogorov atmospheric turbulence on beam quality of the GSM vortex beams. It is shown that the smaller the generalized structure constant and the outer scale of turbulence are, and the bigger the inner scale of turbulence is, the smaller the normalized propagation factor is, the bigger the Strehl ratio is, and the better the beam quality of GSM vortex beams in atmospheric turbulence is. The variation of beam quality with the generalized exponent α is nonmonotonic, when α = 3.11, the beam quality of the GSM vortex beams is the poorest through non-Kolmogorov atmospheric turbulence. GSM vortex beams is less affected by turbulence than GSM non-vortex beams under certain condition, and will be useful in long-distance free-space optical communications.

Influence of atmospheric turbulence on the properties of specular and antispecular beams.

A class of optical fields with specular or antispecular properties can be generated by a Gaussian Schell-model beam passing through a wavefront-folding interferometer. Based on the generalized diffraction integral formula, an analytical expression for the cross-spectral density function of such fields propagating through non-Kolmogorov atmospheric turbulence is derived. It is revealed that the specular and antispecular properties of the beams always maintain during propagation in free space. However, the specularity and antispecularity properties of the beams become different in atmosphere, since they are quickly destroyed by the atmospheric turbulence.

Propagation properties and turbulence distance of partially coherent Sinh-Gaussian beams in non-Kolmogorov atmospheric turbulence

Propagation properties including mean-squared beam width, mean-squared angular spreading, beam propagation M2-factor and turbulence distance of partially coherent Sinh-Gaussian (ShG) beams in non-Kolmogorov atmospheric turbulence have been investigated. With a non-Kolmogorov spectrum, the analytical formulas for the mean-squared beam width, angular spreading and M2-factor have been derived in non-Kolmogorov turbulence. The impact of the turbulent parameter (spectral index, inner scale and outer scale) and the decentered parameter on partially coherent ShG beams is discussed by numerical methods. It can be shown that the mean-squared beam width, angular spreading and M2-factor increase then decrease with increasing spectral index from 3 to 4; and they decrease with increasing inner scale and decreasing outer scale. The turbulence distance decreases then increases with increasing spectral index, and increases with increasing inner scale and decreasing outer scale. In addition, the mean-squared beam width and the M2-factor decrease then increase and exist a minimum values with increasing decentered parameter, while the turbulence distance increases monotonously.

Angle of arrival fluctuations of optical waves considering finite turbulence outer scale under anisotropic turbulence

In this work, new analytic expressions for the variance of angle of arrival (AOA) fluctuations are derived based on the Rytov theory for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. In the derivations, the concept of anisotropy at different turbulence cells is considered and the finite turbulence outer scale is included. Deviations from the classic 11/3 spectral power law behavior for Kolmogorov turbulence are also allowed by assuming spectral power law value variations between 3 and 4. The derived analytic expressions can reduce correctly to the previously published results for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov turbulence in the special case of the finite turbulence inner and outer scales equaling separately zero and infinite. Calculations are performed to analyze the influences of anisotropic non-Kolmogorov turbulence on the derived analytic results.

Scintillation and aperture averaging for Gaussian beams through non-Kolmogorov maritime atmospheric turbulence channels.

Analytic expression of the receiver-aperture-averaged scintillation index (SI) was derived for Gaussian-beam waves propagating through non-Kolmogorov maritime atmospheric environment by establishing a generalized maritime atmospheric spectrum model. The error performance of an intensity-modulated and direct-detection (IM/DD) free-space optical (FSO) system was investigated using the derived SI and log-normal distribution. The combined effects of non-Kolmogorov power-law exponent, turbulence inner scale, structure parameter, propagation distance, receiver aperture, and wavelength were also evaluated. Results show that inner scale and power-law exponent obviously affect SI. Large wavelength and receiver aperture can mitigate the effects of turbulence. The proposed model can be evaluated ship-to-ship/shore FSO system performance.

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.

Intensity distribution and spectral degree of coherence for array beams in non-Kolmogorov atmospheric turbulence

The propagation expressions of the intensity distribution and the spectral degree of coherence for radial array Gaussian Schell-model beams in non-Kolmogorov atmospheric turbulence have been derived. There exists a maximum of the on-axis intensity for radial array beams on propagation. The optimal propagation distance where the maximum appears has been analyzed in detail. The influence of the generalized structure constant and the initial spatial coherence parameter for the correlated superposition beam is different from the uncorrelated one. In particular, the on-axis intensity maximum exhibits a minimum when the generalized exponent α = 3.1. The spectral degree of coherence for the correlated superposition beam is larger than the uncorrelated one, and the difference between the two superposition styles becomes larger when the spatial coherence parameter becomes larger and the turbulence becomes weaker. Moreover, when α = 3.1 the spectral degree of coherence exhibits a minimum.

Temporal power spectra of angle of arrival fluctuations for optical waves propagating through moderate-to-strong non-Kolmogorov refractive turbulence

The temporal statistical property of angle of arrival (AOA) fluctuations is investigated in detail both analytically and numerically. New analytic expressions for the temporal power spectra of AOA fluctuations are derived with the extended Rytov theory for both plane and spherical waves propagating through moderate-to-strong (or strong) non-Kolmogorov atmospheric turbulence. They cover a more wide range of turbulence strength, and can reduce correctly to previously published analytic expressions for the weak non-Kolmogorov turbulence case. The final results indicate that, as turbulence strength increases up to moderate-to-strong (or strong) turbulence regime, the expressions derived in this work deviates from those obtained via the Rytov theory and the discrepancy increases with the increased turbulence strength. These results are useful for the understanding the potential impact of derivations from the standard non-Kolmogorov spectrum.

Multimode Laser Beam Scintillations in Non-Kolmogorov Turbulence

Employing the Rytov solution, the scintillation index at the origin of the receiver plane is evaluated in non-Kolmogorov weak atmospheric turbulence when multimode laser incidence is used. The solution presented can be used when the multimode is composed of even modes. The novelty of this work lies in the theoretical combination of multimode laser beam excitation and non-Kolmogorov turbulence in the scintillation evaluations, which is not known both theoretically and experimentally. The study involves mathematical rigor but no experimental results. Being valid for any power law exponent of the non-Kolmogorov turbulence, the scintillations of the multimode beams are found to be smaller than the scintillation index of a single Gaussian beam. For the multimode laser beam excitation, the scintillation index is smaller at smaller power law exponent values. If the multimode content is formed by beams with larger mode numbers, the scintillations decrease for any non-Kolmogorov realization. When large sized beams are used in the multimode, the scintillations increase as compared to small sized content, and the scintillations become almost the same as the Gaussian beam scintillations. Comparing the multimode structures that have the same number of beams, the ones with higher order modes yield smaller scintillations, and for such multimode structures, very similar scintillation index behaviour versus the power law exponent can be obtained by varying the amplitudes of the modes composing the multimode. The main contribution of this paper is the formulation and evaluation of the scintillation noise in order to understand whether the use of multimode laser excitation will improve the link performance of optical wireless communication systems operating in a non-Kolmogorov atmosphere.

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.

Wave structure function and long-exposure MTF for laser beam propagation through non-Kolmogorov turbulence

Abstract The degrading effects of atmospheric turbulence on an imaging system can be characterized by the atmospheric modulation transfer function (MTF). In this paper, we derived analytically a new expression for the wave structure function (WSF) of a Gaussian-beam based on the weak fluctuation theory. We assumed the beam-wave is propagating through a horizontal path experiencing isotropic and homogeneous non-Kolmogorov atmospheric turbulence where the power spectrum has a generalized spectral power-law exponent which varies between 3 and 4 instead of the fixed classical Kolmogorov power-law exponent of 11/3. Using the WSF, we derived mathematical expressions for the spatial coherence radius and the long-exposure turbulence MTF of the Gaussian-beam wave. These new expressions were used to analyze the influence of power-law variations and beam sizes on the WSF and quality of imaging systems. The simulation results show that different exponent values produce varying effects on both WSF and imaging systems.

Fiber coupling efficiency for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.

Nowadays it has been accepted that the Kolmogorov model is not the only possible turbulent one in the atmosphere, which has been confirmed by the increasing experimental evidence and some results of theoretical investigation. This has prompted the scientist community to study optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, using the method of effective beam parameters and a non-Kolmogorov power spectrum which has a more general power law instead of standard Kolmogorov power law value 11/3 and a more general amplitude factor instead of constant value 0.033, the fiber coupling efficiency for a Gaussian-beam wave has been derived for a horizontal path in both weak and strong fluctuation regimes. And then the influence of spectral power law variations on the fiber coupling efficiency has been analyzed. It is anticipated that this work is helpful to the investigations of atmospheric turbulence and optical wave propagation in the atmospheric turbulence.

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.

Classification of coherent vortices creation and distance of topological charge conservation in non-Kolmogorov atmospheric turbulence.

The analytical expressions for the cross-spectral density function of partially coherent sinh-Gaussian (ShG) vortex beams propagating through free space and non-Kolmogorov atmospheric turbulence are derived, and used to study the classification of coherent vortices creation and distance of topological charge conservation. With the increment of the general structure constant and the waist width, as well as the decrement of the general exponent, the inner scale of turbulence and spatial correlation length, the distance of topological charge conservation will decrease, whereas the outer scale of turbulence and the Sh-part parameter have no effect on the distance of topological charge conservation. According to the creation, the coherent vortices are grouped into three classes: the first is the inherent coherent vortices of the vortex beams, the second is created by the vortex beams when propagating through free space, and the third is created by the atmospheric turbulence inducing the vortex beams.

Temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.

In the past decades, both the increasing experimental evidence and some results of theoretical investigation on non-Kolmogorov turbulence have been reported. This has prompted the study of optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, based on the thin phase screen model and a non-Kolmogorov power spectrum which owns a generalized power law instead of standard Kolmogorov power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave is derived in the weak fluctuation regime for a horizontal path. The analytic expressions are obtained and then used to analyze the influence of spectral power law variations on the temporal power spectrum of irradiance fluctuations.

Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beams through non-Kolmogorov turbulence.

Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian (PCESHG) vortex beams through non-Kolmogorov atmospheric turbulence, including the spectral degree of polarization and evolution behavior of coherent vortices and average intensity are investigated in detail by using the extended Huygens-Fresnel principle and the spatial power spectrum of the refractive index of non-Kolmogorov turbulence. It is shown that the motion, creation and annihilation of the coherent vortices of PCESHG vortex beams in non-Kolmogorov turbulence may appear with the increasing propagation distance, and the distance for the conservation of the topological charge depends on the turbulence parameters and beam parameters. In additions, the evolution behavior of coherent vortices, average intensity and spectral degree of polarization vary significantly for different values of the generalized exponent parameter and the generalized refractive-index structure parameter of non-Kolmogorov turbulence, and the beam parameters as well as the propagation distance.

激光通过非Kolmogorov大气湍流传输光束扩展区间的研究

激光通过非Kolmogorov大气湍流传输光束扩展区间的研究

Two-Frequency Mutual Coherence Function of a Gaussian Beam Pulse Propagated Through Non-Kolmogorov Turbulent Atmosphere

Over the past half century, satellite-laser-communication technology has been the focus in many countries and areas due to its higher data transmission rates, smaller terminals, low probability of intercept, etc. Much manpower and material and financial resources have been put into the development of this technology. Usually, longer pulses can be modeled as if they were continuous-wave pulses during the time when the pulse is transmitted. However, this is not the case for ultrashort pulses that are usually used as a carrier in satellite-laser communication. For satellite-to-ground or ground-to-satellite links, the atmospheric effects are more deleterious to the laser pulse and their analysis is also more complicated. For a long time, laser pulse propagation in the turbulent atmosphere were studied based on the Kolmogorov model. However, increasing experimental evidence and theoretical investigations have shown that the Kolmogorov model is not the only possible turbulent one in the atmosphere, and there exists another turbulence, namely, the non-Kolmogorov turbulence. So it is necessary to perform the analysis of the laser-pulse propagation in the non-Kolmogorov turbulence. The two-frequency mutual coherence function (MCF) plays an important pole in determining the basic characteristics associated with the laser-pulse propagating in the atmospheric turbulence. In this paper, we consider a theoretical power spectrum of the refractive-index fluctuations with a generalized power law, derive the two-frequency MCFs of a Gaussian-beam pulse in weak turbulence for a horizontal path, and analyze the influence of spectral power-law variations on the two-frequency MCFs. We present an analytical expression for a collimated-beam pulse.

一般非Kolmogorov大气湍流路径上平面波闪烁的数值模拟分析

一般非Kolmogorov大气湍流路径上平面波闪烁的数值模拟分析