Effect of non-Kolmogorov turbulence on beam spreading in satellite laser communication

In the past half a century, satellite laser communication has caught the attention of scientists due to its distinct advantages in comparison with conventional satellite microwave communication. For ground-to-satellite and satellite-to-ground data links, the atmosphere is a part of the communication channel; thus, atmospheric turbulence severely degrades the performance of satellite laser communication systems. In general, the Kolmogorov turbulence model is used to study the effect of atmosphere turbulence on satellite laser communications since it has been confirmed by numerous direct measurements of temperature and humidity fluctuations in the atmospheric boundary layer. However, increasing experimental evidence and theoretical investigations have shown that the Kolmogorov theory is sometimes inadequate to describe atmospheric statistics properly, in particular, in some domains of the atmosphere. We analyze the joint influence of Kolmogorov turbulence from the ground to 6 km and non-Kolmogorov turbulence above 6 km on the spot size associated with the uplink and downlink propagation channels for a satellite laser communication system in the geosynchronous orbit, using a power spectrum of non-Kolmogorov turbulence with power law ?5 that describes the refractiveindex fluctuations in the atmosphere above 6 km and considering the combined power spectrum of Kolmogorov and non-Kolmogorov turbulence. Before this analysis, we study the joint influence of the Kolmogorov turbulence from the ground to 6 km and non-Kolmogorov turbulence above 6 km on the scintillation indices of laser beams.     

Influence of non-kolmogorov turbulence on intensity fluctuations in laser satellite communication

Satellite laser communication holds the potential for high-bandwidth communication, but the atmosphere can significantly affect the capability of this type of communication systems for satellite-toground and ground-to-satellite data links to transfer information consistently and operate effectively. Usually the influence of atmosphere on satellite laser communication is investigated based on the Kolmogorov turbulence model. However, both increasing experimental evidence and theoretical investigations have shown that the Kolmogorov theory is sometimes incomplete to describe the atmospheric statistics properly, in particular, in some portions of the atmosphere. Considering a non-Kolmogorov turbulent power spectrum with power law −5 that describes the refractive-index fluctuations in the atmosphere above 6 km, we calculate the scintillation index of a lowest-order Gaussian-beam wave under the weak-fluctuation condition. Then, considering a combined power spectrum of refractiveindex fluctuations and using the expression obtained, we analyze the joint influence of the Kolmogorov turbulence from the ground to 6 km and non-Kolmogorov turbulence above 6 km on the scintillation indices of laser beams used in ground-to-satellite and satellite-to-ground laser communication links. We show that the scintillation index in satellite laser communication is equal to the sum of the scintillation indices induced by the Kolmogorov turbulence from ground to 6 km and that caused by the non-Kolmogorov turbulence above 6 km. Also we investigate variations of the scintillation index with the beam radius on the transmitter, wavelength, the radial distance, and zenith angle. Finally, comparing the scintillation index induced by these two turbulences with the conventional results, we show that the scintillation index induced by these two turbulences is a bit smaller than the conventional results.     

非柯尔莫哥洛夫湍流光束漂移的理论研究

一直以来, 大气湍流对空间光通信影响的研究都是在柯尔莫哥洛夫(Kolmogolov)湍流理论的框架内进行, 该模型已经被人们广泛接受和使用。然而, 近年来国内外众多非柯尔莫哥洛夫(Non-Kolmogolov)湍流的实验报道则表明Kolmogolov湍流理论有时不能完全正确地描述大气湍流的统计规律, 尤其在对流顶层和平流层。为了全面了解大气湍流对空间光通信的影响, 研究Non-Kolmogolov湍流对光波传输的影响成为了首先要面对的问题。基于Non-Kolmogolov湍流功率谱密度, 运用几何光学近似方法推导了弱起伏条件下准直光束和聚焦光束的光束漂移方差, 并给出了简洁的解析表达式; 然后, 利用这一表达式进行了仿真分析。     

Capacity for non-Kolmogorov turbulent optical links with beam wander and pointing errors

The performance of optical wireless communication links depends strongly on the atmospheric conditions and the parameters of the link such as the propagation distance, the operation wavelength, jitter variance, attenuation coefficient and effective beam spot radius at the receiver. The analytical expression for the evaluation of the average capacity of optical wireless communication systems is derived, using the gamma-gamma distribution in the non-Kolmogorov atmosphere turbulence. The impact of atmospheric attenuation, beam wander and pointing errors on the average of the optical wireless communication link is investigated. It is shown that the capacity has a fluctuation curve, when power law α increases, and the power law α of minimum point in fluctuation curve is bigger as the non-Kolmogorov turbulence strength is stronger.     

Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence

Atmospheric turbulence causes strong irradiance fluctuations of propagating optical wave under the severe weather conditions in long-distance free space optical communication. In this paper, the scintillation index for a Gaussian beam wave propagation through non-Kolmogorov turbulent atmosphere is derived in strong fluctuation regime, using non-Kolmogorov spectrum with a generalized power law exponent and the extended Rytov theory with a modified spatial filter function. The analytic expressions are obtained and then used to analyze the effect of power law, refractive-index structure parameter, propagation distance, phase radius of curvature, beam width and wavelength on scintillation index of Gaussian beam under the strong atmospheric turbulence. It shows that, with the increasing of structure parameter or propagation distance, scintillation index increases sharply up to the peak point and then decreases gradually toward unity at rates depending on power law. And there exist optimal value of radius of curvature and beam width for minimizing the value of scintillation index and long wavelength for mitigating the effect of non-Kolmogorov strong turbulence on link performance.     

Non-Kolmogorov湍流大气中小尺度热晕效应线性理论

从小尺度热晕线性理论出发,在non-Kolmogorov谱的基础上,得到了non-Kolmogorov谱湍流下热晕相位补偿的Strehl比表达式,分析了湍流谱对高能激光的相位补偿的影响.研究结果表明湍流谱对湍流热晕效应的相位补偿有重要的影响.在相同的湍流菲涅耳数下,当谱指数越接近于3时补偿效果越差,谱指数接近于4时补偿效果越好.在相同大气相干长度条件下或在相同湍流折射率常量条件下,当谱指数接近于3时,Strehl比随热晕效应的增强而下降变快,当湍流谱指数逐渐接近于4时,Strehl比下降速度变慢.其原因是随着湍流谱指数的增大,湍流热晕相互作用引起的对数振幅起伏增长变慢.     

LIDAR systems operating in a non-Kolmogorov turbulent atmosphere

ABSTRACT

It is well known that in free atmosphere the Kolmogorov power spectrum of the refractive index might not properly describe the actual turbulence behavior. In this paper, we use general non-Kolmogorov power spectrum for theoretical investigation of laser beam propagation in the double-passage problem: transmitter–target–receiver. The major application of our work is the Light Detection And Ranging (LIDAR) system operating at high altitudes, where non-Kolmogorov turbulence may be present. On confining ourselves to the weak turbulence regime, we show that the long-term average beam intensity profile, the long-term beam spread and the scintillation index are substantially affected by the non-Kolmogorov turbulent channels. Our analysis is valid for both bi-static and mono-static configurations, the latter leading to the enhanced backscattering effects.     

Angle of Arrival Fluctuations for Optical Waves Propagating Through Joint Moderate to Strong Atmospheric Turbulence

Satellite laser communication has gained wide attention both at home and abroad. The pointing, acquisition, and tracking (PAT) technology is the kernel of satellite laser communication systems, and the atmospheric layer is a part of the communication channel for satellite-to-ground links. Thus, angle of arrival (AOA) fluctuations caused by atmospheric turbulence inevitably influence long-distance satellite laser communication. Therefore, it is very important to analyze the impact of AOA fluctuations in satellite laser communication systems. According to the actual situation of satellite-to-ground links, a joint atmospheric turbulence power spectrum model is defined that includes Kolmogorov turbulence from the ground to 6 km in portions of the troposphere and non-Kolmogorov turbulence above 6 km in the stratosphere. Based on the extended Rytov theory, we derive the large-scale and small-scale variances of AOA fluctuations propagating in the uplink and downlink channels for a satellite laser communication system and analyze the influence of large zenith angle variations on the AOA fluctuations. It has long been a focus of concern that the expressions for the AOA variance obtained must be concise and of closed form.     

Average capacity for non-Kolmogorov turbulent slant optical links with beam wander corrected and pointing errors

The effects of beam wander corrected and pointing errors on the average capacity of a non-Kolmogorov turbulent atmosphere communication channel are studied. The gamma–gamma irradiance probability density function model has been considered to include the effects of non-Kolmogorov turbulence. An expression for the average capacity under beam wander corrected, pointing errors and the spectral index of refractive-index fluctuation. Simulation results for effects of circular detection aperture of radius, atmosphere turbulence strength and wavelength on average capacity are presented. Our results show that the average capacity has an oscillation in the case of short propagation distance, but in the case of long propagation distance, it has gradually reduced curves. And the turbulence strength has a strong influence on average capacity. In general, turbulence reduces the average capacity; it can reduce average capacity by increasing of the power law α. We can ignore the little effects of wavelength increases on the average capacity.     

Influence of Non-Kolmogorov Turbulence on Bit-Error Rates in Laser Satellite Communications

In satellite–ground laser communications, atmospheric turbulence in the link degrades the performance of the system, so it is very important to estimate its influence on the performance of the system. The bit-error rate (BER) is an important parameter to indicate the communication performance of the system, which is directly used to judge the quality of the communication system. Using the results of our two previous papers, we analyze the joint influence of Kolmogorov turbulence from the ground up to 6 km and non-Kolmogorov turbulence above 6 km on the BER. These kinds of turbulence are associated respectively with the uplink and the downlink propagation channels for the geosynchronous orbit satellite communication system.     

非Kolmogorov湍流相位屏仿真及对光束传输模拟的影响

采用正态分布模型来描述传播路径上功率谱幂值的非均匀性,利用功率谱反演法构建了基于等效结构常数的非Kolmogorov湍流相位屏,并利用多重相位屏法进行了高斯光束在均匀各向同性湍流与非Kolmogorov湍流两种模型下的传输模拟。通过观察模拟光束的光强均匀度、光束漂移以及闪烁指数等,研究了非Kolmogorov湍流对光束传输模拟的影响。结果发现,当光束通过单个非Kolmogorov相位屏时,光强最大值与光强均匀度随着幂值先增大后减小,光束漂移随幂值在一定范围内单调变化。当光束通过多重相位屏时,发现模拟光束的光强闪烁指数会受到相位屏数量以及湍流模型的影响,当相位屏数量较多时,均匀各向同性湍流模型下模拟得到的光强闪烁指数会大于非K湍流模型下的结果,且非K湍流模拟的光束漂移与均匀各项同性湍流模拟得到的光束漂移的相对误差会随着相位屏数量增多而趋于0。     

Capacity of wander and spread beams in log-normal distribution non-Kolmogorov turbulence optical links

We model the average channel capacity of optical wireless communication systems in weak turbulence horizontal channels, using the log-normal distribution models. The effects of beam wander and spread, pointing errors, turbulence inner scale, turbulence outer scale and the spectral index of non-Kolmogorov turbulence on system's performance are included. The model can evaluate the influence of the atmospheric turbulence conditions in the performance of a ground-to-train optical wireless communication system.     

Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence

In free-space optical communication links, atmospheric turbulence causes fluctuations in both the intensity and the phase of the received signal, affecting link performance.Influence of Kolmogorov and non-Kolmogorov turbulence statistics on laser communication links are analyzed for different propagation scenarios, and effects of different turbulence spectrum models on optical communication links are presented. Statistical estimates of the communication parameters such as the probability of fade (miss) exceeding a threshold dB level, the mean number of fades, and BER are derived and examples provided. The presented quantitative data suggest that the non-Kolmogorov turbulence effects on lasercom channels are more severe in many situations and need to be taken into account in wireless optical communication. Non-Kolmogorov turbulence is especially important for elevations above the boundary layer as well as for even low elevation paths over water.     

基于拉盖尔-高斯光束的通信系统在非Kolmogorov湍流中传输的系统容量

涡旋波束在大气湍流中的传输有非常重要的理论研究和实际应用意义. 本文基于利托夫近似和广义惠更斯-菲涅耳原理, 推导出拉盖尔-高斯(LG)光束在非Kolmogorov湍流中斜程传输时的螺旋谱, 并进一步推导出系统的容量. 对基于LG光束的通信系统容量进行了数值计算, 并对指数参数、光束波长、天顶角、湍流内尺度、外尺度、结构常数对系统容量的影响进行了分析比较. 本文的结论能够为LG光束在非Kolmogorov湍流中的通信提供一定的参考价值. 关键词： 拉盖尔-高斯光束 非Kolmogorov湍流 平均容量     

部分相干双曲正弦-Gauss涡旋光束叠加形成的合成相干涡旋在非 Kolmogorov 大气湍流中的动态演化

一些实验表明, 实际大气会偏离理想Kolmogorov模型. 本文基于广义Huygens-Fresnel原理和Toselli等提出的非Kolmogorov湍流模型, 推导出部分相干双曲正弦-Gauss (HSG)涡旋光束通过非Kolmogorov大气湍流的解析传输公式, 并用以对两束部分相干HSG涡旋光束相干叠加和非相干叠加形成的合成相干涡旋在非Kolmogorov大气湍流中的动态演化进行了研究. 结果表明, 合成光束平均光强的演化过程与非Kolmogorov湍流的广义指数α, 源平面上叠加涡旋光束拓扑电荷的符号, 以及叠加方式有关. 合成相干涡旋在非Kolmogorov大气湍流中传输时会出现移动、产生和湮灭. 广义指数α, 拓扑电荷符号, 以及叠加方式都会影响其演化行为. 最后, 将本文所得结果与相关文献做了比较.     

湍流大气传输高斯谢尔光束的到达角起伏

研究了在弱大气湍流起伏环境下以窄带宽高斯谢尔光束为激光光源的大气通信问题,分析了大气湍流强度和光源空间相干度对通信光束到达角起伏的影响.采用窄带宽光场的交叉谱密度函数代替光场互相干函数的近似方法和采用包含大气湍流内外尺度的简化折射率谱密度函数,得出了湍流大气中传输高斯谢尔光束的波结构函数(WSF) 和到达角起伏方差解析近似关系.分析表明,光源的空间相干度和传输光束的湍流扩展是影响高斯谢尔光束的相位起伏结构函数和传输光束到达角起伏的重要因素.     

采用大口径投影光学系统监测远场散斑特征参数

大口径投影光学系统采用低成本、大口径菲涅耳透镜制作,可将远场散斑强度分布投影到CCD成像探测器上。通过CCD图像处理,能够对给定孔径上的接收功率、闪烁指数进行量化评估;在接收孔径足够大、保障散斑不会因为光束漂移效应而脱离菲涅耳透镜的条件下,该系统还可以对光束漂移和特征半径进行量化评估。同时讨论了CCD像元响应非均匀性误差及其影响、CCD辐照响应函数和图像几何投影系数的定标方法。实验表明,系统能够对激光大气传输过程中的远场散斑特征参数进行监测。特别对自由空间激光通信系统而言,可以为大气衰减和多种大气湍流效应综合作用下的中值电平慢衰落研究和检测阈值优化设计提供实验数据支撑。     

Effect of non-kolmogorov turbulence on angle-of-arrival fluctuations of starlight

We revised a non-Kolmogorov turbulent power spectrum for the refractive-index fluctuations based on the consistency between the structure function and its power spectrum and the experimental data of recent lidar measurements. We investigate the joint influence of Kolmogorov turbulence from the ground up to 6 km and non-Kolmogorov turbulence above 6 km on the fluctuations in the angle of arrival (AOA) of starlight. WE show that the AOA fluctuations of starlight are mainly determined by Kolmogorov turbulence nearby the receiver. Non-Kolmogorov turbulence is responsible for 20–40% of the total AOA fluctuations for different apertures of the receiver. In addition, the AOA fluctuations induced by non-Kolmogorov turbulence depend on the receiver aperture, outer scale, and intensity of non-Kolmogorov turbulence.     

多色部分相干偏心光束在non-Kolmogorov湍流中的传输

推导了多色部分相干偏心光束在non-Kolmogorov 湍流中传输的总光强、轴上光谱、相干度的解析表达式, 研究了光束偏心参数β 、湍流广义指数α和源光谱带宽Ω对激光传输特性的影响. 研究表明: β越大, 则光束重心偏离传输轴越远, 相干度的不对称性越明显, 但是, β对轴上光谱几乎没有影响; 湍流广义指数α对总光强、 轴上光谱和相干长度的影响是非单调的, 当α=3.1时, 湍流对光束传输特性的影响最大. 值得指出的是: 在某些传输距离处, 不同α对应的轴上光谱位移量相同; 在某些传输距离处, 轴上光谱位移量为零, 且该传输距离与Ω无关, 但湍流使得该传输距离缩短. 所得结论对多色部分相干偏心光束在 湍流大气中传输的相关应用具有重要意义. 关键词： non-Kolmogorov湍流 多色部分相干偏心光束 光谱强度 相干度     

Analysis of the temporal power spectral models of angel of arrival fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

New analytical expressions for the temporal power spectral models of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through weak non-Kolmogorov turbulence. They consider the finite turbulence inner and outer scales, and have a general power law value in the range of 3–4 instead of the standard power law value of 11/3. The results derived in this work can reduce correctly to the previously published analytic expressions for the case of plane and spherical waves propagation through Kolmogorov turbulence case. These results are useful for the understanding the potential impact of derivations from the standard Kolmogorov spectrum.