Average spreading and directionality of broadband partially coherent beam in non-Kolmogorov turbulence

The average spreading and directionality of broadband partially coherent beam (BPCB) in non-Kolmogorov turbulence is studied. The effects of exponent value α, propagation distance, spectrum width, inner and outer scale parameters is studied in detail. Numerical calculation reveals that the beam width increases with the increasing in spectrum bandwidth just like when propagating in Kolmogorov turbulence, however, the beam width may vary as much as by a factor of 50% with different α. The difference in beam width between monochromatic partially coherent beam (MPCB) and BPCB at the receiving plane may vary from 2% to 10% with different α. The angular spreading is more sensitive to α than the spectrum bandwidth; also it is more sensitive to the inner scale parameters than the outer scale parameter.     

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.     

Annular beam scintillations in non-Kolmogorov weak turbulence

In a weakly turbulent atmosphere governed by the non-Kolmogorov spectrum, the on-axis scintillation index is formulated and evaluated when the incidence is an annular Gaussian type. When the power law of the non-Kolmogorov spectrum is varied, the scintillation index first increases, and reaches a peak value, then starts to decrease, and eventually approaches zero. The general trend is that when turbulence has a non-Kolmogorov spectrum with power law larger than the Kolmogorov power law, the scintillation index values become smaller. For all power laws, collimated annular Gaussian beams exhibit smaller scintillations when compared to pure Gaussian beams of the same size. Intensity fluctuations at a fixed propagation distance diminish for the non-Kolmogorov spectrum with a very large power law, irrespective of the focal length and the thickness of optical annular Gaussian sources.     

非Kolmogorov大气湍流对高斯列阵光束扩展的影响

本文推导出了高斯列阵光束在非Kolmogorov大气湍流中传输的瑞利区间zR、湍流距离zT和远场发散角θ的解析表达式,研究了非Kolmogorov湍流的广义指数α和列阵光束的合成方式对高斯列阵光束扩展的影响.研究表明:不论相干还是非相干合成高斯列阵光束,zR,zT和θ均随着α的增加而呈非单调变化.当α=3.108时,zR和zT取极小值,而θ取极大值,即当α=3.108时高斯列阵光束扩展最厉害,光束扩展受湍流影响也最厉害.非相干合成高斯列阵光束扩展比相干合成的要大,但受非Kolmogorov湍流影响却要小.特别值得指出的是:当自由空间光束衍射较小时,有zTzR,即在瑞利区间范围内大气湍流就对光束扩展有影响;而当自由空间光束衍射较大时,有zTzR,即在瑞利区间范围内大气湍流对光束扩展几乎没有影响.     

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.     

Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle and the first-order approximation of wave structure function, an analytical expression for the average intensity of flattened Gaussian beam (FGB) in non-Kolmogorov turbulence has been derived. The variations of normalized intensity with some parameters, such as wave coherence length, Fresnel number, waist width and the order of FGB are investigated in detail.     

The effect of non-Kolmogorov turbulence on the propagation of cosh-Gaussian beam

The propagation of cosh-Gaussian beam in turbulence with different power spectral density of refractive index is investigated. By using the expansion of mutual coherence function in Taylor series, analytical expression for the average intensity is presented. With the help of this expression, the intensity profiles with different parameters are analyzed. Relative errors of the analytical expression are studied, and the effects of power spectral density on beam spreading and evolvement are discussed in details. It shows that the analytical expression should provide reasonable approximations to study the propagation of cosh-Gaussian in non-Obukhov-Kolmogorov turbulence.     

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.     

A further study on the spreading and directionality of Gaussian array beams in non-Kolmogorov turbulence

It is found that in free space, the curves of the mean-squared beam width may each have a cross point at a certain propagation distance Zc. For Gaussian array beams, the analytical expressions of zc are derived. For the coherent com- bination, Zc is larger than that for the incoherent combination. However, in non-Kolmogorov turbulence, the cross point disappears, and the Gaussian array beams will have the same directionality in terms of the angular spread. Furthermore, a short propagation distance is needed to reach the same directionality when the generalized exponent is equal to 3.108. In particular, it is shown that the condition obtained in previous studies is not necessary for laser beams to have the same directionality in turbulence, which is explained physically. On the other hand, the relative average intensity distributions at the position where the Gaussian array beams have the same mean-squared beam width are also examined.     

大气湍流对激光通信系统的影响

从分析激光在大气湍流场中的传输方程出发,忽略系统中的其它噪声,仅考虑由大气喘流引起的系统误码率,讨论了激光信号在传输过程中的振幅起伏以及强度起伏;推导出由大气湍流引起的光强起伏和系统误码率的关系,结果表明:在弱起伏条件下,对于系统误码率为10－9以下的要求,光强起伏应小于0.67;随着湍流强度C2n的增大,误码率增加很快;采用长波长的激光进行传输可以有效地降低系统误码率.     

Beam propagation factor of radial Gaussian-Schell model beam array in non-Kolmogorov turbulence

The analytical expression for the beam propagation factor (M²-factor) of a radial Gaussian-Schell model (GSM) beam array propagating in non-Kolmogorov turbulence is derived. The influences of beam number, ring radius and generalized exponent on the M²-factor are investigated. The results indicate that the M²-factor has great dependence on the generalized exponent and the beam number. Moreover, there is an optimum ring radius, which leads to a minimum M²-factor and increases with increase in beam number. Further, the M²-factor for the superposition of the intensity is larger than that for the superposition of the cross-spectral density function (CSDF). However, the M²-factor for the superposition of the intensity is less sensitive to the turbulence than that for the superposition of the CSDF.     

Effect of absorption on the spreading of a laser beam

The propagation characteristics of the fundamental Gaussian laser beam in absorptive and active media are investigated. There is a general reduction in the spreading of the beam on propagation in both absorptive and active media. In addition, in an active medium there is a shift of the focal plane and a reduction in the waist size of the beam.     

Effect of the outer scale on the angle of arrival variance for free-space-laser beam corrugated by non-Kolmogorov turbulence

It is well known that atmospheric turbulence causes significant variations of the arrival angle of laser beams used in free-space communications. Usually, angle-of-arrival fluctuations of an optical wave in the plane of the receiver aperture is calculated by Kolmogorov’s power spectral-density model. Unfortunately, recently increasing experimental evidence has shown that atmospheric turbulence statistics does not obey Kolmogorov’s power spectrum model in some parts of the troposphere and stratosphere. These experiments have prompted investigations of the optical-wave propagation through atmospheric turbulence described by nonclassical power spectra. In this paper, employing a new approach and considering a non-Kolmogorov power spectrum with a generalized power law instead of the constant standard power-law value 11/3 and a generalized amplitude factor instead of the constant value 0.033, we derive the variances of the angle-of-arrival fluctuations of the plane and spherical waves in a weak turbulence for the horizontal path. The concise closed-form expressions are obtained and used to analyze the influence of spectral power-law variations on the angle-of-arrival fluctuations. In addition, the outer scale effect is also analyzed.     

Beam propagation factor of partially coherent elegant Hermite-cosh-Gaussian beam through non-Kolmogorov turbulence

Based on the extended Huygens–Fresnel principle and the second moments of the Wigner distribution function, an analytical expression for the propagation factors of partially coherent elegant Hermite-cosh-Gaussian beams (EHChGB) in non-Kolmogorov is derived. The M² factor of partially coherent EHChGB through non-Kolmogorov turbulence is studied analytically and numerically. The results show that partially coherent EHCHGB with higher beam order and longer wavelengths is less affected by 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     

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。     

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。     

Further analysis of scintillation index for a laser beam propagating through moderate-to-strong non-Kolmogorov turbulence based on generalized effective atmospheric spectral model

A new expression of the scintillation index(SI) for a Gaussian-beam wave propagating through moderate-to-strong non-Kolmogorov turbulence is derived, using a generalized effective atmospheric spectrum and the extended Rytov approximation theory. Finite inner and outer scale parameters and high wave number "bump" are considered in the spectrum with a generalized spectral power law in the range of 3–4, instead of the fixed classical Kolmogorov power law of 11/3. The obtained SI expression is then used to analyze the effects of the spectral power law and the inner scale and outer scale on SI under various non-Kolmogorov fluctuation conditions. These results will be useful in future investigations of optical wave propagation through atmospheric turbulence.     

Phase compensation in non-Kolmogorov atmospheric turbulence

Zernike polynomial decompositions are used for investigating phase distortion induced by atmospheric turbulence in optical systems. Closed-form expression of the Zernike-coefficient variances is derived. The finite size of the receiver aperture is analyzed using the filter function which is also particularly effective in the theoretical analysis of lower-order aberrations like tilt terms and piston-removed phase variance. The outer scale of the non-Kolmogorov turbulence is considered. The result shows that the effect of finite outer scale attenuates low-order Zernike mode of optical distortion and longer outer scale can lead to more energy in the tilt terms. The generalized exponent can only enhance tilt terms and attenuate other Zernike modes of optical distortion. Further, for different outer scale and generalized exponent, the residual phase variance decreases with more modes of phase compensation.