A marine atmospheric spectrum for laser propagation

Most refractive index power spectral models currently used in atmospheric optical propagation studies were developed for terrestrial or high altitude environments. The current paper presents a new atmospheric spectral model for the marine environment. An analytical marine atmospheric spectrum is formulated to fit a numerical spectrum with the help of the downhill simplex algorithm. Theoretical irradiance fluctuation expressions are derived from the new spectrum for plane and spherical waves in weak optical turbulence. Comparisons are made between the existing scintillation theory and the new expressions developed for the marine environment, and the comparative advantage of the model is discussed. The results suggest that the current models are adequate for modeling the marine atmosphere in weak optical turbulence for small values of the inner scale of turbulence.     

Expressions of the scintillation index for optical waves propagating through weak non-Kolmogorov turbulence based on the generalized atmospheric spectral model

The high frequency “bump” which occurs in the turbulence spectral model just prior to the turbulence cell dissipation is important for the analysis of the irradiance scintillation for optical wave propagating through atmospheric turbulence. In this study, expressions of the irradiance scintillation index are developed from the generalized modified atmospheric spectral model for optical waves propagating through weak non-Kolmogorov turbulence. Compared with the expressions of the irradiance scintillation index derived from the general non-Kolmogorov spectral model, the new expressions can consider the influences of finite turbulence inner and outer scales and the influence of finite diameter aperture receiver. As the irradiance scintillation is caused mainly by the small scale turbulence cells' diffractive effects for weak turbulence, the turbulence outer scale's influence can be ignored. Numerical simulations show that variable inner scale values produce obvious effects on the irradiance scintillation for non-Kolmogorov turbulence.     

Theoretical expressions of temporal power spectra of irradiance fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

The temporal power spectra of irradiance fluctuations reflect the frequency distribution of temporal statistical property of irradiance fluctuation. In this paper, new analytical expressions of the temporal power spectral models of irradiance fluctuations are developed for optical waves propagating through weak non-Kolmogorov turbulence with horizontal path. They are derived with the general modified atmospheric spectral model, and they consider the finite turbulence inner and outer scales, and have a general spectral power law value in the range of 3 to 4 instead of the standard power law value of 11/3. Numerical calculations are conducted to analyze the influence of non-Kolmogorov weak turbulence on the temporal power spectra of irradiance fluctuations.     

Irradiance scintillation considering finite turbulence inner scale for optical wave propagating through weak non-Kolmogorov turbulence

The turbulence inner scale plays an important role in investigating the irradiance scintillation index for optical wave propagating through atmospheric turbulence. However, previous expressions of the irradiance scintillation index, which were derived based on the general non-Kolmogorov spectral model, did not consider the influences of finite turbulence inner scale. In this study, based on the generalized exponential spectral model for non-Kolmogorov atmospheric turbulence, theoretical expressions of the irradiance scintillation index are derived for plane and spherical optical waves propagating through weak turbulence. The new expressions have considered the influences of the finite turbulence inner scale and the receiver aperture on the irradiance scintillation index. Numerical simulations are performed to analyze these parameters’ influences.     

Analysis of marine atmospheric turbulence effects on infrared imaging system by angle of arrival fluctuations

For the long-range infrared imaging system, the marine atmospheric turbulence degrades seriously the probability of object recognition and tracking. In this study, the angle of arrival fluctuations of an optical wave, which describes the distortion effects of marine atmospheric turbulence on an infrared optical imaging system, is investigated in detail both analytically and numerically. Analytic expressions of the angle of arrival fluctuations are derived for optical plane and spherical waves propagating through weak marine atmospheric turbulence with horizontal path, and they consider simultaneously finite turbulence inner scale, turbulence outer scale, wavelength, and aperture diameters. Numerical calculations are conducted to analyze the influence of marine weak turbulence on the infrared imaging. The results are useful for understanding the potential impact of deviations from the terrestrial turbulence.     

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.     

Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence

Recently the increasing experimental evidences have shown that atmospheric turbulence statistics does not obey Kolmogorov’s power spectrum model in portions of the troposphere and stratosphere. These experiments have prompted the investigations of optical wave propagation through atmospheric turbulence described by non-classical power spectra. In this paper, using an original approach and considering a non-Kolmogorov power spectrum which uses a generalized power law instead of constant standard power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the variances of the angle-of-arrival fluctuations of the plane and spherical waves are derived in weak turbulence for a horizontal path. The concise closed-form expressions are obtained and used to analyze the influence of spectral power law variation on the angle-of-arrival fluctuations.     

Effects of inner and outer scale on the modulation transfer function for a Gaussian wave propagating through anisotropic non-Kolmogorov turbulence

Both experimental results and empirical research have shown that the atmospheric turbulence can present the anisotropic property not only at a few meters above the ground but also at high altitudes of up to several kilometers. This paper investigates the modulation transfer function of a Gaussian beam propagating along a horizontal path in weak anisotropic non-Kolmogorov turbulence. Mathematical expressions are obtained based on the generalized exponential spectrum for anisotropic turbulence, which includes the spectral power law value, the finite inner and outer scales of turbulence, the anisotropic factor, and other essential optical parameters of the Gaussian beam. The numerical results indicate that the atmospheric turbulence would produce less negative effects on the wireless optical communication system with an increase in the anisotropic factor.     

A new method of calculating the orbital angular momentum spectra of Laguerre-Gaussian beams in channels with atmospheric turbulence

Studying orbital angular momentum(OAM) spectra is important for analyzing crosstalk in free-space optical(FSO)communication systems. This work offers a new method of simplifying the expressions for the OAM spectra of Laguerre-Gaussian(LG) beams under both weak/medium and strong atmospheric turbulences. We propose fixing the radius to the extreme point of the intensity distribution, review the expression for the OAM spectrum under weak/medium turbulence,derive the OAM spectrum expression for an LG beam under strong turbulence, and simplify both of them to concise forms.Then, we investigate the accuracy of the simplified expressions through simulations. We find that the simplified expressions permit accurate calculation of the OAM spectrum for large transmitted OAM numbers under any type of turbulence. Finally,we use the simplified expressions to analytically address the broadening of the OAM spectrum caused by atmospheric turbulence. This work should contribute to the concise theoretical derivation of analytical expressions for OAM channel matrices for FSO-OAM communications and the analytical study of the laws governing OAM spectra.     

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.     

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.     

BER and outage probability performance of log-normal distribution non-Kolmogorov turbulent optical links

We model the average bit-error rate (BER) and outage probability for an intensity-modulation/direct detection of tracked or untracked optical wireless communication (OWC) systems with on-off keying in weak turbulence horizontal channels, using the log-normal distribution models. The effects of atmospheric attenuation, beam wander and spread, misalignment and the spectral index of non-Kolmogorov turbulence on system's performance are included. The model can be evaluated the information loss and BER of ground-to-train OWC links.     

近海面大气光学湍流计算模型的比较与改进

通过在黄海北部某海域进行的海上大气光学湍流观测实验,对比分析了不同大气稳定度环境下四种大气光学湍流C2n计算模型的性能。针对中性和近中性环境下模型误差大的问题,基于温度折射率结构参数fT与稳定度的对应关系,利用实测数据和函数拟合,提出了一个新的fT函数形式。误差分析表明采用新的fT参数方案明显提高了C2n模型的计算精度,其性能大大高于其他几种计算模型。     

大气光通信中大气闪烁时间平滑效应研究

利用大气闪烁的时间平滑效应,增加光电探测器曝光时间是克服大气闪烁对大气光通信的瞄准、捕获、跟踪链路影响的有效途径之一.基于科尔莫戈罗夫谱,导出了弱湍流起伏区无限平面波和球面波的大气闪烁时间平滑因子的一般表达式,并且用几何光学近似得到了在大孔径和小孔径接收情况下的时间平滑因子近似表达式.在孔径远大于菲涅耳区尺度时,平面波和球面波的时间平滑因子的近似表达式与精确表达式的误差分别小于6%和3%.分析结果表明,孔径越小,时间平滑效应越显著,并且菲涅耳区尺度对时间平滑效应影响的程度也随着孔径的增加而减弱.     

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.     

Theory of optical scintillation: Gaussian-beam wave model

Abstract

A scintillation model previously developed by the authors is extended in this paper to the case of a propagating Gaussian-beam wave. As in the previous model, we account for the loss of spatial coherence as the optical wave propagates through atmospheric turbulence by eliminating effects of certain turbulent scale sizes that exist between the scale size of the spatial coherence radius of the beam and that of the scattering disc. These mid-range scale-size effects are eliminated through the formal introduction of spatial frequency filters that continually adjust spatial cut-off frequencies as the optical wave propagates. Unlike the previous model, in this paper we include the effect of a finite outer scale in addition to the inner scale. With a finite outer scale, the scintillation index can be substantially lower in strong turbulence than that predicted by a model with an infinite outer scale. This particular behaviour of scintillation in strong turbulence, mostly associated with horizontal paths near the ground, cannot be explained on the basis of previous expressions deduced from the asymptotic theory. Comparisons of the scintillation models with published experimental and simulation data through weak and strong irradiance fluctuations show excellent fits.     

Spectral changes of aberrated stochastic electromagnetic flat-topped beams propagating in turbulent atmosphere

In this paper, taking the electromagnetic partially coherent flat-topped (PCFT) beam as an example, we investigate the spectral changes of stochastic electromagnetic beams with astigmatic aberration propagating through a turbulent atmosphere. The analytic expressions for the spectrum of the beams propagating through the turbulent atmosphere are derived. It is shown that the spectral changes of the electromagnetic PCFT beams in the turbulent atmosphere are closely related with the astigmatism aberration, the strength of atmospheric turbulence, the inner scale of turbulence, the correlation of source and the order of flatness of electromagnetic PCFT beams. It is important to note that the spectral changes of the aberrant electromagnetic PCFT beams are insensitive to the atmospheric turbulence. Some possible explanations have also been given for the interesting physical phenomena.     

The far-field spatial coherence of Gaussian Schell-model beam in turbulence in terms of position vectors

Spatial coherence properties of beam produced by Gaussian Schell-model source when the beam is propagating through atmosphere have been analyzed in terms of position vectors. New expressions for cross-spectral density of optical field and spectral degree of coherence as well as radiant intensity have been developed. Numerical results illustrated in this paper indicate the coherence degradation suffered from atmospheric turbulence and their directional dependence.     

Wander of a Gaussian-Beam Wave Propagated Through a Non-Kolmogorov Turbulent Atmosphere

Both increasing experimental evidence and some results of theoretical investigation have shown that there exist two kinds of turbulence in the aerosphere, Kolmogorov and non-Kolmogorov turbulence. Thus, it is necessary to improve the theory of optical wave propagation through atmospheric turbulence, namely, study the laser-beam propagation in non-Kolmogorov turbulence, before analyzing the joint influence of the Kolmogorov turbulence and non-Kolmogorov one on satellite laser communication. The beam wander will lead to the performance degradation of satellite laser communication systems and exert an influence on the achievement and stability of its links. In this paper, we consider a theoretical power spectrum of refractive-index fluctuations with a generalized power law in order to derive the variance of Gaussian-beam wave wander in weak turbulence for a horizonal path and analyze the influence of spectral power-law variations on the beam wander. We show that the expression for the beam-wander variance is of concise closed form and independent of the optical wavelength.     

远海海面大气光学湍流实验测量

将光纤湍流测量系统搭载于我国的“远望号”航天测量船, 首次实现了远海海面大气光学湍流的空间多点同步测量, 初步获得了远海海面大气光学湍流的基本特征和定量数据. 测量共进行了37天, 测量数据处理包括大气光学湍流强度的统计分析、采用Greenwood湍流空间相关函数模型对实测的光学湍流空间相关函数进行非线性拟合从而获得湍流的空间外尺度, 以及采用分段拟合算法获取光学湍流的功率谱标度指数. 结果表明: 海面大气光学湍流强度中等偏弱, 且无明显规律性的日变化趋势; 空间外尺度较小, 约为0.2-0.3 m; 湍流谱标度指数符合-5/3次方的概率均为25%左右, 低于相应的近地面概率.