Scintillation behavior of cos, cosh and annular Gaussian beams in non-Kolmogorov turbulence

For a non-Kolmogorov spectrum, scintillation aspects of cos, cosh and annular Gaussian beams are investigated. The appropriate mathematical formulation is developed, the derived scintillation index is evaluated and its variation is plotted in graphs. We find that, when the values of the power coefficient of the spectrum are just above 3, low scintillation is encountered, then as the power coefficient is increased, rises will occur with a peak being reached around 3.21. From there onwards, scintillation will drop, as the power coefficient approaches a value of 5. For extreme off-axis positions, there will be slight increases in scintillation at high power coefficient values. At points near on-axis and when the beams have small width sizes, cosh Gaussian beam having a bigger displacement parameter will offer the lowest scintillation. At large width sizes, this advantage will switch to the side of the cos Gaussian beam. In this study, the variation of scintillation with other sources and propagation parameters is examined as well.     

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.     

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。     

Scintillation index of astigmatic annular beams in a turbulent atmosphere

The scintillation properties of astigmatic annular beams in a weak turbulent atmosphere are investigated. Expression for the on-axis scintillation index of an astigmatic annular beam is derived. It is found that the scintillation index of an astigmatic annular beam can be smaller than that of a Gaussian beam, an elliptical Gaussian beam and a stigmatic annular beam in a weak turbulent atmosphere under certain conditions. The scintillation properties of astigmatic annular beams are closely controlled by its beam parameters.     

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.     

Rytov variance equivalence through extended atmospheric turbulence and an arbitrary thickness phase screen in non-Kolmogorov turbulence

An arbitrary thickness phase screen model can describe scintillation index for Gaussian beam propagating through a phase screen more accurate than thin phase screen model. To describing actual scintillation index for Gaussian beam propagating through an extended medium using a phase screen in weak non-Kolmogorov turbulence, the scintillation index and Rytov variance for arbitrary thickness phase screen model are derived. Specially, the ratio of the Rytov variances for a phase screen and extended random media is found under the assumption of equivalence in scintillation index of the two cases. The theoretical results show that the normalized Rytov variance varies with the power law of the turbulence spectrum, the relative thickness of the phase screen, the position of the phase screen, the transmitter beam parameters and the radial position at output plane. The influences of these variables are also simulated. These results will be applied to simulation of adaptive optics and laser communication.     

Equivalence of structure constants in non-Kolmogorov and Kolmogorov spectra

We find the equivalence of the structure constants in non-Kolmogorov and Kolmogorov spectra in a turbulent atmosphere. As the reference point, the spherical wave scintillation index in a non-Kolmogorov medium is used. Relations of the structure constants are found to be functions of the power law of the turbulence spectrum and the Fresnel zone. It will be useful to employ the equivalence of the structure constants in making performance comparisons found with non-Kolmogorov and Kolmogorov spectra.     

Non-Kolmogorov spectrum scintillation aspects of dark hollow and flat topped beams

The scintillation aspects of dark hollow (DH) and flat topped (FT) beams propagating in the turbulent atmosphere containing the non-Kolmogorov power spectrum are investigated. It is found that low scintillations will occur when the exponent of the power spectrum is just above the numeric value of 3. Initially, the rises in scintillations will take place as the exponent becomes larger, but later the scintillation reductions will be experienced as the exponent grows further, eventually minimum scintillations will be seen when the exponent has reached the value of 4. This will be the case, for scintillation variations against propagation distance, source size, wavelength, inner and outer scales of turbulence. Furthermore, it is found that at the small source sizes, DH beams will offer less scintillation than FT beams, while at the large source sizes, the reverse will be applicable.     

Effects of extremely strong turbulent medium on scintillations of partially coherent annular and flat-topped Gaussian beams

Scintillation index of partially coherent annular and partially coherent flat-topped Gaussian beams propagating in horizontal links is found at the receiver origin when these beams propagate in extremely strong atmospheric turbulence. Scintillation index of coherent versions of such beams attain unity saturation value whereas the decrease in the degree of source coherence results in the decrease of the scintillations. At a fixed degree of partial coherence, thin ring sized annular beams possess smaller scintillations than thick ones. For partially coherent flat-topped Gaussian beams, higher flatness yields smaller intensity fluctuations. In extremely strong turbulence, partially coherent annular and partially coherent flat-topped Gaussian beams have smaller scintillations when compared to partially coherent single Gaussian beam scintillations.     

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.     

Concept of area scintillation

Stemming from the results of our earlier investigations, the concept of area scintillation is introduced, which takes into account the intensity distribution over the receiver plane. In this context, the area scintillation of fundamental Gaussian and annular beams is formulated, numerically evaluated and graphically illustrated. From the comparison, it is seen that, under the same source power conditions, annular Gaussian beams provide much less scintillations than the fundamental Gaussian beams at small source size. At large source sizes and at shorter propagation distances, annular beams are still favorable, but, as the propagation range is extended, the reverse becomes true. A review of previous findings leading up to the newly introduced concept is also presented.     

Scintillation calculations for partially coherent general beams via extended Huygens–Fresnel integral and self-designed Matlab function

We present scintillation calculations in weak atmospheric turbulence for partially coherent general beams based on the extended Huygens–Fresnel integral and a Matlab function designed to handle expressions both of the average intensity and the average squared intensity. This way, the integrations are performed in a semi-analytic manner by the associated Matlab function, and this avoids lengthy, time-consuming and error prone hand derivations. The results are obtained for the partially coherent fundamental and higher-order sinusoidal and annular Gaussian beams. By plotting the scintillation index against the propagation distance and source size, we illustrate the on-axis scintillation behaviors of these beams. Accordingly, it is found that within specific source and parameter ranges, partially coherent fundamental, higher-order sinusoidal and annular Gaussian beams are capable of offering less scintillations, in comparison to the fundamental Gaussian beam.     

Annular, cosh and cos Gaussian beams in strong turbulence

For the strong atmospheric turbulence regime, the asymptotic on-axis scintillation behavior of annular, cosh and cos Gaussian beams is theoretically derived and illustrated with numerical examples. It is observed from the plots that annular Gaussian beams exhibit more scintillations than a Gaussian beam, regardless of the amplitude coefficient and source size settings. For small source sizes, cosh Gaussian beams seem to have an advantage over Gaussian beams in terms of reduced scintillation, but for large source sizes a switchover occurs where cos Gaussian beams assume the advantage. Analysis of the effect of inner scale value shows that scintillations increases for all beams as the inner scale increases.     

Spreading of partially coherent polychromatic Hermite-Gaussian beams propagating through non-Kolmogorov turbulence

The spreading of partially coherent polychromatic Hermite-Gaussian (PCPHG) beams propagating through non-Kolmogorov turbulence is studied, where the effect of non-Kolmogorov turbulence and beam bandwidth on the beam width spreading and angular spread is stressed. It is shown that the variation of the relative beam width of PCPHG beams with the generalized exponent parameter of non-Kolmogorov turbulence is non-monotonic. The larger bandwidth of PCPHG beams is, the smaller the relative beam width and the smaller the relative angular spread. Therefore, PCPHG beams with larger bandwidth are less affected by non-Kolmogorov turbulence than those with smaller bandwidth. PCPHG beams are less sensitive to the effect of non-Kolmogorov turbulence than fully coherent polychromatic Hermite-Gaussian (FCPHG) beams and polychromatic Gaussian Schell-model (PGSM) beams. The results are illustrated by numerical examples and interpreted.     

Scintillation properties of dark hollow beams in a weak turbulent atmosphere

The on-axis scintillation index for a circular dark hollow beam (DHB) propagating in a weak turbulent atmosphere is formulated, and the scintillation properties of a DHB are investigated in detail. The scintillation index for a DHB reduces to the scintillation index for a Gaussian beam, an annular beam and a flat-topped beam under certain conditions. It is found that the scintillation index of a DHB is closely related to the beam parameters and can be lower than that of a Gaussian beam, an annular beam and a flat-topped beam in a weak turbulent atmosphere at smaller waist sizes and longer propagation lengths. PACS 42.25.Bs; 42.68.Ay     

Irradiance scintillation index for Gaussian beam based on the generalized anisotropic von Karman spectrum

Experiments and theoretical investigations have shown that the atmosphere turbulence exhibits both anisotropic and non-Kolmogorov properties. In this paper, based on the anisotropic generalized von Karman spectrum and the Rytov approximation theory, new expression for the irradiance scintillation index of optical waves is derived for Gaussian beam propagating through weak anisotropic non-Kolmogorov turbulence. Compared with previously published results, it considers simultaneously the asymmetry property of turbulence cells or eddies in the orthogonal xy-plane, the general spectral power law in the range 3–4 instead of constant value of 11/3 for the Kolmogorov turbulence, and the finite turbulence inner and outer scales. Two anisotropic factors are introduced to parameterize the anisotropy of turbulence cells or eddies in horizontal and vertical directions. In the special cases of these two anisotropic factors equaling one and the finite turbulence inner and outer scales equaling separately zero and infinite, the derived expression can reduce correctly to the previously published results. Calculations are performed to analyze the derived results.     

部分相干双曲余弦厄米高斯光束在非Kolmogorov大气湍流中的传输特性

基于广义Huygens-Fresnel原理和非Kolmogorov大气湍流折射率起伏谱密度函数, 采用Wigner分布函数的二阶矩方法, 推导出了在大气湍流中传输的部分相干双曲余弦厄米高斯光束束宽和M²因子的解析表达式. 研究表明: 相对束宽和归一化M²因子随传输距离的增大而增大; 光束阶数越大、相干长度越小、双曲余弦参数越小, 相对束宽和归一化M²因子受大气湍流影响越小; 相对束宽随束腰宽度的增大存在极大值, 在一定的相干长度范围内, 归一化M²因子随束腰宽度的增大存在极小值; 相对束宽和归一化M²因子随广义指数的变化均存在极大值, 随内尺度的增大而逐渐减小, 随外尺度的增大几乎没有变化.     

椭圆涡旋光束在海洋湍流中的传输特性

本文采用分步相位屏方法来仿真椭圆涡旋光束在海洋中的实际传输情况,并对椭圆涡旋光束在海洋湍流中的传输光强和闪烁因子进行了仿真。研究发现,椭圆涡旋光束在海洋传输过程中,光斑会发生明显的旋转,同时光斑会产生暗核且暗核个数与光束的拓扑荷数相等。一个拓扑荷数为m的相位奇点会分裂成m个拓扑荷数为1的相位奇点,并且海洋湍流越强,光斑受到的干扰越严重。研究还发现,在较弱的海洋湍流中,随着传输距离的增加,椭圆涡旋光束的闪烁因子会低于高斯光束和涡旋光束的闪烁因子,而且在远距离处拓扑荷数越大闪烁因子降低越明显,同时也发现,传播一段距离后涡旋光束的闪烁因子会低于高斯光束的闪烁因子。在较强湍流中,椭圆涡旋光束的闪烁因子会交叠在一起。对于不同强度的海洋湍流,随着均方温度耗散率的增大,椭圆涡旋光束的轴上点闪烁因子也增大。在同一传输距离处,束腰宽度越小的椭圆涡旋光束闪烁因子越小。     

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.     

Polarization fluctuations of Gaussian Schell-model type photon beams in a slant channel with non-Kolmogorov turbulence

Polarization properties of Gaussian Schell-mode type photon beams propagating through the non-Kolmogorov turbulence in a slant channel are studied which are based on the model of quantum field and the effective photon annihilation/creation operator. Our numerical results show that the degree of polarization increases with the increasing of the transverse coherent width of source ρ_s0, the source's transverse size ω₀ and the power law of the turbulent spectrum, but the degree of polarization P decreases as the zenith angle θ increases. The effect of the wavelength of light beam on the degree of polarization of Gaussian Schell-model beams is small.