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.     

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     

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.     

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.     

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.     

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.     

Effects of low-order atmosphere-turbulence aberrations on the entangled orbital angular momentum states

Based on Zernike-model expansion of turbulence phase aberrations and non-Kolmogorov spectrum model of index-of-refraction fluctuation, we analyze the effects of low-order Zernike turbulence aberrations on orbital angular momentum (OAM) entanglement states in a weak fluctuation region. The signal photon detection probability of OAM entanglement states propagating in a slant turbulence channel with non-Kolmogorov turbulence Z-tilt, defocus, astigmatism, and coma aberrations are modeled, respectively. The results demonstrate that turbulence Z-tilt aberration is the dominant aberration, coma is the second, and astigmatism is the third, but that the defocus aberration has no impact on the detection probability. As the power-law exponent of the non-Kolmogorov spectrum increases from 3 to 4, the detection probability decreases.     

The effects of non-Kolmogorov turbulence on the orbital angular momentum of a photon-beam propagation in a slant channel

We analyze the effects of non-Kolmogorov turbulence on the orbital angular momentum of a photon-beam propagation through atmosphere. The probability models of the orbital angular momentum crosstalk for single photons propagation in the channel with the non-Kolmogorov turbulence aberration have been established. It is found that the crosstalk among orbits increases as the orbital angular momentum quantum number of launch beam rises, the ground turbulence strength ${C_n^{2} \left( 0 \right)}$ enhances or the non-Kolmogorov parameter α of turbulence-channel increases. As non-Kolmogorov parameter α approaches 4, the crosstalk probabilities among neighbor orbits are approximately the same.     

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.     

Lens ghost imaging in a non-Kolmogorov slant turbulence atmosphere

Based on the method of computation reference channel and the extended Huygens–Fresnel integral, the model of lens ghost imaging with fully spatially incoherent linear polarization light through a slant turbulent channel has derived. The model shows that the resolution ratio of ghost imaging decreases as the power-law exponent of non-Kolmogorov turbulence increasing or the object location departing from the source. The zenith angle of channel has little influence to the quality of the ghost imaging. The minimum distinguishable centre-separation of double slit decreases as the power-law exponent of non-Kolmogorov turbulence increasing.     

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.     

Block error rate of FSO links over non-Kolmogorov turbulence with exponentiated Weibull distribution

In this paper, we model block error rate (BLER) performance of optical wireless communication systems in strong turbulence slant channels with very slow fading and additive Gaussian noise, using the Exponentiated Weibull distribution models. In a communication system, which transmits data in blocks of N bits, the BLER probability P(M, N) of more than M bit errors in a block is particularly useful in evaluating the wireless optical channel performance. The joint effects of the beam wander and spread, pointing errors and the spectral index of non-Kolmogorov turbulence on system's performance are included. The obtained results can be essential for the designing of such links under real circumstances.     

Pulsed single-photon Bessel beams propagation in non-Kolmogorov turbulent atmosphere

The analytic expressions are derived for the turbulent broadening, the long-term temporal broadening, the acquisition probability of single-pulse and the transmittance probability density of a pulsed space-time Bessel photon-beam propagating along a slant path in weak non-Kolmogorov atmospheric turbulence, based on the assumption of a pulsed Bessel beam with the initial Gaussian temporal shape of pulse and diffraction-free spatial distribution. It is shown that the turbulent broadening and the long-term temporal broadening are the nolinear-increase functions of the index of non-Kolmogorov turbulence and the effect of non-Kolmogorov index on the acquisition probability of single-pulse can be approximatively described by a Gaussian function with a peak value at non-Kolmogorov index close to 3.7 for the case of the input half-pulse width greater than picosecond (ps). The transmittance of probability density is decreasing as the increasing of the structure constant of the index of refraction, the zenith angle of communication channel, the propagation path and the pulse broadening. There is turbulent diffraction for Bessel beam propagation in turbulent atmosphere, but its free-space diffraction-free characteristic is reservation.     

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.     

Propagation properties of partially coherent Hermiteben Gaussian beams through non-Kolmogorov turbulence

The propagation properties of partially coherent Hermite—Gaussian beams through non-Kolmogorov atmospheric turbulence are studied. The effects of non-Kolmogorov turbulence and beam nonparaxiality on the average intensity evolution and the beam-width spreading are stressed. It is found that the evolution of the average intensity distribution and the beam-width spreading depends on the generalized exponent factor, namely, on the non-Kolmogorov turbulence strength for the paraxial case. For the non-paraxial case the effect of the turbulence is negligible, while the beam-width spreading becomes very large. The analytical results are illustrated numerically and interpreted physically.     

Polarization fluctuations of single photon states in a slant channel with non-Kolmogorov turbulence

Polarization properties of single photon states propagating through the non-Kolmogorov turbulence in a slant channel are studied based on the degree of polarization of quantum field. The degree of polarization of single photon states for linearly polarized quantum beam propagation in a slant turbulent channel are developed. Our results show that the effects of the outer scale fluctuations of atmospheric turbulence and the wavelength difference of the beams on the polarization can be ignored and the smaller inner scale of turbulence and larger zenith angle of communication channel will lead to larger fluctuations of the polarization of single-photon states. The effects of the inner scale of turbulence on polarization of single photon states are more significant for bigger refractive-index power and bigger zenith angles.     

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.     

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.     

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.     

Performance of phase compensated coherent free space optical communications through non-Kolmogorov turbulence

The bit-error-rate (BER) performance of coherent free-space optical (FSO) links employing phase compensation techniques is investigated in weak non-Kolmogorov turbulence. Assuming that the amplitude fading and phase fluctuation follow lognormal model and Gaussian distribution respectively and using the expression of non-Kolmogorov turbulence in terms of Zernike polynomials, the signal-to-noise ratio (SNR) at the coherent receiver is analyzed and as a special case, a new closed-form expression using chi-square distribution is obtained. Thus, the influence of different compensation modes and normalized receiver diameter on BER performance is evaluated and an optimum normalized receiver diameter is suggested to achieve the minimum BER. Moreover, the impact of outer scale L₀ and the exponent value α in non-Kolmogorov spectrum is studied with the optimum diameter, which reveals that the BER has an obvious decrease with larger values of L₀ and α.