The effects of tilt corrected residual aberration on the detection probability of single-photon propagation in a slant path turbulent atmosphere

Based on the assumption of a pulse laser beam with an initial Gaussian temporal shape and a collimated fundamental-model Gaussian beam, the Rytov approximation and Kolmogorov spectrum model for the index-of-refraction fluctuation of atmosphere, the effect of turbulence on the probability density, acquisition transmittance probability, transmittance probability density, acquisition probability of single-photon propagation in atmospheric communication channel with z-tilt and centroid-tilt aberration corrected are studied theoretically. The probability density, acquisition transmittance probability, transmittance probability density and acquisition probability models for single-photon propagation in uplink path and downlink path are derived. Our results shown that the detection probability and the acquisition transmittance probability of the single-photon are obvious increase, when the beams are propagation in the z-tilt corrected communication channel.     

大气环境下用于瞄准的激光波束传播特性研究

针对激光瞄准过程中的光斑偏移现象,结合修正的Von Karman谱的折射指数起伏和Hufnagel-Vally湍流模型上的近似积分,研究了高斯脉冲光束在湍流大气中远场水平以及斜程传播时的脉冲展宽和闪烁指数,分析了强湍流条件下1.06 μm准单色光斜程大气传输光强分布与脉冲展宽的关系,对数值结果进行比较,发现远距离传输中波长和距离对波束瞄准偏差影响较大.从理论和实验上对大气环境下激光光斑瞄准偏差进行了分析研究,研究结果表明:将激光光斑全场数据及分析结果应用到现有偏差补偿算法中,可以实现激光瞄准偏差的有效补偿,在大气能见度1 km～3 km范围内,激光瞄准偏差测量误差σA≤0.1 mrad.     

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.     

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.     

贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性

 对等衍射长度贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性作了研究，结果表明，通过选择适当的空间参数，贝塞尔-高斯脉冲光束沿轴上传输时，脉冲宽度不变。传输距离小于无衍射长度时，随衍射角增加，功率谱形状未变，脉冲波形保持不变；传输距离大于无衍射长度时，随衍射角增加，光谱由蓝移变为红移，脉冲展宽。     

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.     

超短脉冲Bessel 光束和空间诱导色散效应

 给出了含时的波动方程的一族特解－超短脉冲Bessel光束，其脉冲光束的空间和时间部分可以做分离变量，空间部分在传输过程中保持Bessel光束不变，而时间脉冲部分的传输行为类似于在普通色散介质中的传输，此效应被称之为空间诱导色散效应。     

Average transmittance of flat-topped beam in non-Kolmogorov medium

The average transmittance of flat-topped beam in non-Kolmogorov turbulence is investigated at the receiver origin. The formulation is based on the extended Huygens–Fresnel principle and the evaluations are made by numerical integration. It is found that as the power-law exponent, structure constant, propagation distance, source size and the degree of flatness of the flat-topped beam increase, the on-axis transmittance decreases. Transmittance decrease is substantial for high power-law exponent values and in strong turbulent regime. Increase in the wavelength of the flat-topped beam causes the average transmittance to increase.     

空间诱导产生艾里-贝塞尔光弹研究

利用波动方程,研究了脉冲贝塞尔光束在自由空间传输时的空间诱导群速度色散(SIGVD)效应. 结果表明,三阶SIGVD能使脉冲贝塞尔光束的时域逐渐演化为艾里分布. 由于艾里-贝塞尔光弹是一种新奇的时、空都不扩展的局域波包, 能在光与物质相互作用的很多应用领域发挥作用.因此,本文提出了 通过色散管理技术补偿二阶SIGVD,利用三阶SIGVD在自由空间产生艾里-贝塞尔光弹的方案. 为分析这种光弹的时空传输特性,数值模拟了它在色散介质中的传输情况. 结果表明,这种光弹能在色散介质中保持空域不衍射、时域不色散的稳定传输.     

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.     

Detection probability of single photons in a slant path atmospheric turbulence communication channel

Using Rytov approximation and modified von Karman spectrum model of the index-of-refraction, the detection probability of single-photon beam propagation in a atmospheric turbulence communication channel is investigated and developed. In this research, the single-photon beam is assumed as a pulse beam which has an initial Gaussian temporal shape of the pulse and a Laguerre-Gaussian fundamental-model spatial distribution. It is found that in order to obtain the messages probability greater than or equal 0.1, we should encode and dispatch 66680 photons in identical information carriers at the transmitting side, and the radius of the detector at the receiving plane must be at least up to 0.4 m when the photons propagate in a turbulent atmosphere communication channel.     

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。     

Slant path average intensity of finite optical beam propagating in turbulent atmosphere

The average intensity of finite laser beam propagating through turbulent atmosphere is calculated from the extended Huygens Fresnel principle. Formulas are presented for the slant path average intensity from an arbitrarily truncated Gaussian beam. The new expressions are derived from the modified von Karman spectrum for refractive-index fluctuations, quadratic approximation of the structure function,and Gaussian approximation for the product of Gaussian function and Bessel function. It is shown that the form of average intensity is not a Gaussian function but a polynomial of the power of the binomial function, Gaussian function, and the incomplete gamma function. The results also show that the mean irradiance of a finite optical beam propagating in slant path turbulent atmosphere not only depends on the effective beam radius at the transmitting aperture plane, propagation distance, and long-term lateral coherence length of spherical wave, but also on the radius of emit aperture.     

啁啾脉冲高斯光束在大气湍流中的传输特性北大核心CSCD

基于广义惠更斯-菲涅耳原理,推导出啁啾脉冲高斯光束在湍流大气中传输的光谱解析表达式,并对解析表达式进行了数值仿真。结果表明:啁啾参数越大,光源谱宽越宽;当光源相对谱宽大于0.336时,轴上点光谱产生蓝移;湍流使得轴上点光谱的相对频移量减小,相对频移量随源光谱宽的增大而非线性增大;增大光束束腰半径可减小湍流对光谱频移、光束展宽的影响。     

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。     

Propagation of modified Bessel-Gaussian beams in turbulence

We investigate the propagation characteristics of modified Bessel-Gaussian beams traveling in a turbulent atmosphere. The source beam formulation comprises a Gaussian exponential and the summation of modified Bessel functions. Based on an extended Huygens–Fresnel principle, the receiver plane intensity is formulated and solved down to a double integral stage. Source beam illustrations show that modified Bessel-Gaussian beams, except the lowest order case, will have well-like shapes. Modified Bessel-Gaussian beams with summations will experience lobe slicing and will display more or less the same profile regardless of order content. After propagating in turbulent atmosphere, it is observed that a modified Bessel-Gaussian beam will transform into a Bessel-Gaussian beam. Furthermore it is seen that modified Bessel-Gaussian beams with different Bessel function combinations, but possessing nearly the same profile, will differentiate during propagation. Increasing turbulence strength is found to accelerate the beam transformation toward the eventual Gaussian shape.     

大气湍流对斜程传输准单色高斯-谢尔光束时间相干性的影响

由第一类零阶贝塞尔函数的级数展开推导出波结构函数在任意湍流条件下的近似表达式。由广义惠更斯-菲涅耳原理、随高度变化的Hufnagel-Valley湍流廓线模型以及波结构函数在任意湍流条件下的近似表达式,导出了斜程传输时准单色高斯-谢尔光束互相干函数的解析式。然后,利用表征光束时间相干性的纵向相干长度(可由互相干函数导出),研究了斜程传输时大气湍流对准单色高斯-谢尔光束时间相干性的影响。研究结果表明,准单色高斯-谢尔光束的时间相干性在整个斜程传输过程中保持不变。最后,对该结果在物理上给予了定性解释。     

Theoretical prediction and experimental validation of the angle-of-arrival probability density of a laser beam in a strong plane-flame turbulence

The propagation of a laser beam through a plane turbulent flame is studied using geometrical optics approximation. The random fluctuations of the refractive index caused by a strong thermal turbulence in the flame create random perturbations of the laser beam direction. From the Markovian process model applied along the whole random path of the beam, the theoretical probability density of the laser beam angle-of-arrival is derived from the analytical solution of the Einstein-Fokker-Kolmogorov equation, which we have determined in terms of a series expansion of spherical harmonics. An experimental setup and a method for measuring this probability density are described. The experimental results obtained are shown to agree with the theoretical predictions.     

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.     

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.