Intensity and coherence properties of light in oceanic turbulence

Using the Rytov method and Belen'kii and Mironov's method of effective beam parameters for strong turbulence regimes, the intensity and coherence properties of a Gaussian beam propagating through the clear-water turbulent ocean are explored. The refractive index fluctuations are described by a recently developed power spectrum combining the effects from both temperature and salinity. Due to the complicated nature of the oceanic turbulence spectrum, the analysis is restricted to numerical computations.     

湍流大气中斜程传输部分相干光的光束扩展

运用维格纳分布函数与广义惠更斯菲涅耳原理,推导出部分相干光束在任意折射率起伏功率谱模型的大气湍流中斜程传输时,其束宽传输的一般解析表达式。在此基础上,以部分相干平顶(PCFT)光束为例,给出了PCFT光束在大气湍流中斜程传输的束宽扩展解析表达式。在合肥地区大气折射率结构常数高度分布模式下开展了数值计算和分析,并与水平传输时的结果进行了比较。研究结果表明,光束在斜程传输时的束宽不仅与光束阶数、空间相干度、束腰半径、湍流的强弱和传输距离有关,还与天顶角密切相关。光束的阶数越高,空间相干性越差,天顶角越小,则其束宽扩展受湍流的影响就越小。当天顶角小于60°时,大气湍流对斜程传输光束束宽的影响明显小于水平传输的情况。     

Intensity fluctuations of spherical acoustic waves propagating through thermal turbulence*

The intensity fluctuations of acoustic waves that propagate through thermal turbulence are investigated under well controlled laboratory conditions. Two heated grids in air are placed horizontally in a large anechoic room and the mixing of the free convection plumes above them generates a homogeneous isotropic random thermal field. The spectrum of refractive index fluctuations is accurately described by a modified von Karman model which takes into account the entire spectrum of turbulence. Experimental data are obtained by varying both the frequency of the spherical wave and the distance of propagation. In this paper we concentrate on the variance of the normalized intensity fluctuations and on their probability distributions. These measurements cover all the regimes from weak scattering to strong scattering including the peak of the intensity variance. Experimental values of the scintillation index are compared with classical theoretical predictions and also with the results of recent numerical simulations. The classical probability density functions (log-normal, exponential, I-K) are tested against the measured probability distributions. The generalized gamma distribution, which varies smoothly from log-normal to exponential as a function of two parameters, appears m represent the experimental data for a very large range of scattering conditions.     

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.     

Effective Radius of Curvature and Rayleigh Length of Partially-Coherent Array Beams Passing Through Oceanic Turbulence

Based on the spatial power spectrum of the refractive index of ocean water, we derive analytical expressions for the effective radius of curvature and Rayleigh length of partially-coherent Hermite–Gaussian linear array (PCHGA) beams propagating through oceanic turbulence. In addition, we discuss theoretically and analyze numerically the influence of oceanic turbulence and array parameters. The effective radius of curvature and Rayleigh length of PCHGA beams increase with the relative strength of temperature and salinity fluctuations, the rate of dissipation of turbulent kinetic energy per unit mass of fluid, the array beam number, beam order, and relative separation distance, but decrease with the increase in the rate of dissipation of the mean-square temperature. The analysis provided here will help to understand the propagation of array beams through ocean turbulence.     

湍流等离子体鞘套中高斯光束的传播特性分析

为了研究高斯光束在湍流等离子体鞘套中的传输特性,根据广义惠更斯-菲涅耳原理,采用基于快速傅里叶变换的功率谱反演法,用多随机相位屏来模拟湍流带来的影响.根据超声速飞行器绕流等离子体流场厚度在厘米级别的特点,光束在两个相位屏之间的传输过程中采用菲涅耳衍射积分的两次快速傅里叶变换算法(double fast Fourier transform algorithm),利用多随机相位屏模拟等离子体鞘套湍流对光束传输产生的影响,解决了多随机相位屏模拟湍流研究中的超短距离传输问题.当飞行高度为45 km,飞行速度为18马赫时,通过对超声速飞行器绕流等离子体流场的统计分析,发现在此飞行条件下折射率起伏方差的强度范围10~(–11)—10~(–14).对高斯光束在湍流等离子体流场中的传输特性进行了数值仿真.结果表明:在等离子体鞘套湍流中折射率起伏强度、波长、传输距离等都是影响高斯光束质量的重要因素.折射率方差越大,传输距离越长,光斑弥散越严重,光强起伏越大,光强减弱也越明显.光束的波长越长,高斯光束抑制湍流的能力越强,光斑弥散程度越小,光强起伏也越小.     

部分相干双曲正弦高斯光束的M~2因子与湍流距离

基于广义惠更斯-菲涅耳原理和维格纳分布函数方法,推导出了部分相干双曲正弦高斯(ShG)光束在湍流大气中M2因子的解析表达式。在此基础上研究了部分相干ShG光束的湍流距离,即湍流引起的光束扩展可忽略的范围。采用Von Karman谱分别对M2因子和湍流距离进行了数值计算,并分析了内外尺度的影响。研究表明:M2因子随束腰宽度和离心参数的增加存在极小值;湍流距离随束腰宽度的增加存在极大值,随离心参数的增加而增加,大气湍流对离心参数较大的光束影响较小。另外,M2因子和湍流距离与折射率结构参数、内尺度、外尺度、波长和相干参数等密切相关。     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

Abstract

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

Propagation of the off-axis superposition of partially coherent beams through atmospheric turbulence

The propagation properties of the off-axis superposition of partially coherent beams through atmospheric turbulence and their beam quality in terms of the mean-squared beam width w(z) and the power in the bucket (PIB) are studied in detail, where the effects of partial coherence, off-axis beam superposition and atmospheric turbulence are considered. The analytical expressions for the intensity, the beam width and the PIB are derived, and illustrative examples are given numerically. It is shown that the maximum intensity I_max and the PIB decrease and w(z) increases as the refraction index structure constant C_n² increases. Therefore, the turbulence results in a degradation of the beam quality. However, the resulting partially coherent beam with a smaller value of spatial correlation parameter γ and larger values of separate distance x_d and beam number M is less affected by the turbulence than that with a larger value of γ and smaller values of x_d and M. The main results obtained in this paper are explained physically.     

圆屋附近大气折射率结构常数的空间分布

 通过两点温度脉动法,测量了孤立建筑物圆屋附近不同位置的折射率结构常数,对比分析了气象塔8.0,6.0 m高度处的折射率结构常数。结果表明：圆屋附近8.2,8.5,9.0 m高度处的折射率结构常数要比非圆屋附近同高度的结果大;距离圆屋等距离垂直方向的折射率结构常数大于水平方向的测量结果;因此将圆屋附近认为是近地面的假设不成立;圆屋附近温度谱幂率基本符合“－5/3”定律。     

Influence of oceanic turbulence on propagation characteristics of Gaussian array beams

Based on the power spectrum of oceanic turbulence proposed by Nikishov, the influence of oceanic optical turbulence on propagation of Gaussian array beams is studied in detail by using five propagation characteristic parameters (i.e., mean-squared beam width, Rayleigh range, turbulence distance, power in the bucket and Strehl ratio). It is shown that the influence of oceanic optical turbulence on propagation of laser beams becomes stronger as τ (ratio of temperature to salinity contribution to the refractive index spectrum) and χ_T (rate of dissipation of mean-squared temperature) increase and ɛ (rate of dissipation of kinetic energy per unit mass of fluid) decreases, which is in agreement with the further analysis of oceanic turbulence shown in this paper. Furthermore, it is concluded that propagation of laser beams is more affected by oceanic optical turbulence in abyssal region than that in active region or oceanic surface.     

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.     

基于M2因子测量的大气湍流参数的确定方法

基于广义惠更斯-菲涅尔原理以及大气湍流理论,推导出部分相干光束在大气湍流中传输的光束传输M ^{2因子的解析表达式.定量分析了表征大气湍流参数的折射率结构常数 C2_n}和涡旋内尺度 l _{0对 M ^{2因子的影响,并由此提出了一种通过实验测量大气湍流中光束的 M 2因子,进而确定出大气湍流参数的新方法.研究结果表明,由于大气湍流对相干性好的光束影响更为明显,在测量中可采用具有高相干性的基模高斯光束作为测量光源,而测量装 关键词： 2因子')" href="#">光束传输 M 2因子 大气湍流参数 湍流折射率结构常数 湍流涡旋内尺度}}     

Higher order mode laser beam scintillations in oceanic medium

Abstract

In a horizontal oceanic optical wireless communication link, the scintillation index (the measure for the intensity fluctuations) of the received intensity caused by the oceanic turbulence is formulated and evaluated when the source is a higher order mode laser. Variations in the scintillation index vs. the underwater turbulence parameters, size of the higher order mode laser source, link length, and the wavelength are examined. Underwater turbulence parameters are the ratio that determines the relative strength of temperature and salinity in driving the index fluctuations, the rate of dissipation of the mean squared temperature, the rate of dissipation of the turbulent kinetic energy, and the Kolmogorov microscale length.     

Effect of oceanic turbulence on polarization of stochastic beams

On the basis of the extended Huygens-Fresnel principle and the unified theory of coherence and polarization of light we determine the changes in various polarization properties of stochastic beams propagating through the turbulent clear-water ocean. The ocean-induced fluctuations in the refractive index are described via the recently developed power spectrum which takes into account both temperature and salinity variations. Numerical examples of changes in the spectral density, the degree of polarization and in the polarization ellipse are given for electromagnetic Gaussian Schell-model beams. We demonstrate, in particular, how polarization of the propagating beam is affected by statistical properties of the source and by several parameters of oceanic turbulence. We find that propagation of light beams in the oceanic turbulence resembles that in the atmospheric turbulence qualitatively, however evolution and asymptotic saturation of polarization in the oceanic turbulence occurs at much shorter distances.     

部分相干光在大气湍流中的到达角起伏

研究了部分相干高斯谢尔光束在大气湍流中的到达角起伏.主要采用湍流内外尺度的修正Von Karmon谱模型及广义惠更斯-菲涅尔原理和交叉谱密度函数推导出了部分相干光在大气湍流中的到达角起伏表达式.对比分析了湍流内外尺度、湍流强度、传输距离、源相干参数以及波长等参数对部分相干光在大气湍流水平路径上传输时的到达角起伏的影响.结果表明:随着传输距离的增加,到达角起伏越来越小;随着大气湍流内外尺度和源相干参数的增加,到达角起伏也越来越大;与部分相干光相比,完全相干光的到达角起伏受湍流影响很小;随着波长和湍流强度的减小,到达角起伏越来越小.     

湍流对离轴列阵高斯光束相干与非相干合成的影响

研究了湍流对离轴列阵高斯光束相干与非相干合成的影响.推导出了相干合成光束的传输方程.采用二阶矩束宽、桶中功率和参数β作为光束质量评价参数比较了离轴列阵高斯光束通过湍流大气的相干与非相干合成,并对主要结果给予了合理的物理解释.研究表明：一方面,不论是相干合成还是非相干合成,湍流都使得合成光束扩展、峰值光强下降,并且子光束数越多,合成光束受湍流影响就越小.另一方面,非相干合成光束较相干合成光束受到湍流的影响要小. 关键词： 相干与非相干合成 湍流大气 离轴列阵高斯光束     

Influence of atmospheric turbulence on the propagation of superimposed partially coherent Hermite-Gaussian beams

The influence of atmospheric turbulence on the propagation of superimposed partially coherent Hermite-Gaussian (H-G) beams is studied in detail. The closed-form propagation equation of superimposed partially coherent H-G beams through atmospheric turbulence is derived. It is shown that the turbulence accelerates the evolution of three stages which superimposed partially coherent H-G beams undergo. The turbulence results in a beam spreading and a decrease of the maximum intensity. However, the larger the beam number M, the beam order m, the separate distance x_d, and the smaller the beam correlation length σ₀ are, the less the power focusability of superimposed partially coherent H-G beams is affected by the turbulence. Specially, superimposed partially coherent H-G beams are less sensitive to turbulence than superimposed fully ones, and than partially coherent H-G beams if the beam power focusability and the maximum intensity are taken as beam criterions. However, the maximum intensity of superimposed partially coherent H-G beams is less sensitive or more sensitive to turbulence than that of superimposed Gaussian Schell-model (GSM) beams depending on σ₀.     

利用闪烁和漂移效应测量大气折射率结构常数的对比分析

 在近海面大气边界层中进行了1 km路径的水平光传输实验，结果表明：利用闪烁和漂移效应推导的大气折射率结构常数之间存在着较大的差异。定量的理论分析揭示了两者不一致的原因在于：闪烁效应主要对路径中部的小尺度湍涡敏感，漂移效应则对发射端附近的大尺度湍涡敏感；随着内尺度变大，漂移效应测量的折射率结构常数将大于闪烁效应测量的折射率结构常数，当内尺度达到20 mm时，前者的测量结果是后者的3倍；当外尺度变小时，漂移效应的测量结果小于闪烁效应的测量结果，当外尺度仅为1 m时，前者的测量结果为后者的1/2；大气折射率3维功率谱的幂律的变化对测量结果的影响非常大，当幂律大于-11/3时，闪烁效应测量的折射率结构常数大于漂移效应测量的折射率结构常数， 最大差异接近于25倍， 当幂律小于-11/3时，漂移效应的测量结果大于闪烁效应的测量结果，两者的差异甚至可达两个量级。     

多光束发射对湍流效应下激光传输的影响

大气湍流引起的光强起伏会导致大气闪烁、光束漂移、到达角起伏和波前畸变等效应.多光束发射技术是克服激光大气传输中光强起伏的有效途径之一.以单光束、双光束、四光束以及八光束发射为例,通过计算峰值光强、环围功率半径以及像散参数等光束质量参数,得到单光束和多光束大气传输的光强起伏特性.结果表明:随着光束数目的增加,峰值光强显著...