大气湍流中光束的高阶强度矩

研究了光束通过大气湍流传输的高阶强度矩, 提出了大气湍流中光束高阶强度矩的推导方法, 并推导出了一至四阶光束强度矩传输的解析表达式. 所得结果具有一般性,任意某一光束在自由空间和大气湍流中传输的高阶强度矩均可作为本文结果的特例. 另一方面, 以高斯光束为例, 研究了其K参数在湍流大气中的传输规律. 研究表明,高斯光束在大气湍流中其K参数并不是一个传输不变量,它与传输距离、束腰半径、湍流内外尺度以及湍流强度均有关.这个结论与采用Rytov相位结构函数二次近似或强湍流近似下的结论不同,本文给出了合理解释. 关键词： 高阶强度矩 大气传输 大气湍流 K参数')" href="#">K参数     

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.     

Effects of coherence and polarization on the beam spreading and direction through atmospheric turbulence

Based on extended Huygens-Fresnel principle, analytical expressions of beam width and far-field angular spreading for electromagnetic Gaussian Schell-model (EGSM) beams propagating in atmospheric turbulence are obtained. The effects of coherence and polarization on beam spreading and directionality in atmospheric turbulence are investigated in detail. A condition is obtained under which beams with different degrees of spatial coherence and polarization will generate the same far-field angular spreading in atmospheric turbulence. Our results have potential application in long-distance free space optical communications.     

Intensity distribution properties of Gaussian vortex beam propagation in atmospheric turbulence

By using wave optics numerical simulation, the intensity-hole effect, beam spreading and wandering properties of Gaussian vortex beam propagation in atmospheric turbulence are investigated quantitatively. It is found that an intensity hole in the center of the beam pattern appears gradually as a Gaussian vortex beam propagates. The size of the intensity hole increases with the increase of the topological charge of the vortex phase. However, the intensity hole could to some extent be filled with optical energy by atmospheric turbulence, especially in strong turbulence. The radius of the intensity hole first decreases and then increases with the growth of turbulence strength. The effective radius of vortex beam with larger topological charge is greater than with a smaller topological charge. But the topological charge has no evident influence on beam wandering.     

Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere

The propagation of an elliptical Gaussian beam (EGB) through an astigmatic ABCD optical system in a turbulent atmosphere is investigated. An analytical formula for the average intensity of an EGB and a generalized tensor ABCD law for the generalized complex curvature tensor are derived. As an application example, we derived an analytical formula for the average intensity of an elliptical flat-topped beam propagating through an astigmatic ABCD optical system in a turbulent atmosphere. As a numerical example, the focusing properties of an EGB focused by a thin lens in a turbulent atmosphere are studied. It is found that the focused beam at the focal plane becomes a circular Gaussian beam when the atmospheric turbulence is strong enough, and the beam width of the circular Gaussian beam is determined by atmospheric turbulence strength, focal length of the thin lens, and wavelength of the initial beam but is independent of the initial beam widths (i.e., initial intensity distribution).     

Spectral properties of apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model beam propagating in turbulent atmosphere

Based on the extended Huygens-Fresnel principle, analytical formulas are derived for the cross-spectral density matrix of an apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model (ETAGSM) beam propagating in a turbulent atmosphere by use of a tensor method. Spectral properties of apertured ETAGSM beam are closely related with the strength of atmospheric turbulence, the aperture widths and the beam's parameters, etc. Our main attention was focused on the influence of the aperture widths, atmospheric turbulence, twist parameters and partial coherence on the spectral properties (including spectral degree of polarization, the spectral degree of coherence and the spectral density) of apertured ETAGSM beam propagating in turbulent atmosphere. Numerical calculation results and analysis are given.     

激光空间相干性对照明均匀性的影响

 研究了激光相干性对照明均匀性的影响，为照明激光器的选择提供了理论参考。其中，部分相干高斯光束分解为模式间相互独立的厄米-高斯光束的迭加。采用相位屏的近似处理方法对激光通过大气湍流的传输进行计算模拟。数值模拟的结果表明：当照明光束的空间相干性降低时，其照明均匀度逐步提高。因此对于照明激光器而言，选择空间相干性较差的激光器对其照明均匀度更加有益。     

Kinetics of Anisotropic Scattering and Optical Turbulence upon Laser Irradiation of AgCl:Ag Films

The kinetics of anisotropic scattering and optical turbulence upon formation of quasi-periodic structures (QPSs) in photosensitive composite AgCl:Ag films irradiated by Gaussian beams of a He-Ne laser is studied. The buildup kinetics of the scattering induced by an unfocused beam is used to find the threshold exposures for the formation of QPSs and an additional spatiotemporal instability resulting from interaction between the gratings during their development. It was established that there exists a threshold for the formation of a strong instability (optical turbulence) when the QPSs are induced by a focused beam. The decay curves of the mean frequency of the chaotic intensity oscillations, as well as the dependence of this frequency on the beam power, are obtained under conditions of turbulence. It is shown that both the turbulence and its decay are controlled by a competition between the microgratings in the QPSs and by gradual widening of the area of active competition under the action of the Gaussian beam. The AgCl:Ag films are shown to be capable of rapidly and repeatedly rearranging the QPSs and the spatial orientation of the anisotropic scattering upon variation of the direction of linear polarization of the laser beam.     

Effect of spatial coherence on the scintillation properties of a dark hollow beam in turbulent atmosphere

With the help of a tensor method, we derive an explicit expression for the on-axis scintillation index of a circular partially coherent dark hollow (DH) beam in weakly turbulent atmosphere. The derived formula can be applied to study the scintillation properties of a partially coherent Gaussian beam and a partially coherent flat-topped (FT) beam. The effect of spatial coherence on the scintillation properties of DH beam, FT beam and Gaussian beam is studied numerically and comparatively. Our results show that the advantage of a DH beam over a FT beam and a Gaussian beam for reducing turbulence-induced scintillation increases particularly at long propagation distances with the decrease of spatial coherence or the increase of the atmospheric turbulence, which will be useful for long-distance free-space optical communications.     

Range of turbulence-negligible propagation of Gaussian Schell-model array beams

For linear Gaussian Schell-model (GSM) array beams, the range of turbulence-negligible propagation, in which all of the spatial and angular spreading and the beam propagation factor increasing due to turbulence can be neglected, has been investigated in detail. It is shown that this range of GSM array beams increases with decreasing turbulent parameter and coherent parameter, and depends on the beam number, the waist width, and the relative beam separation distance. This range of a GSM array beam is larger than that of a coherent Gaussian array beam, and this range of a GSM array beam with a large relative beam separation distance is larger than that of a single GSM beam, implying that a GSM array beam may be more appropriate to be used in atmospheric optical communication links than a coherent Gaussian array beam or a GSM beam.     

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.     

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.     

Partially coherent elegant Hermite–Gaussian beam in turbulent atmosphere

Based on the extended Huygens–Fresnel integral, analytical formulas for the cross-spectral density, mean-squared beam width and angular spread of a partially coherent elegant Hermite–Gaussian (HG) beam in turbulent atmosphere are derived. The evolution properties of the average intensity, spreading and directionality of a partially coherent elegant HG beam in turbulent atmosphere are studied numerically. It is found that the partially coherent elegant HG beam with smaller initial coherence width, larger beam order and longer wavelength is less affected by the atmospheric turbulence. Compared to the partially coherent standard HG beam, the partially coherent elegant HG beam is less affected by turbulence under the same condition. Furthermore, it is found that there exist equivalent partially coherent standard and elegant HG beams, equivalent fully coherent standard and elegant HG beams, and an equivalent Gaussian–Schell-model beam may have the same directionality as a fully coherent Gaussian beam whether in free space or in turbulent atmosphere. Our results can be utilized in short and long atmospheric optical communication systems.     

Light scintillation in oceanic turbulence

The scintillation index of plane and spherical light waves as well as of a Gaussian beam, propagating in the clear-water weakly turbulent ocean, is revealed. The results are of utmost importance for underwater optical communications and sensing. An analysis of the threshold between the weak and strong regimes of oceanic turbulence is made, with the accent on the contribution from salinity-induced turbulence. It is found that strong oceanic turbulence can occur at distances as short as several meters, in striking contrast with atmospheric studies for which the typical distances are on the order of a kilometer.     

Optimized multiemitter beams for free-space optical communications through turbulent atmosphere

Using laser beams with less than perfect spatial coherence is an effective way of reducing scintillations in free-space optical communication links. We report a proof-of-principle experiment that quantifies this concept for a particular type of a partially coherent beam. In our scaled model of a free-space optical communication link, the beam is composed of several partially overlapping fundamental Gaussian beams that are mutually incoherent. The turbulent atmosphere is simulated by a random phase screen imprinted with Kolmogorov turbulence. Our experiments show that for both weak-to-intermediate and strong turbulence an optimum separation between the constituent beams exists such that the scintillation index of the optical signal at the detector is minimized. At the minimum, the scintillation reduction factor compared with the case of a single Gaussian beam is substantial, and it is found to grow with the number of constituent beams. For weak-to-intermediate turbulence, our experimental results are in reasonable agreement with calculations based on the Rytov approximation.     

Atmospheric turbulence and numerical evaluation of bit error rate (BER) in free-space communication

Bit error rate (BER) is an important parameter in free-space optical (FSO) communication. This paper presents the numerical evaluation of BER by studying the propagation of an initial Gaussian laser beam through turbulent atmosphere. Beam scintillation, spreading and wandering were considered as the atmospheric turbulent effects on the laser beam degradation. Different turbulent conditions and laser beam characteristics were applied to the calculations. The results show that the BER can be influenced considerably by atmospheric turbulence. According to these results the laser beam size and wavelength have also significant effects in the BER values.     

Change in degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence

We study the change in the degree of coherence of partially coherent electromagnetic beam (so called electromagnetic Gaussian Schell-model beam). It is shown analytically that with a fixed set of source parameters and under a particular atmospheric turbulence model, an electromagnetic Gaussian Schell-model beam propagating through atmospheric turbulence reaches its maximum value of coherence after the beam propagates a particular distance, and the effective width of the spectral degree of coherence also has its maximum value. This phenomenon is independent of the used turbulence model. The results are illustrated by numerical curves.     

Propagation Characteristics of a Partially Coherent Gaussian Schell-model Array Vortex Beam in the Joint Turbulence Effect of a Jet Engine and Atmosphere

This work investigates the joint effects of jet engine exhaust-induced turbulence and atmospheric turbulence on the propagation of a partially coherent Gaussian Schell-model Array (GSMA) vortex beam. Using the two-process propagation method, analytical formulae are derived for the cross-spectral density, spectral density, degree of coherence, and beam width of the considered beam. The results show that the considered beam takes different shapes; when the spatial coherence is large, the spectral density of the GSMA vortex beam takes an elliptical shape, whereas when the spatial coherence is smaller, the spectral density remains a Gaussian shape. The evolution profile of the degree of coherence weakens gradually when the propagation distance, topological charge, and turbulence strength increase. Moreover, the profile of the degree of coherence takes the Gaussian profile when the propagation distance is longer or turbulence atmospheric is stronger. Furthermore, the results reveal that the corresponding beam spreads faster with a larger propagation distance, lower spatial coherence, and high-strength turbulence. This study also concludes from the results that the beam is affected more when its propagation is near the jet engine exhaust, which means that this latter has a significant impact.     

Propagation properties of a partially polarized electromagnetic twist anisotropic Gaussian Schell-model beam in turbulent atmosphere

Based on the extended Huygens-Fresnel integral formula, analytical formulae for the elements of cross-spectral density matrix of partially polarized electromagnetic twist anisotropic Gaussian Schell-model (TAGSM) beam propagating in turbulent atmosphere can been derived by a tensor method. Our main attention was focus on the effect of the atmospheric turbulence, twist parameters and partial coherence on the spectral degree of polarization, the spectral degree of coherence and the spectral density. Numerical calculation results and analysis are given.     

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.