部分相干光在大气湍流中传输的闪烁指数

实验测量了不同空间相干度的部分相干光在实际大气湍流中传输的闪烁指数。结果表明:随着入射光空间相干度的降低,闪烁随光传输距离增长而增加的趋势变得缓慢,甚至出现减小的情况。此外,与完全相干光的闪烁指数随着径向距离的增加而增加不同,部分相干光的闪烁指数沿着光斑径向距离的增加不一定增加,而有可能出现降低。相干度越低,该效应越明显。     

部分相干光在大气湍流中传输的闪烁指数

实验测量了不同空间相干度的部分相干光在实际大气湍流中传输的闪烁指数。结果表明：随着入射光空间相干度的降低,闪烁随光传输距离增长而增加的趋势变得缓慢,甚至出现减小的情况。此外,与完全相干光的闪烁指数随着径向距离的增加而增加不同,部分相干光的闪烁指数沿着光斑径向距离的增加不一定增加,而有可能出现降低。相干度越低,该效应越明显。     

Effective Rayleigh range of Gaussian array beams propagating through atmospheric turbulence

The analytical expressions for the effective Rayleigh range z_R of Gaussian array beams in turbulence for both coherent and incoherent combinations are derived. It is shown that z_R of Gaussian array beams propagating through atmospheric turbulence depends on the strength of turbulence, the array beam parameters and the type of beam combination. For the coherent combination z_R decreases due to turbulence. However, for the incoherent combination there exists a maximum of z_R as the strength of turbulence varies. The z_R of coherently combined Gaussian array beams is larger than that of incoherently combined Gaussian array beams, but for the coherent combination case z_R is more sensitive to turbulence than that for the incoherent combination case. The larger the beam number is, the longer z_R is, and the more z_R is affected by turbulence. For the coherent combination z_R is not monotonic versus the relative beam separation distance, and the effect of turbulence on z_R is appreciable within a certain range of the relative beam separation distance.     

Angular spread of Gaussian Schell-model array beams propagating through atmospheric turbulence

The closed-form expression for the angular spread of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the angular spread θ _sp of GSM array beams for the superposition of the cross-spectral density function is smaller than of those for the superposition of the intensity. However, the θ _sp of GSM array beams for the superposition of the intensity is less sensitive to turbulence than that for the superposition of the cross-spectral density function. For the superposition of the cross-spectral density function, θ _sp of GSM array beams with smaller coherence length σ ₀, smaller waist width w ₀, smaller beam number N, and larger separation distance x _d are less affected by turbulence than of those with larger σ ₀,w ₀,N, and smaller x _d ; while, for the superposition of the intensity, the effect of turbulence on θ _sp is independent of N and x _d . In addition, the angular spread is nearly the same for the two types of superposition when σ ₀ or w ₀ is small enough, or x _d is large enough. On the other hand, it is found that there exist equivalent GSM array beams for the two types of superposition which may have the same directionality as the corresponding fully coherent Gaussian beam in free space and also in turbulence.     

Generalized Stokes parameters and polarization behavior of flat-topped array laser beam propagating through oceanic turbulence

In present paper, the analytical expression for the cross-spectral density of the phase-locked Partially Coherent Flat-Topped (PCFT) array beams propagating through oceanic turbulence based on the extended Huygens–Fresnel integral is derived. Then, the polarization behavior and generalized Stokes parameters of the phase-locked PCFT array beam propagating through oceanic turbulence using the cross-spectral density matrix elements have been achieved. In this paper, the case of the clearwater oceanic turbulence has been considered, i.e. it has been assumed that the light wave is not affected by suspended organic and inorganic impurities. Due to the above-mentioned reason and the turbulence importance, the impacts of oceanic turbulence have been scrutinized, while the effects of absorption and scattering have been ignored. The changes in the Stokes parameters, the fluctuation of Stokes parameters, and consequently the state of polarization (including the spectral degree of polarization, the orientation angle and the degree of ellipticity) of the phase-locked PCFT array beams for different turbulence conditions upon propagation have been investigated. The results may find possible applications in underwater communication.     

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.     

双曲余弦高斯列阵光束在湍流大气中的光束传输因子

本文推导出了双曲余弦高斯(ChG)列阵光束在湍流大气中的光束传输因子( M ^{2因子)的解析公式,并采用相对 M 2因子研究了湍流对 M 2因子的影响.研究表明,在湍流大气中 M 2因子不再是一个传输不变量,湍流使得 M 2因子增大.非相干合成情况下, M 2因子随着传输距离、光束参数、相对子光束间距和子光束数目的增大而增大.相干合成情况下, M 2因子随光束参数和相对子光束间距的增大呈现振荡上升.相干合成情况下的 M 2因子比 关键词： M2因子)')" href="#">光束传输因子(M2因子) 光束质量 双曲余弦高斯列阵光束 大气湍流}     

Characteristics of a partially coherent Gaussian Schell-model beam propagating in slanted atmospheric turbulence

On the basis of the extended Huygens-Fresnel principle and the model of the refractive-index structure constant in the atmospheric turbulence proposed by the International Telecommunication Union-Radio Communication Sector,the characteristics of the partially coherent Gaussian Schell-model(GSM) beams propagating in slanted atmospheric turbulence are studied.Using the cross-spectral density function(CSDF),we derive the expressions for the effective beam radius,the spreading angle,and the average intensity.The variance of the angle-of-arrival fluctuation and the wander effect of the GSM beam in the turbulence are calculated numerically.The influences of the coherence degree,the propagation distance,the propagation height,and the waist radius on the propagation characteristics of the partially coherent beams are discussed and compared with those of the fully coherent Gaussian beams.     

Spatiotemporal coherence properties of broadband Gaussian Schell-model beams propagating through atmospheric turbulence

The spatiotemporal coherence properties of broadband Gaussian Schell-model (GSM) beams with different spectral bandwidths propagating through atmospheric turbulence are numerically calculated and analyzed. The results show that although the spatial coherence properties of an intermediate-broadband GSM beam almost do not depend on the spectral bandwidth, those of its ultra-broadband counterpart do. The temporal coherence of an ultra-broadband GSM beam not only has radial dependence in the observation plane, but also varies with the increasing propagation distance; however, the same behavior does not hold for an intermediate-broadband GSM beam of which the temporal coherence remains nearly invariable as the radial distance of the observation point or propagation distance changes.     

Scintillation index of the Gaussian beams propagated through the paths with strong turbulence

Theoretical and experimental studies of the local statistical characteristics of Gaussian beams propagated through the paths with strong turbulence were carried out and their results are presented. It is ascertained that the applicability of the scintillation index meanings are substantially limited for the assessment of the performance quality of the optical data transmitting channels. On the basis of the experimental data got under different propagation conditions the peculiarities of the localized intensity distributions and those of the scintillation index are revealed.     

双曲余弦高斯列阵光束通过湍流大气传输的角扩展及方向性

 采用积分变换,推导出了双曲余弦高斯（ChG）列阵光束通过湍流大气传输的二阶矩束宽和角扩展的解析公式,给出了ChG列阵光束与一束高斯光束具有相同角扩展的条件。研究表明:相干合成的ChG列阵光束的角扩展比非相干合成的小,但是,非相干合成的ChG列阵光束的角扩展受湍流影响比相干合成ChG光束小;相干合成情况下,ChG列阵光束的角扩展随离心参数、束腰宽度和相对子光束间距的变化均出现振荡,但在湍流中的振荡减弱,非相干合成情况下,ChG列阵光束的角扩展与相对子光束间距和光束数无关。     

双曲余弦高斯列阵光束通过湍流大气传输的角扩展及方向性

采用积分变换,推导出了双曲余弦高斯（ChG）列阵光束通过湍流大气传输的二阶矩束宽和角扩展的解析公式,给出了ChG列阵光束与一束高斯光束具有相同角扩展的条件。研究表明:相干合成的ChG列阵光束的角扩展比非相干合成的小,但是,非相干合成的ChG列阵光束的角扩展受湍流影响比相干合成ChG光束小;相干合成情况下,ChG列阵光束的角扩展随离心参数、束腰宽度和相对子光束间距的变化均出现振荡,但在湍流中的振荡减弱,非相干合成情况下,ChG列阵光束的角扩展与相对子光束间距和光束数无关。     

Beam spreading of truncated Gaussian beams in Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle and the hard-edge aperture function expanded as the sum of finite-term complex Gaussian function, analytical expression for average intensity of truncated Gaussian beam in Kolmogorov turbulence is derived, and some limiting cases are discussed. The influences of many factors, such as Fresnel number, wavelength, truncation parameter and structure constant on beam spreading are studied with the help of the average intensity formula. We found that the peak value of average intensity decreases and the beam spot spreads with the decrease of Fresnel number. The change of peak intensity against Fresnel number is slower with large aperture than that with small aperture. When Fresnel number is not small enough the influence of turbulence on intensity profiles is so small that can be neglected if structure constant is small.     

Beam propagation factor of radial Gaussian-Schell model beam array in non-Kolmogorov turbulence

The analytical expression for the beam propagation factor (M²-factor) of a radial Gaussian-Schell model (GSM) beam array propagating in non-Kolmogorov turbulence is derived. The influences of beam number, ring radius and generalized exponent on the M²-factor are investigated. The results indicate that the M²-factor has great dependence on the generalized exponent and the beam number. Moreover, there is an optimum ring radius, which leads to a minimum M²-factor and increases with increase in beam number. Further, the M²-factor for the superposition of the intensity is larger than that for the superposition of the cross-spectral density function (CSDF). However, the M²-factor for the superposition of the intensity is less sensitive to the turbulence than that for the superposition of the CSDF.     

大气湍流对径向分布高斯列阵光束扩展和方向性的影响

采用积分变换的技巧,推导出了径向分布高斯列阵光束通过湍流大气传输的二阶矩束宽和远场发散角的解析公式,并详细研究了大气湍流对光束扩展和方向性的影响.研究表明,相干合成情况下,子光束数N越小、径向分布半径r₀越大,列阵光束扩展受湍流影响越小.相干较非相干合成时列阵光束的扩展小,但非相干合成时列阵光束扩展受湍流的影响比相干合成时的小.特别地,N足够小或r₀足够大时,相干与非相干合成列阵光束的远场束宽相等.另一方面,还给出了相干和非相干合成径向分布高斯列阵 关键词： 径向分布高斯列阵光束 大气湍流 相干和非相干合成 二阶矩束宽     

Scintillation behavior of Laguerre Gaussian beams in strong turbulence

In strong atmospheric turbulence, the asymptotic on-axis scintillation behaviors of Laguerre Gaussian (LG) beams are examined. To arrive at the strong-turbulence solution, we utilize the existing filtering approach for weak-turbulence solutions and our recently reported weak-turbulence scintillation index formula for LG beams. In the limiting case, our solution correctly predicts the asymptotic strong-turbulence behavior of Gaussian beam wave scintillation. Investigation of the scintillations versus the propagation distance, source size, wavelength and refractive index structure parameter lead to the conclusion that the LG beams with higher order radial modes can provide less scintillation. The results are applicable to long-haul atmospheric optical communication links.     

Influence of turbulence on the beam propagation factor of Gaussian Schell-model array beams

The analytical expression for the beam propagation factor (M²-factor) of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the M²-factor of GSM array beams depends on the beam number, the relative beam separation distance, the beam coherence parameter, the type of beam superposition, and the strength of turbulence. The turbulence results in an increase of the M²-factor. However, for the superposition of the intensity the M²-factor is less sensitive to turbulence than that for the superposition of the cross-spectral density function. The M²-factor of GSM array beams is larger than that of the corresponding Gaussian array beams. However, the M²-factor of GSM array beams is less affected by turbulence than that of the corresponding Gaussian array beams. For the superposition of the cross-spectral density function a minimum of the M²-factor of GSM array beams may appear in turbulence, which is even smaller than that of the corresponding single GSM beams.     

Scintillation of Airy beam arrays in atmospheric turbulence

We investigate the scintillation properties of Airy beam arrays in atmospheric turbulence. By utilizing the "self-bending" propagation property of Airy beams, the constituent beamlets propagate through relatively independent regions of turbulence but still largely overlap at the on-axis detector. Through numeric simulations, it is shown that the scintillation of an Airy beam array is significantly reduced and close to the theoretical minimum.     

部分相干平顶光束通过湍流大气传输的等效曲率半径

推导出了部分相干平顶光束在湍流大气中传输的等效曲率半径的解析表达式,详细地研究了湍流对其等效曲率半径的影响.研究表明,湍流使得等效曲率半径R减小,但是只有当湍流足够强时等效曲率半径极小值出现的位置z_min才会改变.在弱湍流中,R随着光束相干长度β的增大而增大;但是在强湍流中,R随着β的增大而减小.R随着光束阶数M(N)的增大而缓慢减小.若β越大、 关键词： 等效曲率半径 湍流 部分相干平顶光束