Propagation of partially coherent Gaussian laser beams in graded-index fibres

Using statistical approach the author has solved the equations for the mutual coherence function of partially coherent Gaussian laser beams in graded-index fibres. The expressions for the complex degree of coherence and the intensity distribution have also been shown that the self-focusing length inside the fibre depends upon the degree of coherence. The result have been discussed for both conical and cylindrical guides.     

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.     

部分相干涡旋光束在湍流大气中的传输特性

根据广义的惠更斯-菲涅耳原理,推导了部分相干涡旋光束在湍流介质中传输时光强分布情况的理论公式,详细研究了部分相干涡旋光束在湍流介质中的传输变化规律。研究结果表明,湍流介质的强弱,光源的相干性以及光束所带拓扑电荷数大小均会影响光束传输特性。     

部分相干空心光束在湍流介质中的传输特性

根据广义的惠更斯-菲涅耳原理，得到了相干度为零阶贝塞耳函数的部分相干空心光束在湍流介质中传输特性的理论公式.据此研究了这种光束在湍流介质中的传输变化规律.研究结果表明，湍流介质的强弱，光源的相干性以及光源光斑大小均会影响光束的传输特性.     

部分相干光束经过湍流大气传输研究进展

相较于相干光束,部分相干光束经过湍流大气传输能够有效地抑制湍流引起的光束展宽、光斑漂移及光强闪烁等扰动效应,在自由空间光通信、激光雷达和激光遥感等方面有重要的应用前景.近年来,部分相干光束湍流大气传输研究受到越来越多学者的关注.本文回顾了部分相干光束在湍流大气中传输特性研究的发展历程、理论基础及常用的理论方法,介绍了处理光束经过湍流大气传输的相位屏数值模拟方法,以及如何把该方法运用到处理部分相干光束传输.     

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.     

非傍轴部分相干厄米-高斯光束的相干和非相干合成

推导出二维非傍轴部分相干厄米-高斯（H-G）光束相干合成和非相干合成的交叉谱密度和光强的解析公式,并分析了一些特例. 合成光束的光强不仅决定于f参数,f_σ参数,离轴参数,合成光束的束数和阶数以及传输距离z,而且还决定于合成方式. 对部分相干光的相干合成和非相干合成概念做了物理诠释,其正确性为数值计算例证实. 关键词： 部分相干光的相干和非相干合成 非傍轴部分相干厄米-高斯（H-G）光束 自由空间中的传输方程     

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。     

Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere

The characteristics of partially coherent Bessel-Gaussian beams propagating in turbulent atmosphere are investigated. Based on the extended Huygens–Fresnel principle, the influence of topological charges and coherence of the source on the intensity and the degree of coherence in the received plane are considered. The influence of atmospheric turbulence on beam profile and coherence in the received plane is also analyzed. It is found that a Bessel-Gaussian shaped intensity distribution will eventually transform into a Gaussian distribution after propagating in turbulent atmosphere. Meanwhile, topological charges, coherence of the source and atmospheric turbulence will also influence the propagation characterizations of the beams.     

Propagation of partially coherent beams carrying an edge dislocation through atmospheric turbulence along a slant path

This paper derives the explicit expressions for the average intensity, beam width and angular spread of Gaussian Schell-model (GSM) beams with edge dislocation propagating through atmospheric turbulence along a slant path. The propagation of GSM beams with edge dislocation through horizontal atmospheric turbulence can be treated as a special case through a slant one. The propagation properties of GSM beams with edge dislocation through slant atmospheric turbulence are studied, where the influence of edge dislocation parameters including the slope p and off-axis distance d on the spreading of GSM beams with edge dislocation in atmospheric turbulence is stressed. It shows that the spreading of the intensity profile of GSM beams with edge dislocation along a slant path is smaller than that along a horizontal path in the long-distance atmospheric propagation. The larger the slope vert pvert and the smaller the off-axis distance vert dvert are, the less the beam-width spreading and angular spread of GSM beams with edge dislocation are affected by turbulence. The GSM beams with edge dislocation is less affected by turbulence than that of GSM beams without edge dislocation. The results are illustrated numerically and their validity is interpreted physically.     

多色部分相干偏心光束在non-Kolmogorov湍流中的传输

推导了多色部分相干偏心光束在non-Kolmogorov 湍流中传输的总光强、轴上光谱、相干度的解析表达式, 研究了光束偏心参数β 、湍流广义指数α和源光谱带宽Ω对激光传输特性的影响. 研究表明: β越大, 则光束重心偏离传输轴越远, 相干度的不对称性越明显, 但是, β对轴上光谱几乎没有影响; 湍流广义指数α对总光强、 轴上光谱和相干长度的影响是非单调的, 当α=3.1时, 湍流对光束传输特性的影响最大. 值得指出的是: 在某些传输距离处, 不同α对应的轴上光谱位移量相同; 在某些传输距离处, 轴上光谱位移量为零, 且该传输距离与Ω无关, 但湍流使得该传输距离缩短. 所得结论对多色部分相干偏心光束在 湍流大气中传输的相关应用具有重要意义. 关键词： non-Kolmogorov湍流 多色部分相干偏心光束 光谱强度 相干度     

Spreading of apertured partially coherent beams in turbulent media

The closed-form expression for the mean-squared width of apertured partially coherent beams propagating through turbulent media is derived by using the integral transform technique. The influence of turbulence on the spreading of apertured partially coherent beams is studied quantitatively by examining the relative mean-squared width, which is defined as the ratio of the mean-squared width of an apertured partially coherent beam in turbulence to the mean-squared width of the same beam in free space. On the other hand, the range of turbulence-independent propagation, also a reasonable measure of the resistance of a beam to turbulence, is obtained by examining the mean-squared width. It is shown that the spreading of apertured partially coherent beams is less affected by turbulence with smaller truncation parameter δ and coherence parameter α than with larger δ and α. In addition, the influence of turbulence on the spreading of apertured partially coherent beams increases first and then decreases due to increasing waist width w₀. The results obtained are explained physically.     

Propagation properties of partially coherent Laguerre-Gaussian beams in turbulent atmosphere

To study the propagation properties of partially coherent Laguerre-Gaussian (PLG) beams through turbulent atmosphere, the analytical formulas are derived for the angular width and the beam-propagation factor (M²-factor) of PLG beams by using the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function (WDF). The corresponding numerical results are also calculated. When propagation distance increases, the angular width is found to spread faster for PLG beams with higher beam order, smaller correlation length and bigger structure constant The angular width of PLG beams decreases with increase in waist width (w₀).The M²-factor of PLG beams with higher beam order and smaller correlation length is less affected by turbulence with increase in propagation distance. The propagation properties of the M²-factor for PLG beams with the smaller structure constant are better than that with bigger structure constant . The M²-factor of PLG beams decreases with increase in the wavelength λ, and it is also less affected by turbulence for beams with higher order and smaller correlation length. Furthermore, for the PLG beams with the same beam order, the angular width and the M²-factor keep invariable in free space.     

部分相干双曲余弦厄米高斯光束在非Kolmogorov大气湍流中的传输特性

基于广义Huygens-Fresnel原理和非Kolmogorov大气湍流折射率起伏谱密度函数, 采用Wigner分布函数的二阶矩方法, 推导出了在大气湍流中传输的部分相干双曲余弦厄米高斯光束束宽和M²因子的解析表达式. 研究表明: 相对束宽和归一化M²因子随传输距离的增大而增大; 光束阶数越大、相干长度越小、双曲余弦参数越小, 相对束宽和归一化M²因子受大气湍流影响越小; 相对束宽随束腰宽度的增大存在极大值, 在一定的相干长度范围内, 归一化M²因子随束腰宽度的增大存在极小值; 相对束宽和归一化M²因子随广义指数的变化均存在极大值, 随内尺度的增大而逐渐减小, 随外尺度的增大几乎没有变化.     

利用部分相干光和同心角偏差透镜列阵实现二维靶面均匀辐照

提出利用部分相干光通过透镜列阵系统实现靶而的均匀辐照, 透镜列阵能获得边缘陡峭且顶部较平坦的准近场焦斑, 透镜列阵的适当同心度偏差又使各子束的斑纹相互稍微错开, 使干涉斑纹变密, 而入射的激光是空间相干性减少了的部分相干光, 可进一步抑制了透镜列阵系统焦斑的小尺度不均匀性. 使用广义衍射积分理论, 对高斯-谢尔光束通过透镜列阵光学系统的焦斑光强分布进行了详细的二维模拟研究, 比较了完全相干光与部分相干光经过透镜列阵的匀滑效果. 数值模拟表明, 应用同心度偏差和适当离焦时, 可实现焦斑均匀性和能量利用率同时达到最佳的效果.     

Propagation of partially polarized Gaussian Schell-model beams in anomalously dispersive media

By use of a tensor method, analytical transform formulae for isotropic partially polarized GSM beams propagating in anomalously dispersive media are derived. Based on the derived formula, the propagation properties of isotropic partially polarized GSM beams in anomalously dispersive media are studied in detail. The results show that the polarization and the irradiance distribution and the coherence degree properties are influenced by the anomalously dispersive media and beam's initial coherence. In addition, the evolution of the spectrum shows that spectrum splitting and spectral shift occur during propagation in anomalously dispersive media.     

非均匀部分相干光束在自由空间中的传输

本文介绍了非均匀部分相干光束的概念, 并用数值模拟的方法详细研究了其在自由空间传输后的变化. 研究结果表明, 经过自由空间传输后非均匀部分相干光束会发生不同于传统相干模型光束的显著变化. 这种变化和光束传输距离、光源空间相干度分布、光源光强分布密切相关. 经过传输后, 源平面自相干附近点的空间相干度发生突变, 在短距离传输过程中源平面高相干区域的空间相干度会降低, 接收面各点的空间相干曲线不再相同, 随着传输距离增加, 非均匀空间相干度会逐渐趋于均匀.     

Beam propagation factor of partially coherent Hermite-Gaussian beams through non-Kolmogorov turbulence

Based on extended Huygens-Fresnel principle, an analytical expression of M² factor for partially coherent Hermite-Gaussian (PCHG) beams through non-Kolmogorov turbulence is obtained. Our results show that M² factor of PCHG beams depends on coherence length, beam order m, wavelength, exponent value α, outer scale L₀ and inner scale l₀. The impact of the exponent's variation on the M² factor is analyzed in detail. When the propagation distance fixed, the M² factor of PCHG beams has a maximum for alpha values lower than 11/3.