Asymptotic analysis of finite-beam scintillations in a turbulent medium

Asymptotic analysis of on-axis intensity fluctuation variance of a finite-sized light beam is performed starting from the functional integral representation for the field in a random medium. Collimated, diverging and converging beams with different diffraction properties are considered. A complete set of asymptotes is obtained using the main and additional coherence channels approach to the fourth moment of field analyses. We study the conditions of weak and strong fluctuation regimes for all these types of beams and obtain relatively simple formulae for on-axis intensity variance, which are valid for the case of stratified turbulence. It is shown that scintillations in the vicinity of the beam focus are governed by double-scattering processes for weak scintillations and double scattering from coherence channels for strong fluctuations.     

轴锥镜光强分布的角谱衍射数值分析法

针对理论上推导轴锥镜的衍射光场分布解析式较为困难,且用菲涅耳衍射理论分析时存在近轴近似及不能适用于近场衍射光场分析的问题,采用了严格遵从标量衍射亥姆霍兹方程的角谱衍射波前重建方法,对轴锥镜在单色和准单色高斯光波照射下的横向和轴向衍射光强分布特性,以及在单色均匀平面光波照射下的轴向衍射光强分布进行了数值计算和分析。结果表明,轴锥镜后单色光衍射光强分布在几何光束重叠的菱形区域内为近似无衍射贝塞尔光强分布,轴上光强沿光轴方向呈振荡变化,轴上光强分布规律与入射光波的垂轴横向光强分布有关;入射光的准单色性使得贝塞尔衍射条纹对比度略下降、轴上光强沿光轴方向振荡程度减小,但分布规律与单色光一致。     

分数傅里叶变换面上余弦-高斯光束的变换特性

 利用Wigner分布函数的方法，研究了余弦-高斯光束的分数傅里叶变换特性。导出了余弦-高斯光束在分数傅里叶变换面上光强分布和束宽的解析计算公式，并对此进行了数值模拟计算。研究表明：分数傅里叶变换阶数对余弦-高斯光束的光强分布有明显影响，余弦-高斯光束的轴上光强随分数傅里叶变换阶数呈周期性变化，束宽随分数傅里叶变换阶数也呈周期性变化，周期为2；对给定调制参数的余弦-高斯光束，通过适当选取分数傅里叶变化阶数可以获得平顶的光强分布。     

部分相干平顶光束在梯度折射率介质中的传输特性

利用广义惠更斯-菲涅尔衍射积分方法,推导出部分相干平顶光束在梯度折射率介质中传输的交叉谱密度函数解析表达式,对部分相干平顶光束在梯度折射率介质中的传输特性进行了分析,并进一步讨论了介质梯度折射率系数、光束阶数以及光束相干性对传输特性的影响.结果表明,部分相干平顶光束在梯度折射率介质中传输时的轴上光强分布呈现周期性变化了,且周期由梯度折射率系数决定,而与光束相干性无关.光束阶数越高、相干性越好、介质梯度折射率系数越大,则在介质中的轴上峰值光强越大.并且,在光强峰值位置附近的光强分布随传输距离的变化非常剧烈.     

Characteristics of scintillations and bit error rate of partially coherent rectangular array beams in turbulence

According to the paraxial form of the extended Huygens-Fresnel principle, the analytical formulas of the on-axis average irradiance and the on-axis scintillation index for a rectangular array Gaussian Schell-model (RAGSM) beams in atmospheric turbulence have been derived. The on-axis bit error rate has been analyzed quantitatively. Their effects of the turbulence intensity, the initial correlation length, and the array parameters including the beamlet number (M and N) and the array separation distance (x₀ and y₀) have been discussed. The results show that the correlated and uncorrelated superposition RAGSM beams exhibit the different on-axis intensity distribution, the similar variation of the on-axis scintillation and the bit error rate. At the nearer propagation distance the on-axis scintillation rises against propagation distance with the increasing beamlet number and the decreasing array separation distance, whereas the situation is reversed at the farther propagation distance. The effects of array parameters on the bit error rate are similar to that on the scintillation. For a given propagation distance the scintillation index increases with the stronger coherence and the larger waist width of the array beam.     

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     

矢量非傍轴双曲余弦-高斯光束

 引入了矢量非傍轴双曲余弦-高斯(ChG)光束概念。使用矢量瑞利-索末菲衍射积分公式推导出了矢量非傍轴ChG光束在自由空间传输的解析公式。矢量非傍轴ChG光束轴上和远场的解析式以及傍轴结果作为一般传输公式的特例给出。研究表明,对矢量非傍轴ChG光束,其非傍轴性主要由f参数决定,但偏心参数会影响其横向光强剖面形状和非傍轴行为。     

Intensity distribution around the focal regions of real axicons

We present a theoretical and experimental study of the intensity distribution of a laser beam, after its propagation through a real axicon. We show that, while an ideal axicon generates Bessel-like radial intensity profile and smooth on-axis intensity around the focal region, in practice, the bluntness of the tip of the axicon causes significant deviations from these profiles. In particular, strong oscillations occur on the on-axis intensity. The input beam size also plays a strong role; for small beams the axicon acts more like a conventional lens, while for the large ones, it exhibits two focal regions. We also propose scheme for apodization. In all cases, the experiments match closely with the calculations. Our results show that axicons cannot be assumed to always generate smooth on-axis intensities and the structures coming from the real profiles should be taken into account for most applications.     

Axial intensity distribution and focal shifts of focused partially coherent conical Bessel–Gauss beams

Based on the generalized Huygens–Fresnel diffraction integral and the theory of partially coherent light, the axial intensity distribution and the focal shifts of focused partially coherent conical Bessel–Gauss beams are investigated. The dependence of the maximum on-axis intensity and the associated focal shift on the Fresnel number and the coherence parameter are examined and illustrated numerically. The results related to the J ₀-correlated beams and the fully coherent Bessel–Gauss beams are obtained as particular cases of this study.     

超短脉冲贝塞尔-高斯光束在自由空间的传输特性

 使用复解析信号法研究了束宽与频率无关的超短脉冲贝塞尔-高斯光束在自由空间的传输特性。研究表明：在无衍射长度内,超短脉冲贝塞尔-高斯光束的横向光强分布几乎不变并集中在传输轴附近,轴上脉冲随传输距离增加而展宽。在无衍射长度外,横向光强分布显著扩展。随传输距离增加,轴上光谱蓝移先增加,达到极大值后逐渐减小,最后在远场趋于一渐近值。对单周期的超短脉冲贝塞尔-高斯光束的轴上光谱蓝移先增加,达到极大值0.50 fs^-1。然后逐渐减小,在远场蓝移趋于渐近值0.16 fs^-1。     

Scintillation calculations for partially coherent general beams via extended Huygens–Fresnel integral and self-designed Matlab function

We present scintillation calculations in weak atmospheric turbulence for partially coherent general beams based on the extended Huygens–Fresnel integral and a Matlab function designed to handle expressions both of the average intensity and the average squared intensity. This way, the integrations are performed in a semi-analytic manner by the associated Matlab function, and this avoids lengthy, time-consuming and error prone hand derivations. The results are obtained for the partially coherent fundamental and higher-order sinusoidal and annular Gaussian beams. By plotting the scintillation index against the propagation distance and source size, we illustrate the on-axis scintillation behaviors of these beams. Accordingly, it is found that within specific source and parameter ranges, partially coherent fundamental, higher-order sinusoidal and annular Gaussian beams are capable of offering less scintillations, in comparison to the fundamental Gaussian beam.     

倾斜离轴高斯-谢尔模型光束在大气湍流中通过猫眼光学镜头反射光的光强特性

本文研究了大气湍流和探测光空间相干性对倾斜离轴激光束通过猫眼光学 镜头反射光光强特性的影响. 研究表明: 由于光阑效应以及光束倾斜或离轴, 反射光光强出现振荡和非对称分布现象. 大气湍流不会改变其非对称性, 但湍流中其光强不再振荡. 当猫眼光学镜头存在微弱正离焦δ_max情况下, 轴上光强可达到最大值. 猫眼光学镜头焦距越大, 所需δ_max越大. 但是, 大气湍流和探测光相干性好坏都不会改变所需δ_max值. 在大气湍流中传输距离足够远时, 反射光强会成为离轴类高斯分布. 随着传输距离的增大, 相干性越差的探测光的反射光束扩展可以更小, 这与部分相干光自由空间传输规律完全不同. 探测光相干性越好, 其反射光强受湍流的影响越大, 但差异不大. 本文所得结果对激光主动探测的应用具有意义. 关键词： 猫眼光学镜头 大气湍流 部分相干光 光强     

等衍射长度超短脉冲贝塞耳-高斯光束的传输特性

使用复解析信号法,研究了衍射长度与频率无关的超短脉冲贝塞耳－高斯光束在自由空间中的传输,推导出了解析表达式并进行了理论和计算分析.结果表明：在无衍射长度内,等衍射长度超短脉冲贝塞耳.高斯光束的横向光强分布扩展很小.在无衍射长度之外,横向光强分布有显著扩展.但是,在无衍射长度内轴上脉冲波形仍有展宽.随传输距离增加轴上蓝移单调增加逐渐达到一渐近值.随横向距离增加轴外光谱移动由蓝移变为红移.     

使用离焦望远镜系统合成轴上平顶光束的一种新方法

提出了用平顶多高斯光束作为理想光束和使用离焦望远镜系统合成轴上平顶光束的一种新方法.在近轴近似下,基于柯林斯衍射积分公式推导出轴上光场和入射光场的解析表达式,并做了物理分析.光束阶数N,平顶长度参数L,平顶中心位置z_c和纵向中心空间频率S_c对轴上光强分布的影响用数值计算例做了说明.比较表明,该方法优于文献中使用矩形函数模拟理想光束合成轴上平顶光束的方法. 关键词： 轴上平顶光束 平顶多高斯光束 离焦望远镜系统 傅里叶变换     

非傍轴矢量高斯光束的圆屏衍射

利用矢量瑞利衍射积分公式，推导出非傍轴矢量高斯光束圆屏衍射的解析表示式.非傍轴矢量高斯光束圆屏衍射的轴上场分布、远场表示式、自由空间中的传输公式，以及傍轴近似下高斯光束圆屏衍射的菲涅耳和夫琅禾费衍射公式可以作为一般公式的特例统一处理.数 值计算和比较实例说明了非傍轴矢量高斯光束的光强分布和远场特性.分析表明，在圆屏衍 射中，f参数和截断参数决定光束的非傍轴行为. 关键词： 传输光学 非傍轴矢量高斯光束 圆屏衍射 矢量瑞利衍射积分公式     

Focusing of high polarization order axially-symmetric polarized beams

We study the high numerical aperture focusing properties and typical applications of axially-symmetric polarized beams （ASPBs） with high polarization orders. We calculate the field distribution near focus of an aplanatic system for incident ASPBs with different polarization orders and initial azimuthal angles, and based on the simulation results, we find some unique focusing properties of the beams, such as ever on-axis energy null, strong longitudinal field, and flowerlike intensity distribution at focus. In addition, we can manipulate the three-dimensional （3D） focused field distribution flexibly by use of diffractive optical elements （DOEs）, which will give rise to some interesting applications, and we also discuss possible applications and present an example of a 3D optical chain at last.     

Debye Series of Scattering by a Multi-Layered Cylinder in an Off-Axis 2D Gaussian Beam

The Debye series of light scattering by an infinite multi-layered cylinder in an off-axis 21） Gaussian beam is studied. A simplified but rigorous iterative formula for scattering coefficients is presented. The numerical calculations of scattering intensity by a cylinder in on-axis and off-axis beams are developed. It is indicated that the results of Debye series reach an agreement with those of generalized Lorenz-Mie theory and the off-axis distances vary the results to a great extent. The Debye series components of a two-layered cylinder are further discussed. The relations between them with rainbow phenomena are analysed.     

Partially coherent Lorentz Gaussian beam and its scintillations

We study the scintillation aspects of partially coherent Lorentz Gaussian (LG) beams via numerically integrating the average and average squared intensity expressions. Within the examined range of input and propagation medium parameters, the LG beams are generally found to offer less and less scintillations against the pure Gaussian beam, particularly when the Lorentzian feature of the beam is emphasized more. This lower scintillation property is exhibited for collimated coherent beams with different Lorentz widths and at on-axis and off-axis positions of the receiver plane. When focusing is introduced, at shorter propagation distances the ordering of the beams remains as described above, but at longer propagations distances a complete reversing of the beam order is observed. Raising the turbulence levels by increasing the structure constant inevitably causes rises in scintillations, while preserving the advantage of LG beams over the pure Gaussian beam. Partial coherence reduces scintillations as expected, at the same time nearly eliminating the scintillation differences between the beam types.     

Scintillations of Laguerre Gaussian beams

By using the Rytov method, we formulate and numerically evaluate the scintillations of Laguerre Gaussian beams in weak atmospheric turbulence. Our results indicate that at on-axis positions, Laguerre Gaussian beams with zero angular mode number will have less scintillations than fundamental Gaussian beams, where the amount of scintillations will further decrease with rising radial mode number. When off-axis positions are considered, this situation reverses however, and the scintillations of Laguerre Gaussian beams become generally higher than the fundamental Gaussian beam. Plotted against the source size, the on-axis scintillations of Laguerre Gaussian beams fall below the fundamental Gaussian beam, following the same trend as the fundamental Gaussian beam all throughout the source size range examined.