湍流大气中激光聚焦光束后向散射的数值模拟

 对基于聚焦光束后向散射到达角起伏的湍流测量进行了数值模拟。通过近轴标量波动方程和分形相屏算法,提出了聚焦光束二次传输的数值模型,分别就固定点信标光源和聚焦光束后向散射的到达角起伏方差的统计特征进行了分析,并取得了很好的相关性,得出了可以从聚焦光束的回波图像信号里提取大气湍流信息的结论。讨论了聚焦距离对固定点光源和回波光束的到达角起伏方差相似度的影响。     

Propagation properties of radial partially coherent flat-topped array beams in a turbulent atmosphere

With the help of the tensor method, the analytical expression for the cross-spectral density of the radial partially coherent flat-topped array (RPCFTA) beams propagating in a turbulent atmosphere is derived, where the correlated superposition and uncorrelated superposition are considered. The average intensity, the spatial coherence properties and power in bucket (PIB) of these kinds of beams are investigated in detail. It is shown by numerical results and analysis that the average intensity and the spatial coherence of the correlated or uncorrelated RPCFTA beams will change on propagation and this change is dependent upon the correlation of the source's beamlets and atmospheric turbulence. In addition, the comparisons of the average intensity and the spatial coherence between the correlated and the uncorrelated RPCFTA beams propagating both in turbulent atmosphere and in free space are also given, and some interesting results are obtained. The laser power of focus ability of the single PCFT beam is worse than that of the correlated RPCFTA beam and but better than that of the uncorrelated RPCFTA beam when propagation distance in turbulent atmosphere is far-field plane.     

发射系统遮拦比对均强聚焦光束光斑扩展的影响

 利用数值模拟方法讨论了发射系统遮拦比对均强聚焦光束湍流大气传输光斑扩展的影响。结果表明，对于均强聚焦光束湍流大气传输，在弱湍流效应条件下，光斑扩展受遮拦比影响较大；在较强湍流效应条件下，不同遮拦比光斑扩展变化趋势相同，此时远场光斑扩展主要还是受湍流效应强弱的影响。获得了常用遮拦比条件下均强聚焦光束光斑扩展和湍流效应特征参数的定标关系。     

Beam propagation factor of partially coherent elegant Hermite-cosh-Gaussian beam through non-Kolmogorov turbulence

Based on the extended Huygens–Fresnel principle and the second moments of the Wigner distribution function, an analytical expression for the propagation factors of partially coherent elegant Hermite-cosh-Gaussian beams (EHChGB) in non-Kolmogorov is derived. The M² factor of partially coherent EHChGB through non-Kolmogorov turbulence is studied analytically and numerically. The results show that partially coherent EHCHGB with higher beam order and longer wavelengths is less affected by non-Kolmogorov turbulence.     

激光通道传输热特性对远场光束质量的影响

 通过仿真计算分析了激光在光束控制系统通道内传输所产生的热效应及其对远场光束质量的影响。激光传播由近轴波方程描述，用快速傅里叶变换技术求解；激光热效应引起的流场密度变化采用完全Navier-Stokes方程计算。计算给出了不同波长、不同吸收系数条件下的远场光斑情况。计算结果表明，在典型的工作条件和状态下，较高能量激光在光束控制系统通道内产生的热效应影响不容忽视，它会明显降低远场目标处的能量集中度，增大光斑的发散。     

部分相干洛伦兹-高斯光束在湍流大气中的峭度参数

基于广义惠更斯-菲涅耳衍射积分公式和洛伦兹函数的厄米-高斯展开,导出了部分相干洛伦兹-高斯光束在湍流大气中经傍轴ABCD光学系统的峭度参数的解析表达式,对该峭度参数进行了数值计算。结果表明：空间相干长度和结构常数对峭度参数的影响与部分相干洛伦兹-高斯光束本身的光束参数有关;当空间相干长度小于光束参数时,其影响显著;当洛伦兹部分的光束参数较大或高斯部分的光束参数较小时,结构常数的影响较明显且随传输距离的增大而增强。     

部分相干洛伦兹-高斯光束在湍流大气中的峭度参数

基于广义惠更斯-菲涅耳衍射积分公式和洛伦兹函数的厄米-高斯展开,导出了部分相干洛伦兹-高斯光束在湍流大气中经傍轴ABCD光学系统的峭度参数的解析表达式,对该峭度参数进行了数值计算。结果表明:空间相干长度和结构常数对峭度参数的影响与部分相干洛伦兹-高斯光束本身的光束参数有关;当空间相干长度小于光束参数时,其影响显著;当洛伦兹部分的光束参数较大或高斯部分的光束参数较小时,结构常数的影响较明显且随传输距离的增大而增强。     

一维线阵离轴高斯光束通过湍流大气的传输特性

研究了一维(1D)线阵离轴高斯光束通过湍流大气的传输特性，推导出了其光强传输方程. 研究表明，1D线阵离轴高斯光束通过湍流大气传输经历了三个阶段，即在近场其光强分布为类似于入射光的锯齿状分布，随着传输距离的增加逐渐变为平顶分布，最后在远场成为类高斯分布. 湍流的增强会使光束传输经历三阶段的进程加快. 并且，湍流使得不同子光束数的1D线阵离轴高斯光束的归一化光强分布相接近. 此外，子光束数越多的1D线阵离轴高斯光束受到湍流的影响越小；1D线阵离轴高斯光束较高斯光束受到湍流的影响要小. 关键词： 一维(1D)线阵离轴高斯光束 湍流大气 传输特性     

Spectral properties of partially coherent azimuthally polarized beam in a turbulent atmosphere

In this paper, based on the extended Huygens–Fresnel integral formula, the analytical expression for the beam coherence-polarization (BCP) matrix of the partially coherent azimuthally polarized (PCAP) beams propagating in turbulent atmosphere has been derived. The distribution of the spectral density, the spectral degree of polarization, the spectral degree of coherence and the spectral degree of cross-polarization of the PCAP beams propagating in turbulent atmosphere with different coherences in the source are investigated in detail. It is shown by numerical results and analysis that the distribution of the spectral properties of the PCAP beam will change on propagation in a turbulent atmosphere, and this change is dependent upon the degree of coherence of the source beam and atmospheric turbulence. It is also shown that even through the source beam is chosen as δ_gxx ≠ δ_gyy the distribution of the spectral density, the spectral degree of polarization, the spectral degree of coherence and the spectral degree of cross-polarization in the far field tends to symmetrical profile.     

激光大气传输相位不连续点的时空演化特征的数值计算

 利用激光大气传输4维程序对激光大气传输相位不连续点的时空演化特征进行了数值计算。仿真计算了相位不连续点随光波传输的产生和湮灭过程,以及某一固定传输位置处,畸变光场内的相位不连续点随时间的变化情况。计算结果表明,相位不连续点是随着波前运动的,并且可以成对地产生或湮灭;当传输路径中的某一位置固定时,垂直于传播方向的畸变光场内的相位不连续点所在的位置随时间的变化是不确定的,但在传输条件一定的情况下,该位置处的相位不连续点数目的统计平均值是可以确定的。     

激光大气传输湍流扰动仿真技术

为了研究激光大气传输时湍流效应对激光应用技术的影响,对湍流扰动的仿真进行了分析。介绍了在实验室内进行激光大气传输湍流扰动研究的数值仿真技术和仿真系统。阐述了快速傅里叶变换（FFT）和Zernike多项式两种湍流扰动数值仿真方法,并且对比了两种方法的优劣。利用物理相位屏搭建了实物湍流仿真系统,介绍了其理论模型并进行了仿真实验,对激光经湍流系统传输后的光强能量分布进行了研究分析。结果显示,室内湍流仿真系统能够准确地模拟弱起伏条件下湍流对激光传输的影响。     

Relay propagation of partially coherent flattened Gaussian beam in turbulent atmosphere

Relay propagation of partially coherent flattened Gaussian–Schell beam in turbulent atmosphere has been studied. The analytical expresses of average intensity distribution at target are derived. The effects of spatial correlation length of initial and relay beam on the average intensity are analyzed in details. Study shows that the effects of the variation of spatial correlation length of relay beam are much larger than that of initial beam. The effects of spatial correlation length on relay propagation become smaller and smaller with the increase of structure constant. When the spatial correlation length is large and turbulence is strong, the effects of the variation of spatial correlation length on relay propagation are so small that can be neglected.     

Analysis of beam quality for the laser beams after spectral beam combining

The beam quality of the laser beams after spectral beam combining (SBC) has been analyzed in this paper. Based on the propagation model of the spectral beam combining system, the expression for the output field of an individual beam passing through the spectral beam combining system with lens aberration has been given and the intensity distribution of the combined beam has been studied by the principle of incoherent superposition. Consequently, according to the intensity second-order moments method, the M²-factor of the combined beam has been calculated and the effect of lens aberration on the characteristics of the combined beam has been analyzed quantitatively. It can be shown that the SBC system can improve the beam quality of laser array significantly, and the M²-factor of the combined beam passing through the ideal spectral beam combining system is almost the same as that of an individual beam. For the spectral beam combining system with lens aberration, the spherical aberration has greater effect on the off-axis beam than on the on-axis beam, and the beam quality of combined beam degrades with increase in lens aberration.     

Comparison between relay propagation and direct propagation of Gaussian-Schell-model beam in turbulent atmosphere along a slant path

The relay propagation of Gaussian-Schell-model in turbulent atmosphere along a slant path is studied in this paper. Based on the extended Huygens-Fresnel principle and a quadratic approximation, an analytical formula of average intensity for Gaussian-Schell-model beams in turbulent atmosphere along a slant path is derived, and some special cases are discussed. From the study and the comparison with the direct propagation, we can see that the relay propagation has an advantage over the direct propagation. When the altitude of the target is low, the peak intensity of relay propagation is much larger than that of direct propagation. However, because of the limitation of the relay system aperture for relay propagation and the variation of coherence length for direct propagation, the difference in peak intensity between the two propagations decreases with the increase of the target altitude.     

激光传输大气参量测量精度要求的数值分析

 就激光大气传输湍流热晕相互作用下大气参量测量误差对激光传输效果（平均功率密度）的影响进行了数值分析,并以典型的激光传输条件为例,分析了对激光大气传输影响最为敏感的3个大气参量——风速、吸收系数以及湍流结构常数的测量精度要求。综合不同传输距离下大气参量测量误差对传输效果的影响,大气风速的测量精度要求为±10%,吸收系数及湍流结构常数的测量精度要求分别为±5%和±15%。     

Propagation characteristics of tilted partially coherent rectangular flat-topped beam in turbulent atmosphere

In this paper, the effects of atmospheric turbulence on the intensity distribution of a tilted Rectangular Partially Coherent Flat-Topped (RPCFT) beam were studied. An analytical formula for the intensity distribution was derived. POWER In Bucket (PIB) value is calculated numerically. The effects of source parameters – such as correlation length, order of flatness and tilt coefficient – on the intensity were analyzed. Detailed analysis demonstrates that these parameters have an influence on beam propagation properties. The analyses are illustrated by numerical examples and graphs.     

激光传输模拟中基于衍射过程FFT算法的参量优化

为实现采用相位屏法正确模拟准直激光束经湍流大气的传输特性,根据湍流特性、抽样定理以及两屏间衍射过程FFT算法本身所决定的相邻两屏网格间距之间的关系,得出相位屏间距和网格间距确定网格数目最优取值的解析表达式,数值模拟高斯光束经自由空间和湍流大气传输的远场分布,网格数目取解析式求得的最优值848时,光束经自由空间传输的模拟结果与ABCD定律求得的解析结果完全一致;网格数目取836或860时,等效于光束通过偶数相位屏时被正透镜或负透镜阵列会聚或发散,削弱或夸大湍流大气对光束的影响,模拟结果出现严重偏差。     

Beam propagation of a higher-order cosh-Gaussian beam

On the basis of the second-order moment, the beam propagation of a higher-order cosh-Gaussian beam has been investigated. Two analytical expressions of the M² factor have been derived, which corresponds to the parity of the beam order n. The M² factor is determined by the beam order n and the parameter δ. The influences of the beam order n and the parameter δ on the M² factor are illustrated with numerical examples. The analytical kurtosis parameter has also been presented. The analytical formula is further simplified in the source plane and the far field, respectively. With given appropriate values of n and δ, the kurtosis parameter in the far field is smaller than 3. This research is helpful to the practical applications of a higher-order cosh-Gaussian beam.     

伪部分相干高斯-谢尔模型光束在湍流大气中传播的闪烁孔径平滑效应

采用光传播的数值模拟方法, 对伪部分相干高斯-谢尔模型光束大气传播过程进行数值模拟, 统计分析不同接收口径内的光强起伏特性,计算闪烁的孔径平滑因子, 讨论了表征伪部分相干光的调制相位屏的相对变化频率对闪烁指数的影响, 并将其与充分发展的部分相干高斯-谢尔模型光束及完全相干光的闪烁指数对比. 结果表明: 降低光源相干性可大幅度降低闪烁指数, 但同时其闪烁指数的孔径平滑效应减弱, 在相同接收孔径下, 伪部分相干光闪烁指数的孔径平滑效果要比完全相干光差; 增大调制相位屏的相对变化频率可在一定程度上降低闪烁指数, 随着其相对频率的增大, 伪部分相干光的闪烁指数与部分相干光的结果趋于一致. 关键词： 伪部分相干高斯-谢尔模型光束 湍流大气 孔径平滑闪烁指数 数值模拟     

Double-distance propagation of Gaussian beams passing through a tilted cat-eye optical lens in a turbulent atmosphere

By using the extended Huygens-Fresnel diffraction integral and the method of expanding the aperture function into a finite sum of complex Gaussian functions, an approximate analytical formula of the double-distance propagation for Gaussian beam passing through a tilted cat-eye optical lens and going back along the entrance way in a turbulent atmosphere has been derived. Through numerical calculation, the effects of incidence angle, propagation distance, and structure constant on the propagation properties of a Gaussian beam in a turbulent atmosphere are studied. It is found that the incidence angle creates an unsymmetrical average intensity distribution pattern, while the propagation distance and the structure constant can each create a smooth and symmetrical average intensity distribution pattern. The average intensity peak gradually deviates from the centre, and the central average intensity value decreases quickly with the increase in incidence angle, while a larger structure constant can bring the average intensity peak back to the centre.