截断光束的二阶矩矩阵

采用复高斯展开法和维格纳分布函数(WDF),推导出了截断光束的二阶矩矩阵通过大气湍流的传输公式。研究表明,将硬边光阑的复高斯展开函数引入z=0平面处的WDF中,能够避免截断光束二阶矩的积分发散问题,得到z=0平面处二阶矩的解析结果,并且保证了精度,从而方便地得到截断光束在大气湍流中传输的二阶矩矩阵。实验所得到的结果具有一般性,即无截断光束的二阶矩矩阵通过大气湍流传输和截断光束的二阶矩矩阵在自由空间的传输都可以分别作为特例给出。     

截断平顶光束的广义M2因子和相干模分解

针对Li提出的平顶光束的新描述模型,分别采用广义二阶矩方法和矩形函数的复高斯函数展开方法,推导出平顶光束通过硬边光阑的广义光束传输M2因子和模相关系数的解析表达式.以此为基础,对截断平顶光束的模相关、模结构以及相干模分解进行了分析,建立了截断平顶光束的相干模分解理论.     

高斯光束通过有硬边光阑ABCD光学系统的近似解析传输公式

 对高斯光束通过有硬边光阑近轴ABCD光学系统的传输进行了研究,采用将矩形函数展开为复高斯函数的技巧,推导出了近似的解析传输公式。以高斯光束在有光阑情况下自由空间的传输为例进行了数值计算,对所用方法能节约大量机时的优点和计算误差作了讨论,并进一步推广用于平面波和平顶高斯光束,证实了这一方法具有广泛的应用意义。     

光束通过硬边光阑光学系统变换的改进算法

 使用傅里叶级数与有限个复高斯函数之和的乘积作为硬边光阑的窗口函数的近似式，提出了含硬边光阑近轴ABCD光学系统对光束变换的改进算法。以高斯光束的变换为例，推导出了一个表示为初等函数之和的近似解析传输公式。给出了数值计算结果，并与直接积分Collins公式和使用Wen方法的结果作了比较。研究表明，改进算法能兼顾计算精度和机时，并能用于远场和近场。而使用Wen方法时，在近场（小于0.12倍菲涅尔距离）有明显误差。     

倾斜离轴高斯光束通过猫眼光学镜头的传输特性

运用矩阵光学理论以及将硬边光阑窗口函数展开为有限个复高斯函数之和的方法,进一步推导了倾斜离轴高斯光束通过猫眼光学镜头的解析传输公式,通过数值计算分析得到了倾斜系数和离轴量对猫眼效应反射光光强分布的影响规律.结果表明,斜入射情况下猫眼效应反射光光强分布发生非对称畸变,且倾斜系数较小和较大时有着不同的分布规律.并且,离轴量与倾斜系数共同决定着猫眼效应反射光应用于激光主动探测的可行性.     

双曲余弦高斯光束通过有光阑限制的ABCD光学系统的传输

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究,采用将矩形域函数表示为复高斯函数叠加的技巧,推导出了解析的传输公式,在特殊情况下,该公式简化为在无光阑情况下的传输公式,对双曲余弦高斯光束通过有光阑限制的薄膜镜聚焦进行了数值计算,计算结果与直接由柯林斯（Collins)公式所得结果一致,且此解析方法便于进行物理分析,可节约大量机时。     

截断平顶光束的广义M2因子和相干模分解

针对Li提出的平顶光束的新描述模型，分别采用广义二阶矩方法和矩形函数的复高斯函数展 开方法，推导出平顶光束通过硬边光阑的广义光束传输M²因子和模相关系数的解析表 达式.以此为基础，对截断平顶光束的模相关、模结构以及相干模分解进行了分析，建立了 截断平顶光束的相干模分解理论. 关键词： 截断平顶光束 2因子')" href="#">广义M²因子 模相关系数 相干模分解     

有球差多色高斯光束衍射引起的光谱开关

从空间频率域交叉谱密度函数的传输公式出发，推导出有球差多色高斯光束被硬边光阑衍射 后轴上光谱的解析公式，无像差的结果作为本公式的特例.对所得公式作了详细的数值计算 和物理分析.结果表明，球差高斯光束被硬边光阑衍射后近场的光谱与无像差时比较 有蓝移、红移，也会出现光谱开关.着重分析了球差对光谱开关的影响. 关键词： 现代光学 光阑衍射 光谱开关 球差 多色高斯光束     

通过有光阑近轴ABCD光学系统激光束的近似解析传输公式

 用傅立叶级数展开法研究光束通过有光阑限制的近轴ABCD光学系统的传输特性，导出了光阑透射率函数不同时的传输公式。硬边光阑的情况可作为其它光阑的特例得到，其它光阑也可视作硬边光阑来处理。数值计算表明了该方法快速的优点，并得到与用Collins公式直接积分一致结果。     

拉盖尔-高斯截断级数展开法的应用

 用拉盖尔-高斯截断级数模拟了任意半径的圆孔硬边光阑窗口函数,并应用于研究高斯光束和零阶贝塞尔-高斯光束通过硬边光阑的衍射。对高斯光束和零阶贝塞尔-高斯光束的轴向和横向光强分布的计算结果表明：当积分面不是很靠近光阑时，用参数最佳化选取的拉盖尔-高斯截断级数法与用直接数值积分所得结果符合很好。     

Restoration of Decentered Gaussian Beam with the Combination of a Lens and a Gaussian Aperture

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Intensity correlations of general type beam in weakly turbulent atmosphere

In weakly turbulent atmosphere, intensity correlations at the receiver plane are formulated for a general type optical beam. Evaluating our formula at the appropriate source parameters versus the diagonal distance, intensity correlations for cos Gaussian, cosh Gaussian, annular and flat-topped Gaussian beams are obtained. As compared to Gaussian beam, intensity correlations are found smaller for cos Gaussian and larger for cosh Gaussian beams. Intensity correlations of cos Gaussian, cosh Gaussian and flat-topped Gaussian beams become larger at large source sizes. Thicker annular beams and flatter flat-topped Gaussian beams show larger intensity correlations. Without generalizing, intensity correlations tend to increase when the link length and the structure constant decrease and the wavelength increases. Our results show that the intensity correlations are not only built up using random medium effects, but also using the diffraction pattern formed at the receiver plane for the specific incidence investigated. As a check point, for all source types and medium parameters, our evaluations indicate that intensity correlations approach zero at sufficiently large diagonal distances.     

左手材料平板对傍轴高斯光束聚焦特性分析

在傍轴近似下,推导出了左手材料平板聚焦系统的传输矩阵,并利用ABCD定律得到了高斯光束在左手材料中和经过平板透镜聚焦后的传输公式。高斯光束在左手材料内部和像空间的传输公式的研究表明:像高斯光束和物高斯光束束腰大小一致,即左手材料平板透镜实际上对高斯光束没有聚焦作用。研究同时表明左手材料平板对高斯光束的聚焦与几何光学成像规律完全一致,而不存在一般透镜聚焦时的焦移效应。     

Axial distribution of Gaussian beam limited by a hard-edged aperture

In this letter, the axial distribution of Gaussian beam limited by a hard-edged aperture is studied. We theoretically analyze the axial diffraction of Gaussian beam limited by a hard-edged aperture, and give the simpler formulas of the axial diffraction intensities of Gaussian beam in Fresnel diffraction field and Fraunhofer diffraction field. The corresponding numerical calculation of axial diffraction intensity distribution of Gaussian beam with different wave waist is provided and the evolution of the diffraction distribution with the wave waist of Gaussian beam is explained. As the especial cases of the truncated Gaussian beam,the Gaussian beam in free space and the parallel light limited by the aperture are discussed too, and the system parameters of the truncated Gaussian beam which can cause it to equal to these cases are given.The theoretical results conform to the numerical analysis.     

厄米-余弦-高斯光束的传输特性

 从广义惠更斯-菲涅耳衍射积分出发对厄米-余弦-高斯光束的传输特性作了研究，给出了厄米-余弦-高斯光束通过近轴ABCD光学系统的解析传输公式，以厄米-余弦-高斯光束通过自由空间和薄透镜系统为例做了数值计算和分析，结果表明厄米-余弦-高斯光束在自由空间传输时不能保持其形状不变。厄米-双曲余弦-高斯光束、余弦-高斯光束、厄米-高斯光束的传输公式可作为厄米-余弦-高斯光束的特例得出。     

On the Classical Capacity of General Quantum Gaussian Measurement

In this paper, we consider the classical capacity problem for Gaussian measurement channels. We establish Gaussianity of the average state of the optimal ensemble in the general case and discuss the Hypothesis of Gaussian Maximizers concerning the structure of the ensemble. Then, we consider the case of one mode in detail, including the dual problem of accessible information of a Gaussian ensemble. Our findings are relevant to practical situations in quantum communications where the receiver is Gaussian (say, a general-dyne detection) and concatenation of the Gaussian channel and the receiver can be considered as one Gaussian measurement channel. Our efforts in this and preceding papers are then aimed at establishing full Gaussianity of the optimal ensemble (usually taken as an assumption) in such schemes.     

Critical Behavior of the Gaussian Model with Periodic Interactions on Diamond—Type Hierarchical Lattices in External Magnetic Fields

The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences.The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction onds.The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method.The critical points and all the critical exponents are obtained.The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices.When all the Gaussian distribution constants are the same,the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.     

Analytical structure of Hermite Gaussian beam in far field

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical structure of Hermite Gaussian beam in far field is presented. The structural energy flux distributions are also investigated in the far field. The structural pictures of some Hermite Gaussian beams are depicted in the far field. As the structure of Hermite Gaussian beam is dominated by the transverse mode numbers and the initial transverse Gaussian half width, it is more complex than that of Gaussian beam. The ratios of the structural energy fluxes to the whole energy flux are independent of the transverse mode numbers and the initial transverse Gaussian half width. The present research reveals the internal vectorial structure of Hermite Gaussian beam from other viewpoint.\