光束分数傅里叶变换的Wigner分布函数分析方法

利用Wigner分布函数(WDF)方法，对光束的分数傅里叶变换特性进行了研究.以厄米 高斯(H G)光束为例，导出了H G光束在分数傅里叶变换面上光强分布的解析公式和H G光束在分数傅里叶变换面上束宽的解析计算公式.通过数值计算研究了H G光束光强随分数傅里叶变换阶数变化的规律.研究表明：选取适当的分数傅里叶变换阶数p，在x，y方向可以得到相等束宽的对称光强分布. 关键词： Wigner分布函数 厄米 高斯(H G)光束 分数傅里叶变换     

Wigner分布函数及非整数傅里叶变换

本文研究了Wigner分布函数的特性,利用Wigner分布函数的旋转,将整数域傅里叶变换推广到了非整数域,描述了自由空间光场的演变过程.     

基于联合广义分数相关器的相关峰特性分析

分析了联合广义分数傅里叶变换相关器相关峰的特性,得到通过改变广义分数傅里叶变换的系统参量可以提高广义分数相关峰性能的结论.进行了数值模拟和光学实验,并根据两者的结果对四个相关峰的性能指标相关峰强度最大值、峰能比、识别能力、信噪比进行了比较分析,说明只要适当控制系统参量,联合广义分数傅里叶变换相关器比联合分数傅里叶变换相关器具有更好的相关性能,有助于提高光学相关器识别的准确率.     

用Wigner分布函数方法研究平顶多高斯光束的分数傅里叶变换

本文用Wigner分布函数方法分析了平顶多高斯光束的分数傅里叶变换。导出了分数傅里叶变换面上光的强度、束宽、远场发散角、M2因子和K参数的解析表达式。通过数值模拟研究了分数傅里叶变换阶数对平顶多高斯光束传输性质的影响。     

广义压缩粒子数态的非经典性质及其退相干

研究了三参数的压缩算符产生的广义压缩粒子数态的非经典性质及其在光子损失通道中的退相干问题.利用有序算符内的积分技术和Weyl编序算符在相似变换下的不变性,简洁地导出了广义压缩粒子数态的Wigner函数(Laguerre-Gaussian函数).基于Wigner函数的演化积分公式,解析地推导出了在耗散通道中的Wigner函数表达式.特别地,根据Wigner函数负部体积讨论了其非经典性.     

半无界空间上函数的傅里叶-贝塞尔积分展开

柱坐标系中,本征函数族贝塞尔函数构成完备正交系,因此可作为广义傅里叶级数展开的基.本文从定义在有限区间[0,ρ0]上函数的广义傅里叶级数展开出发,利用贝塞尔函数的渐近展开公式以及贝塞尔函数零点的近似公式,讨论了半无界空间上函数的傅里叶-贝塞尔积分展开问题,得到了本征函数模方的近似表达式.当ρ0趋于无穷时,不连续参量变成连续参量,得到了函数的傅里叶-贝塞尔积分及其展开系数公式.     

分数傅里叶变换啁啾滤波

针对常规傅里叶变换所不能解决的啁啾噪声滤除问题，利用Wigner分布函数分析分数傅里叶变换的空域和频域特性，提出在分数傅里叶变换域进行啁啾滤波的方法。并将该方法应用到图像处理中，对分数傅里叶变换滤除一维和二维图像的啁啾噪声进行了计算机仿真，获得了满意的效果，结果表明该方法在图像处理中的有效性。     

经高斯函数光滑的Wigner算符的性质

鉴于通常的Wigner算符是不正定的,我们提出将其经过以参数k表征的高斯函数光滑以后的广义Wigner算符,在证明其正定和完备性以后,将它发展为量子光场密度算符及其经典对应的新理论,特别地当k=1时,它退化为了在相干态表象中的p-表示.     

Wigner函数在有限温度下介观LC电路中的应用

应用Wigner函数边缘分布理论研究了有限温度下的介观LC电路.结果表明Wigner函数对电路中p2/2L和q2/2C的边缘分布统计平均恰是分别储存在电感和电容中与温度有关的能量.     

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。     

Wigner distribution function display of complex 1D signals

Three optical methods are proposed for the production of the Wigner distribution function (WDF). This function offers an alternative way of representing signals. The WDF depends simultaneously on time (or space) and on frequency. For the production of the WDF we distinguish between real signals, holograms of complex signals and truly complex signals. An important special class of signals are pure-phase functions. The WDF of such phase functions is very useful for testing optical phase structures. Our setups can also be employed for the production of the ambiguity function.     

Physical defects in fiber optics: A theoretical framework in phase space

A Gaussian symplectic map is used to obtain the Wigner distribution function (WDF) of an optical fiber sectioned by a media with different refractive index. It is found that the WDF after the defect is simply the original Gaussian corrected by a polynomial term.     

Wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems

Based on the Collins formula, the relationship between the coordinate transform matrix (WCTM) of the Wigner distribution function (WDF) and the ray transfer matrix (RTM) of an arbitrary first-order optical system has been derived. By using this relation and the definition of fractional Fourier transform (FRT) in terms of WDF rotation, it is concluded that an arbitrary first-order optical system can be generally decomposed into a thin lens and a FRT sub-system whose order is not unique and depends on two concrete decomposing operations on the system. And when the system is reciprocally symmetric, a FRT can be implemented by it. In addition, the composition, that is also the decomposition condition of the complicated FRT optical system by cascading a series of FRT subsystems has also been derived by using the operations of RTM.     

Wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems

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Wigner distribution function of Lorentz and Lorentz–Gauss beams through a paraxial ABCD optical system

Based on the Collins integral formula and the Hermite–Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function (WDF) of Lorentz and Lorentz–Gauss beams through a paraxial ABCD optical system is derived. The properties of the WDF of Lorentz and Lorentz–Gauss beams propagating in free space are demonstrated. The normalized WDFs of Lorentz and Lorentz–Gauss beams at the different spatial points are depicted in the several observation planes. The influences of the beam parameters on the WDF of Lorentz and Lorentz–Gauss beams in free space are also analyzed at different propagation distances. The special WDF of a Lorentz beam results in its higher angular spreading than the Gaussian beam.     

Application of the Wigner distribution function to studying spectral changes of twisted anisotropic Gaussian Schell-Model beams

By using the Wigner distribution function (WDF), a general closed-form expression for the spectrum of twisted anisotropic Gaussian Schell-model (AGSM) beams in passage through a first-order ABCD system is derived. The spectral changes of twisted AGSM beams propagating in free space and through a thin lens, and the spectral changes of conversional Gaussian-Schell model (GSM) beams are treated as special cases of our general expression. Our theoretical and numerical results show that the WDF provides a powerful and simple tool in analyzing propagation properties of general AGSM beams. Specifically, the spectral behavior of twisted AGSM beams and conventional GSM beams can be treated in a unified and analytical way.     

用WDF描述线性CPA系统

利用维格纳分布函数（ＷＤＦ）描述脉宽大于１００ｆｓ的高斯型脉冲通过啁啾脉冲放大（ＣＰＡ）系统时脉冲的时域、频域变化情况,并进行数值模拟计算。