光栅模式的色散方程与对称性

提出了横电、横磁偏振布拉格角入射下光栅模式的色散方程可进一步分解的理论,证明了分解得到的方程与光栅模式对称性间的等价关系。光栅模式的对称性有助于阐释光栅内部衍射过程的物理图像。通过讨论光栅模式方程的根的分布性质,提出了一种提高有效折射率计算效率的方法。     

有限宽双光栅成像效应的分析与应用

用稳相积分法分析了点光源经过2个平行放置的有限宽平面透射光栅组成的系统衍射后的复振幅分布。当两光栅满足双光栅成像条件时,将其衍射成像与无限宽双光栅衍射成像进行对比,得到有限宽光栅对双光栅衍射像的位置没有影响,而衍射像随两光栅之间的相对距离及衍射级数而变化。文中计算了满足双光栅成像条件时,某实验参数下衍射像的大小的情形,结果有限宽双光栅成像被放大了1.22倍。并根据其原理进行白光再现普通透射全息图色彩研究。     

严格耦合波法计算闪耀光栅衍射效率

针对一般标量近似算法精度不高的问题,提出采用S矩阵的严格耦合波的方法计算光栅衍射效率.通过建立完整的闪耀光栅理论模型,对各分层电磁场进行傅里叶级数展开,采用散射矩阵方法求解各谐波系数,完成衍射效率计算.该方法已应用到红外光栅TE和TM 2种模式衍射效率的计算.分析了散射矩阵解决数值运算不稳定的原因,通过与标量近似计算方法进行比较,说明红外光栅衍射偏振特性.     

线偏光闪耀反射光栅衍射特性研究

通过数值方法对线偏光在Littrow装置中的理想导体闪耀光栅的偏振特性进行研究.用时域有限差分程序计算出任意偏振方向线偏光经过闪耀光栅衍射后的电磁场分布,提取衍射波的S偏振和P偏振分量,讨论了与光栅闪耀角和入射光波偏振角的关系.分析了在1530～1570nm光谱范围内,入射光波为线偏振波和园偏振波时,衍射光波的偏振色散特性与光栅闪耀角的关系,并给出了存在偏振色散的光栅闪耀角范围.这些分析和结果对工程设计具有一定的指导意义.     

一种二维光栅结构衍射场计算中的快速收敛方案

基于Lalanne经验法与Gtz法向矢量法的傅里叶因式分解过程,给出了傅里叶模态层吸收法的一个快速收敛方案.通过求解解析边界轮廓函数的梯度矢量,简化了Gtz法向矢量法的傅里叶因式分解过程,使其单波长点计算时间降低两个量级.通过距离反比权重法构造4个典型方向的法向矢量场,降低了法向矢量法在傅里叶因式分解过程中的不确定性.根据这4个典型法向矢量场与Lalanne经验法,提供了5个傅里叶模态层吸收法的收敛性改进矩阵.预先对5个收敛性改进矩阵优选分析,选择一个最优矩阵进行傅里叶模态层吸收法的衍射模拟计算,可以实现快速收敛.计算结果表明,对于硅材料简单结构,优选的改进矩阵相比于非优选矩阵收敛性提高2阶左右,能有效提高衍射场计算速度.该方案可提高光栅设计和集成电路结构分析/测试的效率.     

X射线光栅相位成像的理论和方法

通过对X射线光栅相位衬度成像实验装置的理论分析,提出了光栅位移曲线的表达式,推导出了X射线光栅相位衬度成像方程.根据该成像方程,提出了基于光栅成像相位提取方法.这些理论结果将简化光栅相位衬度成像实验步骤,提高信息获取效率,并为X射线光栅相位衬度成像和计算机断层成像的结合,进一步提出光栅相位衬度CT的简化理论奠定基础. 关键词： X射线 相位衬度成像 光栅衍射 Talbot效应     

叉指电光布拉格衍射光栅分析

叉指电光布拉格衍射光栅能够用于制作集成光学器件。将点匹配法扩展应用于又指电光布拉格衍射光栅分析,将光栅各区域的势函数表示为该区域中满足拉普拉斯方程的一系列基函数的级数,匹配边界上有限个点的边界条件以确定出级数项的系数,从而得到叉指电傲电场分布的解析表达式,在此基础上得到了叉指电光布拉格衍射光栅的一些重要的光学与电学特性参量。将分析结果与测量值进行了对比,发现二者十分吻合。所提出的分析方法简便快捷、精度高,所导出的电场分布的解析表达式和分析结果对叉指电光衍射光栅的优化设计具有重要的意义。     

对透射光栅光强极值位置的探讨

分析了透射光栅衍射光强分布的极值问题.结果表明,除了零级衍射主极大以外,光栅衍射光强的各级主极大的位置与光栅方程所确定的位置并不严格重合.结合一个实例,通过数值计算给出了二者的差异.     

紫外刻划光栅母版及二代版衍射特性的模拟与分析

运用微分理论对刻线密度为1200 lp/mm的紫外刻划光栅母版及其二代复制版的衍射特性做了模拟,指出了二者之间存在的差异,并与测试结果做了对照。数值模拟表明,紫外刻划光栅二代复制版的衍射特性与其母版略有不同,原因是光栅槽形发生了改变,分别给出了采用多项式拟合槽形函数和傅里叶级数拟合槽形函数的方法。此理论分析方法为澄清光栅复制工艺中的争议完善翻版技术以及寻找提高紫外光栅衍射效率的途径提供了很好的理论参考依据。     

光泵气体THz激光器用CO2泵浦源腔内光场模式

CO2泵浦源是光泵气体太赫兹激光器的核心器件之一,其性能直接关系到太赫兹激光器的工作稳定性。CO2泵浦源一般由闪耀光栅作为全反射尾镜,构成特殊的光栅腔实现波长的选支输出。采用传输矩阵的特征向量法对光栅谐振腔的腔内光场模式进行了理论分析与数值模拟,计算了光栅腔的一系列本征模式及相应的衍射损耗。结果表明光栅腔的腔内模式特性等效于一个平凹腔,而对于大菲涅尔数的光栅腔, Littrow波长的附近支线也可能具有衍射损耗较低的低阶模,可能优先于Littrow波长的高阶模起振,导致光栅腔的波长选择性降低。     

处理金属闪耀光栅的多次基尔霍夫积分法

在散射场「通过菲涅耳（Ｆｒｅｓｎｅｌ）反射系数决定于入射场」的边界条件铁定理及等效场原理的支持下,完善了金属闪耀光栅的多次基尔霍夫（Ｋｉｃｈｈｏｆｆ）积分方法;并以利特罗（Ｌｉｔｔｒｏｗ）安装及固定偏向角安装的理想金属导体闪耀光栅对不同波长平面电磁波衍射效率的计算实例,探讨了此方法的稳定性与自洽性。     

基于P范数的核最小对数绝对差自适应滤波算法

为了进一步提高在a稳定分布噪声背景下非线性自适应滤波算法的收敛速度,本文提出了一种新的基于p范数的核最小对数绝对差自适应滤波算法(kernel least logarithm absolute difference algorithm based on p-norm, P-KLLAD).该算法结合核最小对数绝对差算法和p范数,一方面利用最小对数绝对差准则保证了算法在a稳定分布噪声环境下良好的鲁棒性,另一方面在误差的绝对值上添加p范数,通过p范数和一个正常数a来控制算法的陡峭程度,从而提高该算法的收敛速度.在非线性系统辨识和Mackey-Glass混沌时间序列预测的仿真结果表明,本文算法在保证鲁棒性能的同时提高了收敛速度,并且在收敛速度和鲁棒性方面优于核最小均方误差算法、核分式低次幂算法、核最小对数绝对差算法和核最小平均p范数算法.     

A method of numerical solution of cauchy-type singular integral equations with generalized kernels and arbitrary complex singularities

A numerical method is proposed for the approximate solution of a Cauchy-type singular integral equation (or an uncoupled system of such equations) of the first or the second kind and with a generalized kernel, in the sense that, besides the Cauchy singular part, the kernel has also a Fredholm part presenting strong singularities when both its variables tend to the same end-point of the integration interval. In this case any type of real or generally complex singularities in the unknown function of the integral equation may be present near the end-points of the integration interval. The method proposed consists simply in approximating the integrals in the integral equation by using an appropriate numerical integration rule with generally complex abscissas and weights, followed by the application of the resulting approximate equation at properly selected complex collocation points lying outside the integration interval. Although no proof of the convergence of the method seems possible, this method was seen to exhibit good convergence to the results expected in an example treated.     

Particle diffraction by a thin rigid crystal lattice: A formal approach

The diffraction process of a particle by a thin rigid crystal is considered. An integral equation is derived for the particle wave function φ which is quite suitable to obtain physical and mathematical properties. A class of potentials is presented for which the integral equation can be solved by means of the Fredholm theory. The convergence of the Born series for φ is studied, as well as the existence and convergence properties of the transmission and reflection amplitudes T^±. Results are given about φ and T^±: (i) at high energies, (ii) at those special energies such that new diffracted beams appear, and (iii) at glancing incidence on the crystal. Analyticity properties of T^± as functions of the energy are derived and analytic representations for them are presented. The diffraction process when the particle is being simultaneously accelerated by a uniform electric field is also considered. Finally, the generalization to the case of an imperfect thin crystal is treated.     

A method for multi-frequency calculation of boundary integral equation in acoustics based on series expansion

The paper presents a method to solve the problem of multi-frequency calculation of Helmholtz boundary integral equation in acoustics. Based on series expansion, system matrices are independent of wavenumber and become the matrix power series of wavenumber. As a result, all matrices in the matrix power series are only dependent on the structure geometry. In addition, an element transform method to calculate the singular integral and Cauchy singular integral is also discussed because the singular integral need to be solved using the method. The convergence of the series expansion method is also proved in this paper. The effectiveness of the method is confirmed by two numerical examples.     

Symmetry analysis and explicit power series solutions of the Boussinesq–Whitham–Broer–Kaup equation

This paper focus on two aspects. Firstly, symmetry analysis is performed for the Boussinesq–Whitham–Broer–Kaup equation which can degenerate to the Boussinesq equation, the Whitham–Broer–Kaup equation and the Broer–Kaup equation. As a byproduct, the similarity reductions and exact solutions of the equation are constructed based on the optimal systems. Secondly, the explicit solutions are considered by the power series method. Moreover, the convergence of the power series solutions are shown. The physical significance of the solutions is considered from the transformation group point of view.     

用于混沌时间序列预测的组合核函数最小二乘支持向量机

针对混沌时间序列的预测问题,考虑到单一核函数的最小二乘支持向量机无法明显提高预测精度,提出了一种组合核函数的最小二乘支持向量机预测模型,模型中采用多项式函数与径向基函数组合构建核函数.同时,还对遗传算法进行了改进,使之具有更快的收敛速度和更高的精度,改进的遗传算法适用于解决预测模型中的参数优化问题.通过典型的Lorenz时间序列、Mackey-Glass时间序列、太阳黑子数时间序列以及具有混沌特性的网络流量时间序列对该模型进行了验证.仿真结果表明所提出的模型是有效的.     

New method for solving fractional partial integro-differential equations by combination of Laplace transform and resolvent kernel method

In this article, we obtained the approximate solution for a new class of Time-Fractional Partial Integro-Differential Equation (TFPIDE) of the Caputo-Volterra type in which the integral is not limited to the convolution type. This new class of TFPIDE is distinct from the common problem with the convolution integral kernel. The general expression of the analytical solution for this special type of TFPIDE was derived using a combination of Laplace transform and the resolvent kernel method. In the process, Laplace transform will transform the equation into a second kind Volterra integral equation in terms of the transformed function. Two main problems in deriving the approximate analytical solutions were identified as Case I and Case II problems. To obtain the approximate solutions for Case I and Case II problems, numerical methods were designed based on approximation of the resolvent kernel with truncated Neumann series as well as approximation of the Laplace transform based on truncated Taylor series. Several numerical examples are presented to indicate the plausibility, mechanism and performance of the proposed methods.     

大口径多层介质膜光栅衍射效率测量及其在制作工艺中的应用

多层介质膜光栅是高功率激光系统的关键光学元件.为了满足国内强激光系统的迫切需求, 在大口径多层介质膜光栅的研制过程中,建立了单波长自准直条件下的衍射效率测量方法及其误差分析. 结果表明误差主要由探测器的噪声和测试人员的差异产生,对衍射效率测试精度的影响是±1%. 在此基础上,将光栅衍射效率及其分布测量技术应用于光栅制作工艺中, 作为大口径光栅无损检测的一种手段,如判断光栅掩模是否能进行离子束刻蚀、 离子束刻蚀的在线监测和是否需要再刻蚀,从而实现对大口径多层介质膜光栅离子束刻蚀过程的定量、 科学控制,提高了离子束刻蚀光栅制作工艺的成功率.利用上述技术,已成功研制出多块最大尺寸为 430 mm× 350 mm、线密度1740线/mm、平均衍射效率大于95%的多层介质膜光栅. 实验结果表明,该方法操作简单、测量快速准确,不必检测光栅微结构. 为大口径多层介质膜光栅研制的无损检测工程化奠定了基础.     

各向异性介质三维电磁响应模拟的Ho-GEBA算法

本文基于积分方程法研究并建立了一种模拟横向同性介质中任意各向异性异常 体三维电磁响应的高阶广义扩展Born近似(Ho-GEBA)算法. 首先利用逐次迭代技术给出积分方程的广义级数展开解, 为保证其收敛性, 引入一种各向异性条件下满足压缩映射的迭代算子. 然后利用异常体区域分解技术, 并结合扩展Born近似原理, 得到各向异性介质三维电磁响应的Ho-GEBA解. 为提高效率, 计算过程中采用并矢Green函数的解析表达式. 最后通过数值计算实例对比验证了本文算法的有效性. 关键词： 高阶广义扩展Born近似 积分方程 电磁模拟 解析Green函数