ILDC理论中虚假奇异点判断及消除

研究了ILDC理论中虚假奇异点的判断及消除问题.给出了虚假奇异点的判断条件,并通过无穷逼近取极限的方法,消除了绕射系数中的奇异点,数值计算结果表明该方法的有效性.最后还进一步讨论了虚假奇异点判断条件的物理意义,证明了这些奇异点确实是位于阴影边界及反射边界的虚假奇异点.     

三维时域有限元-边界元方法中奇异积分计算

研究三维时域有限元一边界元混合方法中奇异积分的计算.将其中的一些积分进行等价变形以降低奇异性.并给出了积分等价变形过程中所遇到的数值错误的一种解决方法,这一数值错误与时域有限元一边界元方法中的固有处置有关.讨论了频域中格林函数奇异点提取法推广应用于时域混合方法中奇异积分的计算,指出,频域中奇异点提取法的一些处理不适宜于时域奇异积分.数值实验检验了所给处理方法.     

pnpn结构器件模型的分析与模拟

将基本半导体方程归一化为奇异振动问题，采用渐近和数值技术，研究了ｐｎｐｎ结构器件模型解的分歧现象，确定了模型解唯一以及模型解出现Ｓ分歧的歧点，由此获得了Ｊ－Ｕ渐近解析表达式。实际例子表明，所获Ｊ－Ｕ的解析式与数值解结果一致。     

一维四元周期性PT对称结构中的光学简并点调控研究

本文提出了一种一维四元周期性宇称-时间（PT）对称结构，系统地研究了增益-损耗系数、入射角和周期数对相干完美吸收激光点和奇异点这两类光学简并点的影响规律。当周期数一定时，通过改变增益-损耗系数可以在不同的入射角下灵活地调控相干完美吸收激光点和奇异点这两类光学简并点。对比分析了PT对称引起的奇异点以及与周期结构相关的Bragg共振点处的反射特性，结果显示：当光束分别沿着左右两边入射时，在奇异点处只有一个方向入射的反射率为0，从而表现为单向无反射特性；而Bragg共振点处的反射率在光分别沿着左右两边入射时都为0，从而表现为双向透明特性。进一步研究了周期数对两类光学简并点的影响，发现相干完美吸收激光点数目随着周期数的增加而增多，而奇异点数目则不受周期数的影响。最后，利用光学简并点的可控特性实现了光自旋霍尔效应等光学现象的操控。     

平面电路分析中奇异函数积分的计算

在利用边界元法分析平面电路问题时,常会遇到一些被积函数在积分区域内具有奇异性的积分。本文提出了求解这类积分的新思路,即先采用适当的变量代换达到分离变量或改变奇异点在积分区域内位置的目的,然后采用奇异点去除法计算出简化后积分的值。该方法不仅能求解数值方法所无法求解的积分,而且由于尽可能地采用了解析方法,因而具有计算速度快,精度高等特点,该方法为奇异积分的计算提供了一种行之有效的手段。     

波导截面TM 波截止波数的快速计算方法

在计算任意波导截面TM 波截止波数的问题上,矩量法不可避免的要处理奇异点的问题,因此在快速性和简洁性上均存在很大不足。本文提出了一种便捷的计算方法:首先推导出相应截止波数下波导的电场积分方程,采用Gauss-Legendre公式将积分数值化,然后运用矩量法进行处理后得到一个矩阵方程,最后利用迭代法找出这个矩阵的特征值,从而避开了奇异点使得问题的求解更加便捷。     

导体线面连接问题中奇异函数积分的计算

在线面连接问题中，电流展开函数包含体展开函数、线展开函数和连接点展开函数三类。求解电场积分方程的积分项是电流基函数及其散度分别与自由空间格林函数的乘积，由于连接点展开函数含有一个奇异点，所以被积函数中含有两个奇异点。本文通过积分变换消除了奇异点，并将二重积分化为一重积分，使计算精度得到提高。计算实例验证了本文方法的正确性。     

非厄米光学系统中奇异点的传感应用

奇异点是非厄米系统参数空间中至少两个本征值和相应本征态同时简并的点,奇异点附近的异常光学现象,尤其是本征频率分裂对极小微扰的敏感特性,在超灵敏光学传感中有重要应用。本文主要结合近几年国内外关于奇异点的研究,介绍了奇异点及其在光学传感方面的相关理论,分析了奇异点传感和狄拉克点传感的不同;并着重总结奇异点传感在纳米颗粒检测、温度传感、折射率传感、光学陀螺仪和石墨烯生物化学传感等方面的最新研究进展。     

四元数及其在火控系统仿真中的应用

在火控系统仿真中，用Euler（欧拉）角描述坐标变换，可能会出现奇异点，用四元数进行坐标变换，可以避免奇异声、出现，另外还可以减少计算时间。     

基于极大似然估计的奇异点检测

信号的奇异点往往包含信号比较重要的信息,对其进行检测和定位在许多实际问题中都有重要的意义。根据脉冲型奇异点的特点,提出了一个基于极大似然估计的脉冲奇异点检测方法。该方法利用Bernoulli概型来建模,用于对脉冲奇异点的检测,将脉冲奇异点的检测问题转化为一个参数估计问题,并利用极大似然估计方法给出了参数的估计。通过对大量的仿真信号及真实信号脉冲奇异点的检测证明,该检测方法计算简单,行之有效。     

Treatment of singularities in the physical theory of diffraction

The diffraction coefficients describing scattering from an edged body in the physical theory of diffraction are reformulated so as to provide improved behavior in the neighborhood of singularities. Numerical results show that as singularities are approached, the reformulated coefficients are better behaved than the original by several orders of magnitude.     

修正劈表示的边缘等效电磁流的改进及在电磁散射中的应用

本文介绍了修正劈的概念和用其表示的等效边缘电磁流（ＥＥＣ）公式，并应用它们计算了圆盘双站雷达散射截面（ＲＣＳ）；提出一种确定修正劈方向的法则，这种法则是根据几何绕射理论（ＧＴＤ）中有关参数的定义确定的，因而它不是经验的法则。修正劈表示的ＥＥＣ仅利用了经典的Ｋｅｌｌｅｒ锥上的绕射系数公式和修正劈的概念就可得到任意入射和观察方向的ＥＥＣ，它克服一般ＥＥＣ在Ｋｅｌｌｅｒ锥外的方向上定义模糊的缺点。数值结     

Analytical-Numerical Calculation of Diffraction Coefficients for a Circular Impedance Cone

An analytical-numerical computation of diffraction coefficients is described for a semi-infinite impedance cone of circular cross section illuminated by an electromagnetic plane wave. To enable an incomplete separation of variables, both the incident and scattered fields are expressed in terms of the Kontorovich-Lebedev (KL) integrals; an inversion of the Leontovich condition on the cone's surface yields equations for the spectra, whose Fourier coefficients satisfy certain functional difference equations of the second order; the latter are then converted to integral equations of the second kind which are solved numerically; using the so obtained spectra in the KL-integrals for the scattered field and evaluating the integrals in far field leads to diffraction coefficients. Numerical results are included both for verification purposes and for displaying the diffraction behavior for different incident and diffraction angles, as well as for several cone impedances.     

径向偏振光束经三角形点阵列板衍射的偏振奇点

根据夫琅禾费衍射积分公式推导出径向偏振光束通过三角形点阵列板(TMP)衍射后的传输表达式,通过理论计算模拟并进行实验验证,得到衍射场光强分布图,衍射场光强成周期性排列。并用复Stokes场来分析径向偏振光束衍射场偏振奇点的变化规律。结果表明,衍射场的光强分布随着三角形点阵列板N值的改变而改变,偏振奇点的数目随着三角形点阵列板的N值的增大而增多。另外,光束参数(波长和光束束宽)、传输距离和三角形点阵列板的参数(三角板边长)均对偏振奇点的位置产生影响。改变三角形点阵列板的N值,伴随有偏振奇点的产生和湮灭现象。     

Weakly dispersive spectral theory of transients, part II: Evaluation of the spectral integral

In the spectral theory of transients formulated in Part I of this paper, the transient response for weakly dispersive wave processes has been expressed in terms of canonical integrals in the complex spatial wavenumber domain. The real and complex singularities in the integrands, which dominate the behavior of the spectral integrals, have been categorized and associated with generic physical wave processes. The integrals are now evaluated by Contour deformation around the singularities. This yields general expressions for the transient Green's function that are applicable to a broad class of propagation and diffraction problems. The generic results, which can be grouped into contributions from real or complex singularities; express the transient field in terms of compact (and therefore physically incisive) wave spectra, in contrast to alternative procedures that always constrain the spectra to be real. These aspects, together with simplifying explicit wavefront approximations, are explored in the present paper, with the application to specific problems relegated to Part III.     

Incremental diffraction coefficients for planar surfaces

Exact expressions for incremental diffraction coefficients at arbitrary angles of incidence and scattering are derived directly in terms of the corresponding two-dimensional, cylindrical diffraction coefficients. The derivation is limited to perfectly conducting scatterers that consist of planar surfaces, such as the wedge, the slit in an infinite plane, the strip, parallel or skewed planes, polygonal cylinders, or any combination thereof; and requires a known expression (whether exact or approximate) for the two-dimensional diffraction coefficients produced by the current on each different plane. Specifically, if one can supply an expression for the conventional diffraction coefficients of a two-dimensional planar scatterer, one can immediately find the incremental diffraction coefficients through direct substitution. No integration, differentiation, or specific knowledge of the current is required. Special attention is given to defining ambiguously all real angles and their analytic continuation into imaginary values required by the incremental diffraction coefficients     

基于过完备表示的图像去噪算法

提出一种基于过完备线形变换集合的图像去除白高斯噪音算法.对于每个变换使用阈值技术进行图像去噪,图像恢复使用加权平均来融合去噪结果.采用稀疏集中度来计算图像稀疏分解的测度,而权重依赖该结果.对于图像稀疏区域,拥有较大的权.该方法不需要设计复杂的变换系数统计模型,与使用复杂的有向变换和图像统计模型方法相比,取得了较高的去噪性能.该方法简洁高效,尤其是对包含奇异特征的图像得到了较好的去噪结果.实验结果证实了所提方法的有效性.     

Théorie asymptotique de la diffraction en optique physique appliquée aux antennes à réflecteur

In physical optics approximation, the high frequency asymptotic analysis is used to obtain the scattered field from a given reflector. The results for a circular flat reflector are compared with numerical exact solution. The derived physical optics diffraction coefficientsare found to be numerically in good agreement with those of the geometrical theory of diffraction (GID).Transition functions are introduced in those coefficients to remove the singularities at stradow and reflection boundaries. This asymptotic analysis is generalized for reflectors of arbitrary shape. The derived formal expression of diffraction dyadic is shown to be similar to the one of GTD only for axially symmetric reflectors. In this case, the diffracted field has a simple practical formula. Results for a paraboloid reflector fed by a short dipole are compared to physical optics solution.     

Electric field singularities at sharp edges of planar conductors

The electric field behavior around printed conductors with a polygonal contour, as used in antennas and microwave circuit components, is investigated. The diffraction problem posed by these geometries involves edge and vertex conditions as well as boundary conditions. These can collectively be described by means of a simple singularity function that gives the distribution of zeros of the electric field on the flat conductor surfaces and of its singularities along the conductor edges. The analysis is based on solving the vector Helmholtz equation for the plane-sector perfect conductor in a conical coordinate system, and the static case is derived from a limit process. The values of the singularity function for the electric field components are explicitly reported for the more commonly encountered 90° and 270° sectors and for 90° bitriangular antennas. Systematic extension to sectors of arbitrary aperture, to composite configurations, and to their polygonal combinations is also indicated     

DESIGN OF 2-D QUASI-OPTICAL BEAM SPLITTERS USING ANALYTICAL GRADIENTS

Quasi-optical systems comprised of diffractive phase elements (DPEs) are designed as beam splitters. The design tasks are reformulated as optimization problems in which target functionals are defined. Analytical gradients are derived to those functionals, which can be passed to gradient methods to efficiently determine the DPEs. Rayleigh-Sommerfeld diffraction integrals are applied to compute the wave propagation in free-space between parallel planes in the quasi-optical systems. Numerical results for several beam splitters are depicted. Furthermore a procedure is proposed, how the phase functions of the DPEs could be smoothed out.