广义柱形坐标系各向异性完善匹配吸收媒质

Ｂｅｒｅｎｇｅｒ提出的完善匹配层只能用于直角坐标系。本文将完善匹配各向异性吸收媒质推广到广义柱形坐标系。推导是在广义柱形坐标系均匀媒质的Ｍａｘｗｅｌｌ方程与直角坐标系各向异性媒质的Ｍａｘｗｅｌｌ方程之间等效基础上进行的。得出了广义柱形坐标系完善匹配层电导率计算公式。     

广义正交坐标系下FDTD算法的吸收边界条件

本文由广义正交坐标系下的波动方程，通过微分算子的分解得到两个单向波方程，利用差分析似方法得到广义正交坐标系下Ｍｕｒ二阶吸收边界条件，并与文献结合给出了直角和圆柱坐标系下的Ｍｕｒ二阶吸收边界条件进行对比和补充。     

二元相位光栅抗反射特性的耦合波分析

运用Ｍａｘｗｅｌｌ方程组和电磁场的边界连续条件，本文导出了二元相位光栅的严格的耦合波方程，分析了二元相位光栅的抗反射特性。在适当选取光栅的几何参数时，光栅的反射率可以减至几乎为零。实验测试结果与理论值基本相符。     

二元光学用于改善红外光学表面反射特性的研究

基于电磁场Ｍａｘｗｅｌｌ方程组及其边界条件，导出了二元光学器的严格耦合波衍射方程，分析了二元位相光栅的反射特性，在适当选取光栅的几何参数时，光栅的反射率可以减小到近似为零，这种减反射光栅的特性优于传统减反膜。     

Maxwell方程用于电磁脉冲在损耗介质中的传播问题

Ｍａｘｗｅｌｌ方程组是否适用于电磁脉冲在损耗介质中的传播是个有争议的问题,Ｈ．Ｆ．Ｈａｒｍｕｔｈ在他的书中持完全否定的态度。我们从经典的Ｍａｘｗｅｌｌ方程出发,利用时域有限差分法在二维和三维空间模拟了电和磁阶跃电磁脉冲激励的平面电磁波在损耗介质中的传播,并与Ｈａｒｍｕｔｈ书中所给的算例进行了比较,在极限情况下二者符合得很好。这说明Ｈａｒｍｕｔｈ只是给出了一种电磁脉冲在损耗介质中传播问题的解题方法,     

时域有限面积法解手征介质涂层导体柱的电磁散射

本文将时域有限面积法推广应用于研究任意截面复合手征介质涂层导体柱的电磁散射问题,建立了数值求解复合手征介质问题的时域基本方程.本文使用正交贴体计算网格,并选用适合正交曲线坐标系的二阶精度吸收边界条件,提高了计算精度.对典型的复合手征介质涂层导体柱的RCS计算表明,数值计算结果与级数解相吻合.     

一般正交曲线坐标系中的降维时域有限差分法

相对于常规的时域有限差分法(FDTD),降维时域有限差分法(R-FDTD)减少了约1/3的存储量。本文推导得出了一般正交曲线坐标系(GOC)中的降维时域有限差分法的基本公式,给出了其计算步骤,为在一般正交曲线坐标系中应用降维时域有限差分法奠定了基础。数值实验证实了这一方法的有效性。     

正交曲线坐标系中单位基矢的导数

用数学方法分析具体的电磁场问题时,对于简单的情况,常可利用对称性、迭加原理、镜象法、复变函数等方法去求解。对于比较复杂些的情况,一般的步骤是按照问题中的边界形状,选取适当的坐标系,把一般的电磁场方程组(常表成与坐标系无关的微分方程式)和定解条件,用该坐标系中场量的分量表示出来,然后用求解数学物理方程定解问题的方法或数值计算的方法求出解析解或数值解。坐标系常选用某种正交曲线坐标系,如圆柱面坐标系,球面坐标系,椭圆柱面坐标系,抛物柱面坐标系……等等。要想把一般的电磁场方程组     

曲线坐标系下电子运动的张量分析

本文在作者的宽电子束聚焦的普遍理论的基础上进一步由Newton方程和Lorentz力的逆变形式和协变形式以及广义变分原理来探讨曲线坐标系中以静电电位、磁标位或磁矢位表示的静电场和静磁场中电子运动轨迹,采用沿主轨迹的Frenet-Serret局部坐标系和转动局部坐标系,在最普遍的情况下给出了曲线坐标系下各种形式的电子运动方程和轨迹方程。     

相对论修正下的宽电子束聚焦的普遍理论

本文由曲线坐标系下的相对论修正普遍轨迹方程出发,考虑包含阴极物面的宽电子束聚焦的情况,推导了曲线坐标系下的主轨迹方程与曲近轴轨迹方程,研究了满足正交条件的近轴系统的特性。曲线坐标系下的细电子束聚焦问题以及非相对论修正的宽电子束聚焦问题均可视为本文的特例。     

Electromagnetic Waves in Toroidal Vessels of Arbitrary Cross Section Filled with Radially Inhomogeneous Dielectric Medium

In this paper, analytical solutions of Maxwell's equations in cylindrical coordinates are presented for toroidal resonators filled with homogeneous or inhomogeneous unmagnetized plasma or another dielectric medium. It is shown that the electromagnetic boundary conditions valid on a conducting toroidal surface of arbitrary meridional cross section can be satisfied by the general solution since the general solution contains an infinite set of arbitrary constants. A method is given to show how these constants and the eigenfrequency of the resonator can be calculated for a given cross section of the toroidal vessel.     

Prolate spheroidal wave functions of large frequency parametersc=kfand their applications in electromagnetic theory

Maxwell's equations in prolate spheroidal coordinates have been separated into three second-order differential equations. These differential equations, satisfied byxiandeta, were solved for the frequency parameter c > 10 and the separation constant m = 1, i,e., the uniform circumferential excitations. The asymptotic solutions of the equations for any positive integer m > 1 and c > 10 are given. Thereby, the radiation fields of the metallic prolate spheroid of any length excited by an arbitrary source can be calculated.     

Numerical dispersion and stability characteristics of time-domainmethods on nonorthogonal meshes

The familiar finite-difference time-domain method for discretizing Maxwell's curl equations on orthogonal grids has been extended to nonorthogonal grids by a number of researchers. While it is difficult to determine the dispersion and stability characteristics of these methods when applied on arbitrary grids, analysis of the idealized but representative case of a uniform skewed mesh proves to be quite tractable in 2-D. This analysis demonstrates that numerical dispersion errors are small for well-resolved spatial wavelengths and that these methods converge to the continuous-space solution in the limit as the cell and time step sizes vanish. Grid anisotropy (variations in wave propagation speed as a function of the propagation angle relative to the mesh coordinates) increases as the mesh is skewed. In spite of this, there exist some angles where waves propagate through the skewed mesh with virtually no dispersion. This analysis also provides a stability limit for the time step size in terms of geometrical mesh quantities     

Toroidal Resonators and Waveguides of Arbitrary Cross Section

After introducing a new method to solve Maxwell's equations using a complex electromagnetic field vector F, a rotational coordinate system xi, Theta, psi is introduced. In this coordinate system, the field vector components F/sub xi/, F/sub Theta/ may be expressed by F/sub psi/. This component can be obtained from a two-dimensional Hehlmholtz equation. Specifying xi, Theta by cylindrical coordinates r, z the complex Maxwell equation curl F= gamma F is solved for the axisymmetric case (/spl part///spl part/psi = 0) and for the nonsymmetric case. The differential equations for magnetic field lines are solved and surfaces on which the normal component of B and the tangential components of E vanish are recognized as metallic walls of toroidal resonators of various arbitrary cross sections. In the Appendix the results of the new method are compared with well known results for circular cylindrical waveguides.     

Finite-difference time-domain algorithm for solving Maxwell'sequations in rotationally symmetric geometries

In this paper, an efficient finite-difference time-domain algorithm (FDTD) is presented for solving Maxwell's equations with rotationally symmetric geometries. The azimuthal symmetry enables us to employ a two-dimensional (2-D) difference lattice by projecting the three-dimensional (3-D) Yee-cell in cylindrical coordinates (r, φ, z) onto the r-z plane. Extensive numerical results have been derived for various cavity structures and these results have been compared with those available in the literature. Excellent agreement has been observed for all of the cases investigated     

A class of symmetrical condensed node TLM methods derived directlyfrom Maxwell's equations

A series of general transmission line matrix (TLM)-type methods, which include the symmetrical condensed node method, are derived directly from Maxwell's curl equations without recourse to transmission line models. Written as a system of conservation laws, Maxwell's equations in 3-D plus time are decomposed along the orthogonal characteristic directions of a rectangular grid. The Riemann invariants in this method correspond to the voltage pulses of the TLM method. A new method of handling inhomogeneous media is proposed based on a new transfer event. The dispersive nature of these schemes is also investigated     

Local field analysis of bent graded-index planar waveguides

A local field analysis is proposed for bent planar waveguides with arbitrary refractive index profiles. Exact vector wave equations that include the gradient index, or polarization correction, term are derived for both transverse electric and transverse magnetic modes from Maxwell's equations in a local bent coordinate system. The approximate local field and correction to the propagation constants are obtained by perturbation analysis. As an example of the method, an infinitely extended parabolic index profile is studied     

Finite Element Analysis of Lossy Waveguides-Application to Microstrip Lines on Semiconductor Substrate

The development of Maxwell's equations is made considering the electromagnetic fields as vector distributions. With the aid of the finite element method, an analysis of lossy shielded inhomogenous waveguides of arbitrary shape is described. To solve the complex matrix system an iterative procedure is presented. The method is applied to study the propagation on MIS or Schottky contact microstrip lines.     

Vector Variational Formulation of Electromagnetic Fields in Anisotropic Media

Maxwell's equations can be cast into a basic differential operator equation, the curlcurl equation, which lends itself easily to variational treatment. Various forms of this equation are associated with problems of practical importance. The formulation includes the treatment of loss-free anisotropic media. The boundary conditions associated with electromagnetic-field problems are treated in detail and the uniqueness of the solution is discussed. A functional is derived for the curlcurl equation in Cartesian and cylindrical coordinates.     

The electromagnetic field in rotating coordinates

It is shown that electromagnetic field equations in rotating coordinates, obtained by several authors, are faulty due to their basis in incorrect expressions for the divergence and curl operators and the three-dimensional spatial vectors. A four-dimensional (4-vector) tensor formulation is used to show that Maxwell's equations are shown to be valid in rotating coordinates