推广的赫姆霍兹定理及其在电磁理论中的应用

本文证明了在直角、画柱和球坐标系的规则边界的系统内,一个任意的矢量一定可以分解为无旋场、横电模场和横磁模场三个相互正交的分量,每一个分量都可用一个标量函数来描述。并在此基础上证明了这些系统内的{L、M和N}矢量波函数系的完备性。由此说明了一个矢量函数空间不仅可以通过它在欧氏空间中的射影分解为三个不相交的子空间,同样可以通过它在矢量波函数系上的射影分解为三个不相交的子空间。     

论自由空间中旋量电场与无旋电场间的正交性

本文从自由空间中的赫姆霍兹定理证明了电旋量场和电无旋场之间的正交性,从而也证明了电的矢量波方程可以分解为无旋场方程和旋量场方程。     

两层旋电磁介质球电磁散射的球矢量波函数解

在均匀旋电磁介质球矢量波函数的基础上,利用球Bessel函数的特性,给出了两层旋电磁介质球内的电磁场用波函数表示的表达式.在平面波入射情况下,应用电磁场在球边界上切向电场和磁场连续与远区辐射条件,导出了两层各向异性旋电磁介质中电磁场用矢量波函数表示的展开函数所满足的方程组,求出了两层旋电磁介质球的散射场用均匀各向同性波函数展开的展开系数,进而得出了两层旋电磁介质球对平面波的电磁散射特性.理论分析和数值计算的结果表明:当两层旋电磁介质球的媒质参数相同时,本文所得的结果可退化为单层各向异性旋电磁体解析解.     

关于并矢Green函数的完备形式的讨论

本文从电流源对矩形波导的激励说明了由L类矢量波函数所得的无旋场就是空间电荷场,而所谓并矢Green函数中的奇异项—只是空间电荷场的一部分,它反映了空间电荷场在源区的不连续性。     

导体球涂覆各向异性铁氧体介质电磁散射的解析解

该文用球矢量波函数对各向异性铁氧体介质涂覆导体球的电磁散射解析解开展研究。各向异性铁氧体介质中电磁场的球矢量波函数解可表示成第一、二、三、四类球矢量波函数之和。根据球Bessel函数的性质,可以得出导体球涂覆各向异性铁氧体介质的球矢量波函数解析解。应用铁氧体与自由空间分界面上电磁场切向连续和在导体球面上切向电场等于零的边界条件以及球矢量波函数切向正交性质,可分别得出铁氧体介质中电磁场和散射场的展开系数。给出了平面波入射情况下的数值计算结果。该文的结果可应用于有关微波器件、天线以及目标特征的分析和计算。     

矢量波函数空间的电磁矢量恰当射影

提出了一种简化电磁场问题求解的新方法，将电磁场矢量的无旋场部分和无散场部分各自应用一个满足二阶方程的标量函数表示出来，然后由此分析了电磁场矢量在矢量波函数空间的恰当射影问题，并给出用一个标量格林函数构造的无散电磁场并矢格林函数。     

规则边界下电磁场的本征函数和并矢格林函数

本文给出了在直、柱和球坐标系中的规则边界条件下的M和N类矢量波函数及其归一化积分的普遍形式,并由此得到了相应的格林函数的普遍形式。     

随机球粒媒质的弹性多散射

从多散射场的基本积分方程出发,利用场的矢量球波函数展开及矢量球波函数的坐标变换迭加公式,导出了求解随机球粒媒质的弹性多散射场矢量球波函数展开系数的一组耦合线性方程,从而建立起一种新的分析随机球粒媒质的弹性多散射理论。不同于现有方法,本文方法得到了整个空间的多散射场。     

非对称单脊波导的特性计算

从矢量波函数空间的偏微分算子理论出发,给出完备的旋量波函数空间的本征函数系及电磁波基本方程组,由此推导出数学形式简洁的并矢格林函数及基于旋量波算子空间本征函数系的电磁场量,在脊波导的耦合边界上模式匹配,推导出计算公式,给出了两个分析脊波导的实例,得到主模和第一个高阶模的截止频率,非对称脊波导的电中心线偏移量.     

单轴各向异性球对任意方向入射平面波的散射

基于球矢量波函数的正交完备性,给出了具有任意传播方向两种极化模式的平面波用球矢量波函数展开的形式,导出了其展开系数的具体表达式.研究了单轴各向异性介质球对任意方向入射平面波的散射,利用球矢量波函数及傅里叶变换方法得到了各向异性介质球的内场展开式,结合切向连续边界条件给出了散射系数.数值分析了介电常数张量元、有耗、无耗、尺寸参数、入射角和方位角等对单轴各向异性介质球的雷达散射截面的影响.     

EXTENDED HELMHOLTZ THEOREM AND ITS APPLICATION IN ELECTROMAGNETIC THEORY

It is proved that in a regular boundary system of rectangular,cylindrical or sphericalcoordinate,an arbitrary vector function can be separated into three orthogonal parameters:TEmodel field,TM model field and irrotational field.Each of these components can be determinedfully by a scalar function.On the basis of this theorem,the completeness of vector wave functionsystem{L,M,and N}is proved also.Thus it is explained that a vector function space can beprojected into three uncrossed subspaces not only in Euclidean space but also in the subspace ofvector wave function space.     

电磁场在矢量波函数空间的完全射影定理

证明了广义的亥姆赫兹定理－电磁场在矢量波函数的完全射影定理。在这一定理中每一个任意的电磁矢量函数都可以在矢量波函数空间中被唯一地分离成三个独立的分量,每一个分量都可以用一个标量函数来表示。     

均匀波导管横截面上矢量本征函数的完备性

证明了在均匀波导横截面Ｓ上有界变差并满足一定边值条件的横向矢量函数可以按横向本征矢量序列｛ＥεＴ，ＥμＴ｝或｛ＨεＴ，ＨμＴ｝展开为级数，展开式按Ｌ２范数收敛于被展开的函数。同时还论证了Ｓ上有界变差并在周界上为０或法向导数为０的纵向矢量函数可以分别按Ｅ模或Ｈ模的纵向本征矢量展开。但如被展开的矢量函数在波导内并不满足齐次场方程其纵向部分和横向部分只能分别展开。     

A NEW METHOD FOR SOLVING DYADIC GREEN''''S FUNCTION OF ELECTROMAGNETIC FIELD

A new method for solving electromagnetic field boundary value problem is given.Byusing this method,the boundary value problem of the vector wave equation can be transformedinto the independent boundary value problem of scalar wave equations and the two additionalvector differential operations.All the dyadic Green's functions got by eigenfunction expansionof the dyadic Green's function can be got by this method easily and some of the dyadic Green'sfunctions for complex systems which are very difficult to get by the ordinary method have beengot by this new method.The dyadic Green's function for a dielectric loaded cavity is one of thegiven examples.     

Three-dimensional orthogonal vector basis functions for time-domain finite element solution of vector wave equations

Three-dimensional (3-D) orthogonal vector basis functions are developed for the time-domain finite element solution of vector wave equations. These basis functions enforce both the tangential continuity of the electric field and the normal continuity of the electric flux. The stability of the resulting time-domain finite element schemes is investigated and demonstrated to be guaranteed. The use of the proposed basis functions completely eliminates the matrix solution at each time step required by the time-domain finite element solution of vector wave equations. The computational cost thereby scales as O(N/sub t/N) with N/sub t/ and N denoting the number of time steps and the number of unknowns, respectively. Defined over tetrahedral elements, the proposed basis functions increase the solution efficiency without compromising the geometry modeling flexibility. Both numerical results and comparison with traditional vector basis functions demonstrate the accuracy as well as the efficiency of the proposed three-dimensional orthogonal vector bases.     

求解电磁场并矢格林函数的新方法

本文提出了求解电磁场边值问题的新方法:把矢量波方程的边值问题化为对应的标量波方程的边值问题加上两个附加的矢量微分运算的问题。用这种方法可以很方便地求解所有现在用并矢格林函数的本征展开法所能求得的各种并矢格林函数。可以求解用现有的方法很难求解的比较复杂系统的并矢格林函数。文中给出了加载的谐振腔的并矢格林函数就是其中的一例。     

微波炉炉腔内电磁场仿真

利用高频电磁场软件对微波炉建模,设置腔体内的介质材料的电特性参数,仿真得到的反射系数和相位图与矢量网络分析仪实测值比较,误差小于8%,吻合较好,证明本方法是有实用价值.还对该方法进行了误差分析和讨论.进而研究波导管与腔体相对位置对微波炉匹配性能的影响.这些对微波炉开发工程师在微波炉冷匹配时提供理论指导,缩短了微波炉新平台开发时间,提高了竞争力.     

Electromagnetic plane wave scattering by a system of two uniformlylossy dielectric prolate spheroids in arbitrary orientation

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, an exact solution is obtained for the scattering by two uniformly lossy dielectric prolate spheroids in arbitrary orientation embedded in free space, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Rotational-translational addition theorems for spheroidal vector wave functions are employed to transform the outgoing wave from one spheroid into the incoming wave at the other spheroid. The field solution gives the column vector of the unknown coefficients of the series expansions of the scattered and transmitted fields expressed in terms of the column vector of the known coefficients of the series expansions of the incident field and the system matrix which is independent of the direction and polarization of the incident wave. Numerical results in the form of curves for normalized bistatic and monostatic radar cross sections are given for a variety of two-body system of uniformly lossy dielectric prolate spheroids in arbitrary orientation having resonant or near resonant lengths and different distances of separation     

On cylindrical near-field scanning techniques

The agreement between the coupling equations obtained in the literature by using the reciprocity theorem and the scattering matrix formulation is demonstrated. The field is expanded in cylindrical vector wave functions and the addition theorem for these functions is used. The communication may serve as a tutorial introduction to the cylindrical scanning techniques.