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。     

A new method for solving Dyadic Green’s Function of electromagnetic field

A new method for solving electromagnetic field boundary value problem is given. By using this method, the boundary value problem of the vector wave equation can be transformed into the independent boundary value problem of scalar wave equations and the two additional vector differential operations. All the dyadic Green’s functions got by eigenfunction expansion of the dyadic Green’s function can be got by this method easily and some of the dyadic Green’s functions for complex systems which are very difficult to get by the ordinary method have been got by this new method. The dyadic Green’s function for a dielectric loaded cavity is one of the given examples. This project is supported by the National science Fundation of China     

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。     

印刷螺线天线的分析计算

本文运用全波分析法对印刷螺旋天线进行了算法分析,根据Helmholtz方程在边界处满足的边界条件系统推导了单层印刷螺旋天线在自由空间和媒质中赫兹矢量位形式的并矢格林函数。在其计算中采用了离散复镜像理论,适当提取渐近项,以加快积分的收敛速度,并避免了数值计算中非常麻烦的极点处理问题。通过矢理法推导了阻抗矩阵的激励矩阵。并对一由绝缘材料支撑的印刷螺旋天线进行了计算,为工程设计提供了理论依据。     

Dyadic eigenfunctions and natural modes for hybrid waves in planar media

A new formulation for studying electromagnetic wave propagation in an open, planarly layered medium is presented based on eigenfunctions of the Hertzian potential dyadic Green's function operator. Due to the complicated coupling of scalar components of potential at material interfaces, elevation of the usual vector eigenfunction problem to dyadic level is found to lead to a convenient, compact representation of wave propagation phenomena. Although we study the source-free problem here, the three columns of the eigenfunction dyadics represent (up to an excitation-dependent amplitude) the vector fields excited by a given three-dimensional source. The general theory of dyadic eigenfunctions is presented, including orthogonality and the possibility of associated functions (root functions) at modal degeneracies, and an example of propagation in a grounded dielectric slab environment is provided.     

Dyadic Green's functions for a coaxial line

The eigenfunction expansions of the dyadic Green's functions for a coaxial line have been derived based on the method ofbarbar{G}_{m}, whereby the irrotational vector wave functionbar{L}is not needed. A dyadic boundary condition for the discontinuity of the tangential component ofbarbar{G}_{m}has been used to facilitate the derivation of the expression for the electric dyadic Green's function.     

Spheroidal vector wave eigenfunction expansion of dyadic Green'sfunctions for a dielectric spheroid

The dyadic Green's functions for defining the electromagnetic (EM) fields for the inner and outer regions of a dielectric spheroid are formulated. The dyadic Green's function for an unbounded medium is expanded in terms of the spheroidal vector wave functions and the singularity at source points is extracted. The principle of scattering superposition is then applied into the analysis to obtain the scattering spheroidal dyadic Green's functions due to the existing interface. Coupled equation systems satisfied by scattering (i.e., reflection and transmission) coefficients of the dyadic Green's functions are obtained so that these coefficients can be uniquely solved for. The characteristics of the spheroidal dyadic Green's functions as compared with the spherical and cylindrical Green's dyadics are described and the improper developments of the spheroidal dyadic Green's function for the outer region of a conducting spheroid in the existing work are pointed out     

完全导电圆锥并矢Green函数

本文运用算子法和并矢运算的分布理论法,求解了完全导电圆锥并矢Green函数,且证明解是满足电磁基本方程的。     

矩形介质谐抵腔的格林函数问题

本文讨论了求解平面分层媒质系统的并矢格林函数问题的一种新方法。这一方法的特点就是把并矢格莱函数问题转化为标量格林函数来解决。文中详述了介质加载的矩形腔的并矢格林函数的求解方法和结果。     

Dyadic Green's functions inside/outside a dielectric elliptical cylinder: theory and application

Dyadic Green's functions in two regions separated by an infinitely long elliptical dielectric cylinder are formulated in this paper. As an application, the plane electromagnetic wave scattering by an isotropic elliptical dielectric cylinder is revisited by applying these dyadic Green's functions and the scattering-to-radiation transform. First, the dyadic Green's functions are formulated and expanded in terms of elliptical vector wave functions. The general equations are derived from the boundary conditions and expressed in matrix form. Then the scattering and transmission coefficients coupled to each other are solved from the matrix equations. To verify the theory developed and its applicability, we revisit the plane electromagnetic wave scattering (of TE- and TM-polarizations) by an infinitely long elliptical cylinder, and consider it as a special case of electromagnetic radiation using the dyadic Green's function technique. The derived equations and computed numerical results are then compared with published results and a good agreement in each case is found. Special cases where the elliptical cylinder degenerates to a circular cylinder and where the material of the cylinder is isorefractive are also considered, and the same analytical solutions in both cases are obtained.     

Electromagnetic dyadic Green's function in cylindricallymultilayered media

A spectral-domain dyadic Green's function for electromagnetic fields in cylindrically multilayered media with circular cross section is derived in terms of matrices of the cylindrical vector wave functions. Some useful concepts, such as the effective plane wave reflection and transmission coefficients, are extended in the present spectral domain eigenfunction expansion. The coupling coefficient matrices of the scattering dyadic Green's functions are given by applying the principle of scattering superposition. The general solution has been applied to the case of axial symmetry (n=0, n is eigenvalue parameter in φ direction) where the scattering coefficients are decoupled between TM and TE waves. Two specific geometries, i.e., two- and three-layered media that are frequently employed to model the practical problems are considered in detail, and the coupling coefficient matrices of their dyadic Green's functions are given, respectively     

Spherical wave expansion of the time-domain free-space dyadic Green's function

The importance of expanding Green's functions, particularly free-space Green's functions in terms of orthogonal wave functions is practically self-evident when frequency domain scattering problems are of interest. With the relatively recent and widespread interest in time-domain scattering problems, similar expansions of Green's functions are expected to be useful in the time-domain. In this paper, an expression, expanded in terms of orthogonal spherical vector wave functions, for the time-domain free-space dyadic Green's function is presented and scattering by a perfectly conducting sphere is studied as an application to check numerically the validity and to demonstrate the utility of this expression.     

Cylindrical vector eigenfunction expansion of Green dyadics for multilayered anisotropic media and its application to four-layered forest

A complete eigenfunction expansion of the dyadic Green's functions (DGFs) for planar, arbitrary multilayered anisotropic media using cylindrical vector wave functions is presented. These formulations are constructed based on the principle of scattering superposition. For the scattering dyadic Green's function in each layer, the scattering coefficients of TE and TM modes are determined from the boundary conditions matched at the planar interfaces. The explicit representation of the DGFs after reduction to the isotropic case agrees well with the existing results corresponding to the isotropic media. The general DGFs for multilayered anisotropic media are then reduced to those for a four-layered forest where the trunk layer is modeled as anisotropic medium. Application is further made for radio-wave propagation through forests of a four-layered geometry, whereas it is shown how these Green dyadic formulations are used in a practical way and how the field distributions due to a dipole can be obtained.     

用电磁场算子理论求波导复合系统的本征值

该文用并矢格林函数方法通过虚拟边界的电场和磁场的耦合求解波导复合结构的本征值,所采用的并矢格林函数没有奇异项,可以用标量格林函数来表示并进行计算,因此不仅可以计算横电与横磁模的基模和高次模式,还可以计算存在两个孪生模式的复合系统。该文同时还对经典场论中常用的一些定理,如面旋度定理进行了探讨。     

有源加载准光腔的并矢格林函数

由近轴近似得到了有源加载准光腔的矢量波函数,并由矢量波函数展开方法得到了有源加载情况下准光腔中的并矢格林函数。由此可以得到腔中电磁场的积分解。     

论求解并矢Green函数的交换算子法

本文基于广义函数论证明了求解并矢Green函数的交换算子法的正确性,并把此法发展为计算并矢Green函数的一种普遍方法。作为示例,用此法求解、计算了矩形波导的并矢Green函数。     

有源随机球粒媒质的非弹性多散射

依据有源分子的等效偶极子模型,本文首先用并矢格林函数方法给出了含有有源分子的单球粒的非弹性散射分析。然后,以建立的随机球状颗粒媒质的弹性多散射理论为基础,导出了含有有源分子的随机球粒媒质的非弹性多散射理论,给出了非弹性多散射场在整个空间的矢量球波函数展开,展开系数可由一组耦合线性方程解得。     

关于矩形腔电并矢格林函数的讨论

本文通过对Tat所给出的短形胶的电并矢格林函数形式进行变换，发现这类并矢格林函数形式的空间不对称性，即选择不同的方向作为领示矢量，所得到的并失格林函数形式是不同的，这在物理上显然是不合理的。     

INELASTIC MULTIPLE SCATTERING BY ACTIVE RANDOMLY DISTRIBUTED SPHERICAL SCATTERERS

According to the model of equivalent dipoles for active molecules, the analysisof inelastic EM scattering by active molecules embedded in a sphere is given by the method ofdyadic Green's functions at the first, and then based on the theory of elastic multiple scattering byrandomly distributed spherical scatterers, a new theory for analysis of inelastic multiple scatteringby active molecules embedded in randomly distributed spherical scatterers also is developed. Thistheory gives the expansions of the multiple scattering fields in all space region in terms of vectorspherical wave functions in which the expansion coefficients can be solved from a set of coupledlinear equations.     

The eigenfunction expansion of dyadic Green's functions forchirowaveguides

A general method of formulating eigenfunction expansion of dyadic Green's functions in lossless, reciprocal and homogeneous chirowaveguides is presented. Bohren's decomposition of the electromagnetic field is used to obtain the vector wave functions. The method of G¯¯_m is used to rigorously derive the magnetic and electric dyadic Green's functions. A specific application to the cylindrical chirowaveguide illustrates the method