基于频域广义传输矩阵方法的电磁散射特性分析

多尺度复杂电子系统的电磁场问题难以用单一的计算电磁学方法进行高效数值计算.基于区域分解方法和惠更斯等效原理，提出了频域广义传输矩阵（generalized transition matrix，GTM）方法:将系统分解为多个子模块，通过电场积分方程（electric field integreal equation，EFIE）把各个子模块的电磁特性进行提炼，再考虑所有子模块之间的电磁耦合，计算系统整体电磁场分布.GTM方法把多尺度问题转化为尺度相对比较单一的问题进行处理，在分析各种复合结构、非均匀各向异性介质、大型相控阵天线等电磁散射特性时，提供了灵活的解决方案.论文给出了GTM在手征介质、开口腔体以及Vivaldi相控阵天线电磁特性分析中的应用算例，当未知量个数压缩到原来的十分之一时，GTM计算结果与直接用矩量法（methed of moment，MoM）求解的计算结果非常吻合.GTM可以简洁地表示目标问题的电磁散射特征，与传统MoM相比，大幅度减少了基函数的数量，具有较高的计算精度和效率.     

Extended boundary condition integral equations for perfectly conducting and dielectric bodies: Formulation and uniqueness

The equivalence theorem is used to derive novel generalized boundary condition (GBC) integral equations for the tangential components of the electric and magnetic fields on the interfaces of a finite number of dielectric or conducting scatterers. Closed surface, plane, and line extended boundary conditions (EBC) equivalent to the GBC are introduced. The GBC integral equations can now be replaced by any of these EBC integral equations whose solutions are unique and easy to obtain numerically using the moment method. A perfectly conducting sphere and a dielectric sphere in the electrostatic field of two equal and opposite point charges are presented as simple examples of the general procedure.     

A numerically efficient finite-element formulation for the generalwaveguide problem without spurious modes

A numerically efficient finite-element procedure without spurious modes is presented for the analysis of propagation characteristics in arbitrarily shaped metal waveguides loaded with linear materials of arbitrary complex tensor permittivity and permeability. The method is straightforwardly derived from the first-order Maxwell curl equations and comprises both the transversal and longitudinal components of the electric and magnetic fields. Hence, all necessary boundary conditions on the tangential field components are a priori satisfied by the trial functions. With this formulation, an absence of spurious modes has been found. Furthermore, by imposing the additional boundary conditions on the normal components of the magnetic induction and electric displacement fields, the dimension of the resulting matrix equation can be significantly reduced. For the fundamental modes, both the convergence order and the accuracy of the presented method are found to be significantly higher than those of comparable methods when applied to some numerical examples     

Adaptive processing using a single snapshot for a nonuniformlyspaced array in the presence of mutual coupling and near-fieldscatterers

This paper presents an adaptive technique to extract the signal of interest (SOI) arriving from a known direction in the presence of strong interferers using a single snapshot of data. The antenna elements in this method can be nonuniformly spaced and there can be mutual coupling between them. In addition, near-field scatterers can also be present. First, the voltages induced in the antenna elements of the array due to interferers, mutual coupling between the elements, and near-field scatterers is preprocessed by applying a transformation matrix to these voltages through a rigorous electromagnetic analysis tool. This electromagnetic preprocessing technique transforms the voltages that are induced in a nonuniformly spaced array containing real antenna elements to a set of voltages that will be produced in a uniform linear virtual array (ULVA) containing omnidirectional isotropic point radiators. In the transformation matrix we would like to include various electromagnetic effects like mutual coupling between the antenna elements, presence of near-field scatterers and the platform effects on which the antenna array is mounted. This transformation matrix when applied to the actual measured voltages yields an equivalent set of voltages that will be induced in the ULVA. A direct data domain least squares adaptive algorithm is then applied to the processed voltages to extract the SOI in the presence of interferers. Limited numerical examples are presented to illustrate the novelty of the proposed method     

Scattering From Axisymmetric Dielectric Scatterers: A Hybrid Method of Solving the Surface Integral Equations

Scattering of EM waves from homogeneous dielectric scatterers is formulated in terms of two surface integral equations, for the components of the total electric and magnetic fields that are tangential to the surface of the scatterer. Two equivalent systems of such equations may be used, corresponding to the two types of Maue's integral equations for perfectly conducting scatterers. The appearance of surface divergence terms of both components in the dielectric case, in addition to the unknowns themselves, causes serious complications when the method of solution is based on some kind of division of the scatterer surface into patches; these complications become particularly apparent in the process of evaluating the locally dominant self-patch contribution to the surface integrals. They can be effectively avoided if a third equivalent system of surface integral equations is used, arising from a proper summation of the original two systems; then, the two singular Green functions that appear in the surface divergence terms are replaced by their non-singular difference and this, followed by a further transformation of these critical terms, results in the complete elimination of the surface divergence terms. The self-patch contribution can then be evaluated analytically and this helps reduce the size of the matrix, via which the values of the tangential field components at the patch centers are calculated. Scatterers of considerable electrical size, for instance spheres with ka of the order of 10 or 15, can then be treated with moderate size matrices. Numerical results for spheres, sphere-cone-spheres and other shapes are obtained and compared with results from other methods. Apart from spheres, results for other shapes are very rare and limited to small sizes in the literature.     

Generalized reaction and unrestricted variational formulation of cavity resonators. I. basic theory

Based on the reciprocity theorem, the reaction concept in electromagnetic theory is generalized to the cases where both surface electric and magnetic currents overlap across boundaries, i.e., neither the E-field, nor H-field meets the continuity conditions. An improved systematic method is then developed to obtain unrestricted variational expressions in a cavity resonator for which the tangential components of the trial fields can be discontinuous across its interior boundaries.     

Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body

The method of moments technique for analyzing electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body is presented based on the combined field integral equations. The body is assumed to be illuminated by a plane wave. The surface equivalence principle is used to replace the body by equivalent electric and magnetic surface currents. These currents radiating in unbounded free space produce the correct scattered field outside. The negatives of these currents produce the correct total internal field, when radiating in an unbounded chiral medium. By enforcing the continuity of the tangential components of the total electric and magnetic fields on the surface of the body, a set of coupled integral equations is obtained for the equivalent surface currents. The surface of the body is modeled using triangular patches. The triangular rooftop vector expansion functions are used for both equivalent surface currents. The coefficients of these expansion functions are obtained using the method of moments. The mixed potential formulation for a chiral medium is developed and used to obtain explicit expressions for the electric and magnetic fields produced by surface currents. Numerical results for bistatic radar cross sections are presented for three chiral scatterers - a sphere, a finite circular cylinder, and a cube.     

高阶张量阻抗边界条件的纵向电磁场分量表达式

首先导出转换矩阵表示的有导体或各向同性介质衬底的旋转对称双各向异性媒质平面的精确阻抗张量。然后利用多项式近似和横向与纵向场分量的基本方程组推导出相应的近似高阶张量阻抗边界条件。该阻抗边界条件是用纵向电磁场分量表示的二个关系式,表达式中的阻抗和导纳算符是介质涂层平面法向导数的三次幂多项式。所导出的高阶张量阻抗边界条件能够直截了当地模拟双各向异性介质涂层对电磁场的影响,并能够方便有效地简化相关电磁场边值问题的求解。     

Physics-based preconditioner for iterative algorithms in MoM-problems

An efficient method to solve electromagnetic scattering problems involving several metallic scatterers or bodies composed of dielectric and metallic regions is proposed. For this, the block Jacobi preconditioner is combined with the iterative transpose-free quasi-minimum residual (TFQMR) algorithm. For best performance, the blocks for the preconditioner are chosen according to individual scatterers or groups of scatterers, or according to the electric and magnetic current basis functions for dielectric/metallic scatterers.     

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。     

Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles

In recent work, we derived generalized sheet transition conditions (GSTCs) for the average (or "macroscopic") electromagnetic fields across a metafilm, which, when properly designed, can have certain desired reflection and transmission properties. A metafilm is the two-dimensional equivalent of a metamaterial, and is essentially a surface distribution of electrically small scatterers characterized by electric- and magnetic-polarizability densities. In this paper, the GSTC is used to calculate the reflection and transmission coefficients of the metafilm. These coefficients are derived for both TM and TE polarized plane waves with arbitrary incidence angles. We show that the reflection and transmission properties of the metafilm are expressed in terms of the electric and magnetic polarizabilities of the scatterers themselves, and we derive conditions on the polarizabilities of the scatterers required to obtain total transmission and/or total reflection. We show various examples to illustrate the validity of the GSTC for the analysis of a metafilm. By controlling the polarization densities of the scatterers in the metafilm, a "smart" and/or "controllable" surface can be realized. We propose a metafilm composed of spherical magneto-dielectric particles for achieving such a controllable surface. To validate the results for the spherical particle metafilm, we show comparisons with a full-wave computation obtained from a mode-matching technique applied to the doubly infinite array of spherical scatterers. The results in this paper are in principle scalable; that is, the dimensions of the scatterers can range from relatively large to relatively small depending on the frequencies of interest.     

Scattering analysis of a large body with deep cavities

A numerical scheme is presented for simulating electromagnetic scattering from a large and arbitrarily shaped body, coated with inhomogeneous composite materials, with large and deep cavities. This numerical scheme employs the higher order vector finite-element method (FEM) to discretize the fields inside the cavities and coatings and the higher order boundary integral (BI) method to terminate the FEM computational domain. A highly efficient special solver is designed to eliminate the unknowns inside the cavities, which yields a computed relation (CR) matrix over the cavity's aperture between the tangential electric and magnetic fields. This CR matrix is then combined with the finite element-boundary integral (FE-BI) matrix equation to form a complete linear system for the discrete fields everywhere in the computational domain. The resulting system is solved iteratively using a novel preconditioner derived by replacing the BI with a corresponding absorbing boundary condition (ABC).     

Matrix analysis of discontinuities in nonreciprocal waveguides: analytical description for magnetooptical slab waveguides

A new analytical formalism to study the effect of discontinuities in a nonreciprocal waveguide has been developed. The analysis is based on 1) the general orthogonality relation obtained from the reciprocity theorem, 2) the modal expansion of the transverse electromagnetic fields within the waveguide, and 3) the continuity of the tangential components of such electromagnetic fields at both sides of the discontinuity. The formalism is presented in a matrix form, which allows the treatment of several discontinuities as a simple summation and product of coupling and propagation matrices. The matrix formalism is developed for magnetooptic waveguides in the three different orientations of the magnetization, and, within this context, two practical applications of magnetooptic isolators are studied.     

Equivalent circuit representation of lossy coplanar waveguides

The study of the dispersion properties of planar transmission lines including metallic losses with the generalized transverse resonance method is formalized in building an equivalent network of the cross-section which specifies the relationships between the tangential components of the fields on each side of the interfaces. Virtual sources represent the trial quantities chosen to describe the problem. With twoport type boundary conditions, the trial quantities are not easily defined from physical considerations, but the virtual sources obey to specific rules. This purpose is illustrated in studying the attenuation in lossy suspended coplanar transmission lines.     

Scattering at a nonchiral-chiral interface in a coaxial waveguide

A formally exact full-wave solution is presented for the problem of scattering at a nonchiral-chiral interface in a coaxial waveguide. The field components for the axisymmetric modes in a coaxial chirowaveguide are initially obtained. A new orthogonality relation for the modes is then proposed and used to find expansion coefficients for the electromagnetic fields in the coaxial chirowaveguide. The scattering matrix for the nonchiral-chiral dielectric discontinuity in a coaxial waveguide is finally derived by enforcing the continuity conditions of the tangential field components across the interface. Numerical results for the reflection and transmission coefficients at the nonchiral-chiral interface in a coaxial waveguide are presented     

A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section

A new method is introduced for formulating the scattering problem in which the scattered fields (and the interior fields in the case of a dielectric scatterer) are represented in an expansion in terms of free-space modal wave functions in cylindrical coordinates, the coefficients of which are the unknowns. The boundary conditions are satisfied using either an analytic continuation procedure, in which the far-field pattern (in Fourier series form) is continued into the near field and the boundary conditions are applied at the surface of the scatterer; or the completeness of the modal wave functions, to approximately represent the fields in the interior and exterior regions of the scatterer directly. The methods were applied to the scattering of two-dimensional cylindrical scatterers of arbitrary cross section and only the TM polarization of the excitation is considered. The solution for the coefficients of the modal wave functions are obtained by inversion of a matrix which depends only on the shape and material of the scatterer. The methods are illustrated using perfectly conducting square and elliptic cylinders and elliptic dielectric cylinders. A solution to the problem of multiple scattering by two conducting scatterers is also obtained using only the matrices characterizing each of the single scatterers. As an example, the method is illustrated by application to a two-body configuration.     

Electromagnetic radiation from a prolate spheroidal antenna enclosed in a confocal spheroidal radome

The solution of electromagnetic radiation from a prolate spheroidal antenna, excited by a delta voltage across an infinitesimally narrow gap and enclosed in a confocal radome, is obtained. The method used is that of separating the scalar wave equation in prolate spheroidal coordinates and representing the solution in terms of prolate spheroidal wave functions. A simplified solution of the electric and magnetic fields, taking into account the symmetry of the antenna in the /spl phi/ direction, is obtained. Boundary conditions are then applied on the tangential fields to obtain a linear system of equations. The system of equations is cast into matrix form and solved using an iterative technique for the unknown expansion coefficients of the fields. Radiation patterns of the antenna are obtained and presented here for the first time.     

改变散射体RCS方向特性的有源加载方法研究

散射体的雷达横截面积(RCS)随着观测角度的不同而发生变化。对高频区的散射体电磁散射特性进行了建模,根据各个散射中心的位置关系和信号入射角度,计算散射体在特定方向上的RCS。提出了集中式和分布式的有源加载方法改变散射体RCS方向特性,通过施放有源干扰信号使散射体在特定方向上的RCS方向图出现凹点。仿真结果表明,该方法可以有效改变散射体的RCS方向特性,在特定方向上实现散射体射频隐身。     

Analysis of electromagnetic scattering from dielectrically coatedconducting cylinders using a multifilament current model

A method of moments solution is presented for the problem of transverse magnetic scattering from dielectrically coated conducting cylinders. The solution uses fictitious filamentary electric sources of yet unknown currents to simulate both the field scattered by the cylinder and the field inside the dielectric coating. The simulated fields obey the boundary conditions, namely, the continuity of the tangential components of the electric and magnetic fields across the air-dielectric interface and the vanishing of the tangential component of the electric field at the perfect conductor, at selected sets of points on these respective surfaces. The result is a matrix equation that is readily solved for the unknown current. The currents can be used to determine approximate values for the fields and field-related parameters of interest. The procedure is simple to implement and is general in that cylinders of smooth but otherwise arbitrary shape and coating of arbitrary complex permittivity can be handled. Illustrative examples are considered and compared with available data, demonstrating the efficiency of the solution     

The theory of functionals of stochastic backscattered fields

The theory of wave scattering by anisotropic statistically rough surfaces, which is an important part of statistical radiophysics, is considered. A new analytic method is developed and generalized for solving problems of radar imaging. The method involves analytic determination of the functionals of stochastic backscattered fields and can be applied to solve a wide class of physical problems with allowance for the finite width of an antenna’s pattern. The unified approach based on this method is used to analyze the generalized frequency response of a scattering radio channel, a generalized correlator of scattered fields, spatial correlation functions of stochastic backscattered fields, frequency coherence functions of stochastic backscattered fields, the coherence band of a spatial-temporal scattering radar channel, the kernel of the generalized uncertainty function, and the measure of noise immunity characterizing radar probing of the Earth’s surface or extended targets. The introduced frequency coherence functions are applied for thorough and consistent study of techniques for measuring the characteristics of a rough surface, aircraft altitude, and distortions observed when radar signals are scattered by statistically rough, including fractal, surfaces. To exemplify urgent applications, radiophysical synthesis of detailed digital reference radar terrain maps and microwave radar images that was proposed earlier is considered and improved with the use of the theory of fractals.