Electromagnetic radiation and scattering from finite conducting anddielectric structures: surface/surface formulation

An efficient and accurate numerical procedure for the analysis of the electromagnetic scattering and radiation from arbitrarily shaped, composite finite conducting and dielectric bodies is proposed. A set of coupled electric field integral equations involving surface equivalent electric and magnetic currents is used. The coupled integral equations are solved through planar triangular patch modeling and the method of moments. Two separate, mutually orthogonal vector functions for each edge connecting a pair of triangular patches have been developed. Numerical results for disk/cone and cylinder/cone structures are compared with other available data. Limited comparison with experimental data has also been made     

Analysis of transient scattering from composite arbitrarily shapedcomplex structures

A time-domain surface integral equation approach based on the electric field formulation is utilized to calculate the transient scattering from both conducting and dielectric bodies consisting of arbitrarily shaped complex structures. The solution method is based on the method of moments (MoM) and involves the modeling of an arbitrarily shaped structure in conjunction with the triangular patch basis functions. An implicit method is described to solve the coupled integral equations derived utilizing the equivalence principle directly in the time domain. The usual late-time instabilities associated with the time-domain integral equations are avoided by using an implicit scheme. Detailed mathematical steps are included along with representative numerical results     

Analytical and numerical solution to the two-potentialZakharov-Shabat inverse scattering problem

An analytical and a numerical method are presented in order to solve the inverse scattering problem associated with the two-potential Zakharov-Shabat coupled mode equations. The numerical solution, which uses leapfrogging in space and time, represents a direct numerical solution to the coupled Gel'fand-Levitan-Marchenko (GLM) integral equations as an extension of the authors' previous work on GLM equations of simpler form. The analytical method, which is applied for one-pole reflection coefficients, consists in constructing appropriate differential operators which transform the coupled GLM equations to ordinary linear differential equations. An application of these methods for nonuniform transmission line synthesis is presented     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

Analysis of an aperture coupled microstrip antenna

A microstrip patch antenna that is coupled to a microstripline by an aperture in the intervening ground plane is analyzed. Coupled integral equations are formulated by using the Green's functions for grounded dielectric slabs so that the analysis includes all coupling effects and the radiation and surface wave effects of both substrates. A Galerkin moment method solution of the coupled integral equations agrees quite well with measured data. Design data are contained in parameter studies, many of which are verified by experimental results.     

Waveguide excited microstrip patch antenna-theory and experiment

An arbitrarily shaped microstrip patch antenna excited through an arbitrarily shaped aperture in the mouth of a rectangular waveguide is investigated theoretically and experimentally. The metallic patch resides on a dielectric substrate grounded by the waveguide flange and may be covered by a dielectric superstrate. The substrate (and superstrate, if present) consists of one or more planar, homogeneous layers, which may exhibit uniaxial anisotropy. The analysis is based on the space domain integral equation approach. More specifically, the Green's functions for the layered medium and the waveguide are used to formulate a coupled set of integral equations for the patch current and the aperture electric field. The layered medium Green's function is expressed in terms of Sommerfeld-type integrals and the waveguide Green's function in terms of Floquet series, which are both accelerated to reduce the computational effort. The coupled integral equations are solved by the method of moments using vector basis functions defined over triangular subdomains. The dominant mode reflection coefficient in the waveguide and the far-field radiation patterns are then found from the computed aperture field and patch current distributions. The radar cross section (RCS) of a plane-wave excited structure is obtained in a like manner. Sample numerical results are presented and are found to be in good agreement with measurements and with published data     

Rigorous Full-Wave Analysis of Rectangular Microstrip Patch Antenna on Suspended and Composite Substrates

In this paper, Galerkin’s method in the Fourier transform domain is applied to the determination of the resonant frequencies and half-power bandwidth of rectangular microstrip patch on composite and suspended substrates. Using Galerkin’s method in solving the integral equation numerically, the complex resonant frequency of the microstrip antenna on suspended and composite substrates is studied with sinusoidal functions as basis functions, which show fast numerical convergence. The validity of the solution is tested by comparison of the computed results with experimental data. Finally, numerical results for the effects of suspended and composite substrates on the resonant frequency and half-power bandwidth are also presented.     

Hybrid numerical method for harmonic 3-D Maxwell equations:scattering by a mixed conducting and inhomogeneous anisotropicdielectric medium

This article deals with a hybrid numerical method for solving harmonic Maxwell equations in the classical electrodynamic context. This formulation can be used with any body of arbitrary three-dimensional geometry, of perfectly conducting material or dielectric, with locally inhomogeneous and anisotropic behavior laws, and with or without dielectric losses. The mathematical formulation is presented along with applications validating it. The exterior problem is treated by the integral equation method while local equations are used for the dielectric parts of the body. A global variational formulation of the coupled problem is developed for use in discretization by the finite element method. Boundary finite elements are used for integral operators connected with the exterior problem. Localized finite elements are used for the interior problem. Difficulties of irregular frequencies, also called resonant frequencies in the perfectly conducting case, arising from the integral formulation are analyzed in detail and an efficient solution is developed     

Self-consistent solution of the diffusion and current spreading problems in oxide stripe lasers using integral equations: An application to triple lasers

The problem of current spreading and diffusion in oxide stripe lasers leads to two coupled boundary value problems. This paper presents an efficient method for the simultaneous solution of these two problems based on the conversion of the two-dimensional Laplace equation representing the current spreading into integral equations by means of a contour integral. The power of the method is illustrated by its application to a coupled triple-stripe laser. Highlights of the numerical method are discussed.     

Coupling by slots in rectangular waveguides with arbitrary wall thickness

A method for evaluating the coupling between two rectangular waveguides, coupled by a slot of arbitrary dimensions in a wall of arbitrary thickness is described. The method is based on the solution, by numerical techniques, of a pair of coupled integral equations. Results for typical shunt and series slots are presented.     

Moment method with isoparametric elements for three-dimensionalanisotropic scatterers

A new method for computing the frequency-domain electromagnetic fields scattered from, and penetrating into, arbitrarily shaped, three-dimensional, lossy, inhomogeneous anisotropic scatterers is presented. The method is based on a general volume integro-differential formulation of the scattering problem, and consists of the numerical solution of the coupled integral equations by the moment method and point matching. A particularly powerful feature of this method is that the numerical model of the scatterer is obtained by parametric volume elements and the basis functions used to represent the field within each element are the same used in the finite-element method. Element integration problems due to the singular kernel of the integral equations are treated in some detail. Numerical results for both the isotropic and the anisotropic spherical scatterer are presented, including comparisons with results obtained by different numerical methods for the isotropic cases considered. The capability of the numerical code presented here to deal with cases where the material parameters of the scatterer are given by singular matrices is discussed for two particular examples     

Generalized formulations for electromagnetic scattering fromperfectly conducting and homogeneous material bodies-theory andnumerical solution

A generalized E-field formulation for three-dimensional scattering from perfectly conducting bodies and generalized coupled operator equations for three-dimensional scattering from material bodies are introduced. A fictitious electric current flowing on a mathematical surface enclosed inside the body is used to simulate the scattered field, and, in the material case, a fictitious electric current flowing on a mathematical surface enclosing the body is used to simulate the diffracted field inside the body. Application of the respective boundary conditions lead to operator equations to be solved for the unknown fictitious currents, which facilitates calculation of the fields in the various regions, using the magnetic vector potential integral. The existence and uniqueness of the solution are discussed. These alternative operator equations are solvable using the method of moments. The numerical solution is simple to execute, rapidly converging, and general in that bodies of smooth but otherwise arbitrary surface, both lossless and lossy, can be handled effectively. Comparison of the results with available analytic solutions demonstrates the accuracy of the moment procedure     

Numerical analysis and validation of the combined field surfaceintegral equations for electromagnetic scattering by arbitrary shapedtwo-dimensional anisotropic objects

The numerical solution of coupled integral equations for arbitrarily shaped two-dimensional, homogeneous anisotropic scatterers is presented. The combined theoretical and numerical approach utilized in the solution of the integral equations is based on the combined field formulation and is specialized to both transverse electric (TE) and transverse magnetic (TM) polarizations. As opposed to the currently available methods for anisotropic scatterers, the present approach involves integration over the surface of the scatterer in order to determine the unknown surface electric and magnetic current distributions. The solution is facilitated by developing a numerical approach employing the method of moments. The various difficulties involved in the numerical effort are pointed out, and ways of overcoming them are discussed in detail. The results obtained for two canonical anisotropic structures, namely, a circular cylinder and a square cylinder, are given and validated by results obtained by alternative methods     

Scattering by Conducting Bodies Coated With Bi-Isotropic Materials

Electromagnetic scattering by arbitrarily shaped conducting bodies coated with general bi-isotropic materials is formulated in terms of the surface integral equation method. In order to facilitate the implementation of the surface equivalence principle, a field decomposition scheme is utilized to split a bi-isotropic media into two equivalent isotropic media. By enforcing the boundary condition on the interfaces of the body, a set of coupled integral equations is finally obtained for the unknown surface currents and then numerically solved using the moment methods combined with the vector triangular basis function. The fast multipole technique has been embedded into the algorithm to accelerate the solution process. The validity of theoretical formulations is verified by numerical results and their comparisons. The calculated results for bi-isotropically coated conducting spheres and oblate spheroids are compared with the exact solution and the existing data, and excellent agreements are observed.     

An efficient method for the analysis of a structure comprising an appendage attached to a planar surface of a conducting body

A technique is presented to efficiently solve for the currents on an appendage, e.g., antenna, attached to a planar surface of a conducting body. The appendage may be embedded in a homogeneous, dielectric material. The technique presented alleviates the complications associated with the point where the appendage is attached to the body. To illustrate the method, a wire antenna attached to an axisymmetric body is analyzed in detail. A set of coupled integral equations are formulated, appropriate quantities are expanded into Fourier modes, and coupled integral equations are derived for the Fourier coefficients of the unknowns. These equations are solved and the input admittance of the wire antenna is determined from the computed currents and is corroborated by measurements.     

Scattering from a perfectly conducting surface with a sinusoidal height profile: TE polarization

A method for the analysis of scattering from periodic structures based on the numerical solution of the integral equations is further developed. Using periodicity (Floquet's theorem), the range of the integral equations is reduced to a single period where the kernels are the Green's functions for periodic arrays. The numerical solution of the integral equations is obtained using the method of moments. Efficient numerical methods for the computation of the periodic Green's functions which allows their rapid evaluation with good accuracy are reported. A new treatment of the singularities which includes the effect of the surface curvature is given. Numerical results for the transverse electric scattering from a conducting surface with a sinusoidal height profile are presented, and several interesting physical phenomena are explored including Brewster angle effects and diffraction grating anomalies.     

Volume integral equations for analysis of dielectric branchingwaveguides

Novel forms of volume integral equations are developed for the exact treatment of wave propagation in two-dimensional dielectric branching waveguides. The integral equations can be obtained by considering the condition at a point far away from the junction section. An approximate solution by the Born approximation and a numerical solution by the moment method establish the validity of the new volume integral equations. The numerical results are discussed from the viewpoint of energy conservation and reciprocity. The solution is exact if sufficiently large computer memory and computational time are used. The method can be extended to problems of a more general nature (i.e. the incident TM mode), and complex configurations of branching waveguides. The basic idea is also applicable to techniques using boundary (surface) integral equations which are applicable to three-dimensional problems     

位积分方程组矩量法用于精确计算非均匀介质柱的电磁散射

位积分方程组的主要特点是以电磁位为未知函数,这些未知函数在具有不同电磁参数的介质分界面处是连续的,因而在矩量法的实现过程中能够非常方便地应用高阶插值基函数来展开未知函数,以便获得高精度的解。但是,经典的点匹配方案使该模型的数值稳定性较差。本文用位积分方程组矩量法模型计算任意截面非均匀介质柱的电磁散射,采用三角形离散方案和高阶插值基函数,在测试过程中应用新提出的测试方法,克服了原位方程组矩量法模型的数值不稳定性。对矩量法矩阵中自阻抗元素的奇异性处理方法也作了详细介绍。文中提供的数值结果表明,该方法是精确、稳定的。     

基于近区后向散射场幅度的二维导体目标的逆散射

本文给出了一种改进的基于多方向多入射频率的平均波照射下的近区散射场度测量值反演导体目标轮廓的逆散射场的幅度值反演导体目标轮廓的逆散射方法。     

Electromagnetic analysis of an antenna embedded in a compositeenvironment

This paper addresses the problem of an antenna embedded in a hole dug in the ground. The composite medium configuration consists of a half-space dielectric (representing the Earth-air interface) containing a cylindrical hole filled with a different dielectric medium. The wire antenna resides within this hole, on the axis. The solution strategy is based on decomposing the problem into simpler subproblems, which are treated sequentially. First we calculate a numerical dyadic Green's function for the composite medium by solving an integral equation formulated over a background consisting of the unperturbed dielectric half space (for which the Green's functions are known in a spectral integral form). This integral equation is solved via the fictitious currents method, which is a special case of the method of moments. We then solve the integral equation for the antenna currents using this numerical Green's function and determine the input impedance and radiation pattern