Electromagnetic scattering by multiple three-dimensional scatterersburied under multilayered media. II. Numerical implementations andresults

For pt.I see ibid., vol.36, no.2, p.526-34 (1998). In part I of this paper, coupled electric-field integral equations for dielectric objects, conducting objects, and multiple dielectric and/or conducting objects were derived when they were buried under one-dimensional (1D) multilayered media. In part II of this paper, numerical implementations for these integral equations are developed by use of the method of moments, in which the “self-actions” in the method are treated special because of the presence of singularity. Sample numerical results are presented for several cases of interest, which show the validity of the scheme     

Scattering by an arbitrary cylinder at a plane interface: broadsideincidence

The problem of the determination of the fields scattered by an infinite dielectric cylinder of arbitrary cross section located at the interface between two semi-finite dielectric media is reduced to the solution of integral equations for unknown functions defined on the boundaries. These boundary functions are chosen so as to minimize their number. The incident field is that of a plane monochromatic wave. The derivation of the integral equations is given for the transverse electric (TE) mode for a dielectric cylinder and for a perfectly conducting cylinder. The exact electromagnetic fields are obtained from the solutions of the integral equations by integration, and the radar cross section can be computed from the far-field approximation. Sample outputs of the computer programs that implement this solution are shown     

Three-dimensional subsurface analysis of electromagnetic scatteringfrom penetrable/PEC objects buried under rough surfaces: use of thesteepest descent fast multipole method

The electromagnetic scattering from a three-dimensional (3D) shallow object buried under a two-dimensional (2D) random rough dielectric surface is analyzed. The buried object can be a perfect electric conductor (PEC) or can be a penetrable dielectric with size and burial depth comparable to the free-space wavelength. The random rough ground surface is characterized with Gaussian statistics for surface height and for surface autocorrelation function. The Poggio, Miller, Chang, Harrington, and Wu (PMCHW) integral equations are implemented and extended. The integral equation-based steepest descent fast multipole method (SDFMM), that was originally developed at UIUC, has been used and the computer code based on this algorithm has been successfully modified to handle the current application. The significant potential of the SDFMM code is that it calculates the unknown moment method surface electric and magnetic currents on the scatterer in a dramatically fast, efficient, and accurate manner. Interactions between the rough surface interface and the buried object are fully taken into account with this new formulation. Ten incident Gaussian beams with the same elevation angle and different azimuth angles are generated for excitation as one possible way of having multiple views of a given target. The scattered electric fields due to these ten incident beams are calculated in the near zone and their complex vector average over the multiple views is computed. The target signature is obtained by subtracting the electric fields scattered from the rough ground only from those scattered from the ground with the hurled anti-personnel mine     

An FDTD near- to far-zone transformation for scatterers buried instratified grounds

The finite-difference time-domain (EDTD) technique is being used with increasing frequency for modeling the scattering characteristics of buried objects. The FDTD has, for some time, been able to model the near-zone scattered fields of buried objects due to near-zone sources. This is adequate for modeling the scattered returns of ground-based ground-penetrating radar, but not for airborne radar. This paper describes an FDTD-compatible technique whereby far-zone scattered fields of objects buried in a stratified ground can be calculated. This technique uses the equivalence principle to model a buried object in terms of equivalent electric and magnetic currents. The fields radiated by these currents in the presence of a stratified ground are then calculated using the reciprocity theorem and the well-known field equations for plane waves in a stratified media. Numerical results are presented that show excellent agreement between this technique and both analytical and numerical results     

TE scattering by partially buried and coupled cylinders at theinterface between two media

The scattering of transverse electric (TE) illumination by partially buried conducting cylinders and by coupled conducting cylinders in two media is studied. The conducting cylinders are of general cross section and of infinite extent. Data depicting far-zone scattered fields for various cylinders and media parameters of interest are presented, and the highly lobate patterns which differ significantly from those due to cylinders in homogeneous space are discussed and explained     

Electromagnetic scattering and radiation by surfaces of arbitraryshape in layered media. I. Theory

An accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed. The key step in this procedure is a formulation of the so-called mixed-potential electric field integral equation (MPIE) that is amenable to an existing advanced solution technique developed for objects in free space and that employs the method of moments in conjunction with a triangular-patch model of the arbitrary surface. Hence, the goal is to immediately increase analysis capabilities in electromagnetics, yet remain compatible with the large existing base of knowledge concerning the solution of surface integral equations. Three alternative forms of the MPIE in plane-stratified media are developed, and their properties are discussed. One of the developed MPIEs is used to analyze scatterers and antennas of arbitrary shape that penetrate the interface between contiguous dielectric half-spaces     

Single integral equation for electromagnetic scattering bythree-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation     

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.     

两媒质半空间复杂形体电磁散射

本文利用矢量波函数变换方法讨论了两媒质半空间的电磁散射问题，从Ｍａｘｗｅｌｌ方程出发，讨论了单矩法在三维复杂形体散射问题上的实施。并在数学球面上将内部区域的有限元解与外部区域矢量波函数变换的结果相匹配，从而得到复杂埋入体的电磁散射特性。作为检验和示例，本文计算了在平面波照射下自由空间导体球，埋入导体球，埋入介质覆盖钝锥等的散射场，其中一些结果与可供比较的经典解或其它算法的结果进行了比较，吻合较好。     

RCS of two-dimensional structures consisting of both dielectricsand conductors of arbitrary cross section

The problem of determining the electromagnetic field scattered by two-dimensional structures consisting of both dielectric and conducting cylinders of arbitrary cross section is considered. The conductors may be in the form of strips and the dielectrics may be in the form of shells. The conductors may be partially or fully covered by dielectric layers, while the dielectrics may be partially covered by conductors. Only homogeneous dielectrics are studied. Both the transverse electric (TE) and the transverse magnetic (TM) cases are considered. The problem is formulated in terms of a set of coupled integral equations involving equivalent electric and magnetic surface currents radiating in unbounded media. The method of moments is used to solve the integral equations. Simple expansion and testing procedures are used. Numerical results for scattering cross sections are given for various structures     

TM scattering by an impedance sheet extension of a paraboliccylinder

An integral equation and method of moments (MM) solution are presented for the two-dimensional (2-D) problem of transverse magnetic (TM) scattering by an impedance-sheet extension of a perfectly conducting parabolic cylinder. An integral equation is formulated for a dielectric cylinder of general cross section in the presence of a perfectly conducting parabolic cylinder. It is then shown that the solution for a general dielectric cylinder considerably simplifies for the special case of TM scattering by a thin multilayered dielectric strip that can be represented as an impedance sheet. The solution is termed an MM/Green's function solution, where the unknowns in the integral equation are the electric surface currents flowing in the impedance sheet; the presence of the parabolic cylinder is accounted for by including its Green's function in the kernel of the integral equation. The MM solution is briefly reviewed, and expressions for the elements in the matrix equation and the scattered fields are given. Sample numerical results are provided     

Current induced by TE excitation on coupled and partially buriedcylinders at the interface between two media

An analysis is described for determining the current induced by transverse electric (TE) excitation on coupled conducting cylinders near the planar interface separating two semi-infinite homogeneous half-spaces of different electromagnetic properties and on partially buried conducting cylinders. The conducting cylinders, of general cross section, are of infinite extent and the excitation is transverse electric to the cylinder axes. Coupled integral equations for the currents induced on the cylinders are formulated and numerical methods for solving them are presented. Data showing the induced current distribution for various cylinders and media parameters of interest are presented and discussed. Relative to the homogeneous space case, the presence of the two media significantly alters the current distribution, especially near the interface     

Comparison of Integral-Equation Formulations for the Fast and Accurate Solution of Scattering Problems Involving Dielectric Objects with the Multilevel Fast Multipole Algorithm

We consider fast and accurate solutions of scattering problems involving increasingly large dielectric objects formulated by surface integral equations. We compare various formulations when the objects are discretized with Rao-Wilton-Glisson functions, and the resulting matrix equations are solved iteratively by employing the multilevel fast multipole algorithm (MLFMA). For large problems, we show that a combined-field formulation, namely, the electric and magnetic current combined-field integral equation (JMCFIE), requires fewer iterations than other formulations within the context of MLFMA. In addition to its efficiency, JMCFIE is also more accurate than the normal formulations and becomes preferable, especially when the problems cannot be solved easily with the tangential formulations.      

Stabilization of Integral-Equation Formulations for the Accurate Solution of Scattering Problems Involving Low-Contrast Dielectric Objects

The solution of scattering problems involving low-contrast dielectric objects with three-dimensional arbitrary shapes is considered. Using the traditional forms of the surface integral equations, scattered fields cannot be calculated accurately if the contrast of the object is low. Therefore, we consider the stabilization of the formulations by extracting the nonradiating parts of the equivalent currents. We also investigate various types of stable formulations and show that accuracy can be improved systematically by eliminating the identity terms from the integral-equation kernels. Traditional and stable formulations are compared, not only for small scatterers but also for relatively large problems solved by employing the multilevel fast multipole algorithm. Stable and accurate solutions of dielectric contrasts as low as 10^-4 are demonstrated on problems involving more than 250000 unknowns.     

Method of radar detection and identification of metal and dielectric objects with resonant sizes located in dielectric medium

Mathematical model of a radar detection and identification system to be used for finding different objects buried in the ground or in other dielectric media is considered. In the suggested model scattering characteristics of 3D resonant objects are calculated by solving 2nd kind Fredholm integral equations for equivalent current densities on the object??s surface. Based on the obtained results we derive a method of detection and identification for specific types of objects which incorporates analysis of their natural resonant frequencies. Potentialities of the developed method for detection and identification of different types of mines are estimated.     

Scattering by arbitrarily cross-sectioned layered, lossy dielectric cylinders

The scattering properties of TM or TE illuminated lossy dielectric cylinders of arbitrary cross section are analyzed by the surface integral equation techniques. The surface integral equations are formulated via Maxwell's equations, Green's theorem, and the boundary conditions. The unknown surface fields on the boundaries are then calculated by flat-pulse expansion and point matching. Once the surface fields are found, scattered field in the far-zone and radar cross section (RCS) are readily determined. RCS thus obtained for circular homogeneous dielectric cylinders and dielectric coated conducting cylinders are found to have excellent agreements with the exact eigenfunction expansion results. Extension to arbitrary cross-sectioned cylinders are also obtained for homogeneous lossy elliptical cylinders and wedge-semicircle cross-sectioned cylinders, with and without a conducting cylinder in its center. RCS dependences on frequency and conductivity as well as the matrix stability problem of this surface integral equation method are also examined.     

A numerical solution to full-vector electromagnetic scattering bythree-dimensional nonlinear bounded dielectrics

This paper deals with electromagnetic scattering by nonlinear dielectric objects. In particular, a numerical approach is developed that is aimed at determining the distributions of the electromagnetic field vector inside a three-dimensional nonlinear, inhomogeneous, isotropic scatterer illuminated by a time-periodic incident electric field vector. An integral-equation formulation for the full-vector scattering problem is considered, and the nonlinear effect is taken into account by introducing equivalent sources and a Fourier-series representation. A system of integral equations (for each harmonic vector component and for the static term) is obtained that includes the internal electric field distribution as the unknown. After discretization, the solution is reduced to solving an algebraic system of nonlinear equations. Some preliminary numerical results are reported concerning scatterers that exhibit a specific (quadratic) dependence of the dielectric permittivity on the total electric field. The harmonic components of the scattered electric field outside the objects are also computed     

Transmission through dielectric-filled slots in a conductingcylindrical shell of arbitrary cross section: TE case

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory     

Procedures for noninvasive electromagnetic property and dosimetrymeasurements

Five different formulations are presented that can be used to determine local values of the complex permittivity, electric field, polarization current density, and rate of energy deposition, within an inhomogeneous dielectric object of arbitrary shape. These formulations were obtained from the matrix equations for moment-method solutions of the electric field integral equation. Implementation of these formulations requires knowledge of the shape of the object and the incident electric field, and measurements of the scattered electric field at a number of points external to the object. The use of a new type of model, with antenna arrays for measurements, has caused a substantial improvement in matrix conditioning. Results of numerical simulations using 21-cell models with high dielectric contrast (bone/muscle) suggest that all five formulations have sufficient accuracy to warrant experimental testing using cylindrical scatterers with transverse magnetic polarization     

粗糙海面上三维金属目标的电磁散射特性分析

该文采用矩量法(MoM)计算粗糙海面上三维金属目标的电磁散射特性。计算了位于半空间媒质中的电偶极子和磁偶极子的矢量位并矢格林函数和标量位格林函数,并将其应用于矩量法中。把海水视为下半空间媒质,粗糙海面为位于上半空间中的介质表面。通过建立介质和金属混合目标的积分方程,并采用迭代方法求解矩阵方程以得到该模型的散射特性,数值结果验证了本文方法的有效性。