Electromagnetic scattering from composite objects using a mixtureof exact and impedance-boundary conditions

Different surface integral equations for characterizing the electromagnetic scattering from a surface impedance object partially coated with dielectric materials are presented. The impedance boundary condition (IBC) is applied on the impedance surface and the exact boundary condition is applied on the dielectric surface. The resulting integral equations are solved for bodies of revolution using the method of moments. The numerical results are compared with the exact solution for a sphere. Other geometries are considered, and their results are verified by comparing results of the numerical solutions which were obtained using different formulations. The internal resonance problem is examined. It is found that the combined field integral equation (CFIE) can be used at any frequency and with any surface impedance     

Scattering from bodies of revolution

The problem of scattering of a plane electromagnetic wave from an arbitrary metallic body of revolution is solved by a theoretical method for arbitrary incidence and polarization. The method permits numerical computations by high-speed digital computers, and examples are given. The incident wave is expanded in cylindrical modes, and an integral equation is solved for the induced current distribution of each mode. The scattering cross section, including the back-scattering or radar cross section, is found by summation of the mode scattered fields. The method is limited to a maximum perimeter length of twenty wavelengths. While the cases discussed in the paper pertain to perfectly conducting bodies, other surface boundary conditions, an arbitrary surface impedance or coatings by lossy dielectrics, can also be treated with equal precision.     

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.     

非同轴多层介质椭圆柱体的电磁散射—任意方向斜入射电磁波

本文基于椭圆柱谐基函数展开，对非同轴任意多层介质椭圆柱体的电磁散射进行了严格地电磁场分析，利用Ｍａｔｈｉｅｕ函数及其加法定理，在各层边界面上进行场的匹配，获得了任意方面斜入射电磁波下电磁散射解析解。     

Electromagnetic scattering by inhomogeneous dielectric bodies ofrevolution embedded within stratified media

A method of moments (MoM) solution for scattering by heterogeneous bodies of revolution (BOR) embedded within a multilayered environment is given. A modal volume integral equation (VIE) is formulated in the mixed potential form and solved with the use of the specialized basis functions     

Solution of the problem of diffraction by a grating of bodies of revolution with the use of the modified null field method

The 3D problem of scattering by a grating consisting of coaxial impedance bodies of revolution is solved with the help of the modified null field method. A system of integral equations is derived, and numerical results are obtained for the scalar and vector formulations of the problem.     

Analysis of a wire antenna in the presence of a body of revolution

The problem of an arbitrarily oriented thin-wire antenna located near a body of revolution is analyzed. The usual integrodifferential equation for a thin wire in unbounded space is generalized to account for scattering from the nearby body. The presence of the body is accounted for by a numerical dyadic Green's function. The modified wire equation is solved by standard numerical techniques to obtain the current distribution on the wire. The effects of various bodies on input admittance are compared with results for an isolated antenna. Measured and theoretical input admittance data for a monopole near several different bodies of revolution are found to be in good agreement.     

The use of the FFT for the efficient solution of the problem ofelectromagnetic scattering by a body of revolution

The enhancement of the computational efficiency of the body of revolution scattering problem is discussed with a view of making it practical for solving large body problems. The problem of the electromagnetic scattering by a perfectly conducting body is considered, although the methods provided can be extended to multilayered dielectric bodies as well. Typically, the generation of the elements of the moment method matrix consumes a major portion of the computational time. It is shown how this time can be significantly reduced by manipulating the expression for the matrix elements in a manner that allows one to compute them efficiently by using the fast Fourier transform (FFT). A technique for extracting the singularity of the Green's function that appears within the integrands of the matrix diagonal is also presented, further enhancing the usefulness of the FFT. It is shown that, with the use of the method discussed here, the computational time can be improved by at least an order of magnitude for large bodies in comparison to that for previous algorithms     

A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies

A method for calculating the electromagnetic scattering from and internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies is presented. A volume integral equation is formulated and solved by using the method of moments. Tetrahedral volume elements are used to model a scattering body in which the electrical parameters are assumed constant in each tetrahedron. Special basis functions are defined within the tetrahedral volume elements to insure that the normal electric field satisfies the correct jump condition at interfaces between different dielectric media. An approximate Galerkin testing procedure is used, with special care taken to correctly treat the derivatives in the scalar potential term. Calculated internal field distributions and scattering cross sections of dielectric spheres and rods are compared to and found in agreement with other calculations. The accuracy of the fields calculated by using the tetrahedral cell method is found to be comparable to that of cubical cell methods presently used for modeling arbitrarily shaped bodies, while the modeling flexibility is considerably greater.     

Accurate analysis of two-dimensional electromagnetic scattering from multilayered periodic arrays of circular cylinders using lattice sums technique

A very efficient and accurate method to characterize two-dimensional (2-D) electromagnetic scattering from multilayered periodic arrays of parallel circular cylinders is presented, using the lattice sums technique, the aggregate T-matrix algorithm, and the generalized reflection and transmission matrices for a layered system. The method is quite general and applies to various configurations of 2-D periodic arrays. The unit cell of the array can contain two or more cylinders, which may be dielectric, conductor, gyrotropic medium, or their mixture with different sizes. The periodic spacing of cylinders along each array plane should be the same over all layers, but otherwise the cylinders in different layers may be different in material properties and dimensions. The numerical examples validate the usefulness and accuracy of the proposed method.     

Diffraction of the electromagnetic field by bodies of revolution with a chiral coating

A new realization of the modified method of discrete sources is proposed for solving the 3D vector problem of scattering of the electromagnetic field by a body of revolution with a chiral coating. The method is tested for the problem of scattering by a sphere with a dielectric coating. Numerical results are presented for bodies of various geometries.     

A Spectral Integral Method and Hybrid SIM/FEM for Layered Media

This paper first presents a spectral integral method (SIM) for electromagnetic scattering from homogeneous dielectric and perfectly electric conducting objects straddling several layers of a multilayered medium. It then uses this SIM as an exact radiation boundary condition to truncate the computational domain in the finite-element method (FEM) to form a hybrid SIM/FEM, which is applicable to arbitrary inhomogeneous objects. Due to the high accuracy of the SIM, the sampling density on the radiation boundary requires less than five points per wavelength to achieve 1% accuracy. The efficiency and accuracy of the developed methods have been demonstrated with several numerical experiments for the TM_z case. The TE_z case can be obtained by duality     

The null field approach to electromagnetic scattering fromcomposite objects: the case of concavo-convex constituents

Time-harmonic electromagnetic scattering from a composite body consisting of a (dielectric or metallic) core plus one or several dielectric coatings was studied using the null-field approach. Previously developed null-field approaches to scattering from composite bodies do not apply when these coatings are of concavo-convex shapes. The authors examine this case and develop alternative null-field approaches to such geometries. While the scattering problem is usually solved by determination of the total transition matrix, referring to spherical waves, for the composite scatterer, the authors' approaches lead to different algebraic expressions for the transition matrix. Two main alternatives are studied. One of these makes use of Q-matrices for open surfaces while the other is based on a limit procedure applied to a previously developed formalism for layered scatterers. The numerical accuracy of the results is less than that obtained for homogeneous scatterers of similar exterior shape and electrical size. The convergence of the numerical implementation of the equations is studied in terms of several indicators such as dependence on the truncation order, the accuracy with which general constraints such as symmetry and unitarity are fulfilled, and the influence of different choices of expansion functions obtained from a moment-method solution     

Combining an extrapolation technique with the method of moments forsolving large scattering problems involving bodies of revolution

The purpose of this work is to combine an extrapolation technique with the method of moments (MoM) to solve scattering problems involving large bodies. It has been shown in a previous work that the current induced on the smooth parts of large scatterers may be represented as a series of complex exponential functions with a few terms. Based on this concept, a hybrid set of basis functions is constructed using entire domain functions of complex exponential type on the smooth portion of the scatterer, complemented by subdomain basis functions near edges and discontinuities. An extrapolation procedure is developed in which the scattering problem is first solved for a portion of the scatterer using the conventional MoM. Next, a set of entire-domain basis functions, whose behaviour could be extrapolated with an increase in the size of the scatterer, is extracted from this original solution. The procedure outlined has the very desirable feature that the total number of basis functions remains unchanged even as the scatterer size is increased, allowing for large scatterers to be handled with a relatively small number of unknowns. The extrapolation technique is applied to scattering problems from bodies of revolution (BORs), and numerical results for an open cylinder and a barrel-shaped BOR are presented     

Scattering from inhomogeneous penetrable bodies of revolution

A systematic procedure for studying scattering from inhomogeneous penetrable bodies in which the inhomogeneity is modeled by piecewise homogeneous layers, is presented. The procedure utilizes the block tridiagonal property of the system matrix to simplify the computations and is applied to examples of dielectric bodies of revolution. An extension of the technique permits the solution of a composite missile/plume scattering problem.     

Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution

This investigation is concerned with the numerical solution of time-harmonic electromagnetic scattering by axisymmetric penetrable bodies having arbitrary cross-sectional profiles and even continuously inhomogeneous consistency. The initiation of this effort involved the discovery and development of the coupled azimuthal potential (CAP) formulation, which is valid in generally lossy isotropic inhomogeneous rotationally symmetric media. Electromagnetic fields in such regions can be represented, using the CAP formulation, in terms of two continuous potentials which satisfy a self-adjoint system of partial differential equations or, equivalently, a variational criterion. Using an optimized variational finite-element algorithm in conjunction with a triregional unimoment method, a versatile computer program is described that provides scattering solutions for each of multiple incident fields impinging upon an arbitrarily shaped inhomogeneous penetrable body of revolution. An extensive evaluation of the accuracy and convergence of the algorithm is presented, which includes comparison of scattering computations and experimental measurements atX-band for several solid and hollow plexiglas bodies of revolution with maximum interior dimensions of over 4 wavelengths.     

An application of the boundary element method to the magnetic fieldintegral equation

A boundary element method (BEM) for the solution of electromagnetic scattering problems using the magnetic field integral equation (MFIE) is discussed. The discretized form of the MFIE is written in indicial notation with no limitations placed on the order of either the geometric or functional approximation. By considering several different types of boundary elements, it is determined that geometric errors can be significant and degrade the accuracy of the numerical solution. It is shown that a higher-order approximation for the current could significantly improve the accuracy of the numerical solution. The superparametric boundary element in which the geometry was given quadratic approximation and the current was given linear approximation was more efficient than elements using lower-order approximations. The BEM results are compared to the results obtained using the dielectric bodies of revolution (DBR) code     

A potential integral equations method for electromagneticscattering by penetrable bodies

A method for computing the electromagnetic scattering by general inhomogeneous penetrable bodies is presented. The method is based on the volume equivalence principle and it uses the electromagnetic potentials as unknowns. The resulting coupled integral equations system is solved by the method of moments in combination with cubical and curvilinear meshes in the special case of purely dielectric scatterers. To show the accuracy of the method, numerical results of the transmitted and of the scattered fields are compared with existing analytical and experimental results     

Electromagnetic scattering from axially inhomogeneous bodies of revolution

The electromagnetic scattering from partially or totally penetrable bodies of revolution (BOR) is formulated in terms of coupled Fredholm integral equations, solved by the method of moments (MM). The scatterers can have axial inhomogeneities, formed by dissimilar dielectric materials. The case of conducting bodies with axially discontinuous coatings is also treated. The penetrable regions can be lossy, characterized by complex permeability and permittivity. Boundary conditions are rigorously treated everywhere including the intersection of the various regions. The solutions are expressed in terms of combinations of two special matrices arising from the Galerkin technique. These solutions are implemented numerically for a class of generic axially inhomogeneous BOR scatterers. Numerical results given for various conducting/dielectric cylinder combinations using this formulation are compared with experimental data. For special cases where comparisons are possible, the present analysis replicates the results of the Mie theory.     

Full-wave analysis of microwave scattering from short vegetation: an investigation on the effect of multiple scattering

A full-wave solution for polarimetric scattering from a cluster of randomly oriented three-dimensional lossy dielectric structures above an impedance surface is presented to investigate the importance of multiple scattering. The problem is formulated using an integral equation in conjunction with the exact image representation of dyadic Green's function for the half-space problem. Then, the integral equation is solved for the induced equivalent polarization currents using the method of moments. The accuracy of the numerical code is verified using other existing numerical results and experimental observations. The model is then used to examine the effect of multiple scattering among a cluster of relatively short stems and is shown that multiple scattering significantly affects the cross-polarized backscatter whereas it has a moderate effect on the copolarized backscattering depending on the stem density.