Scattering by an infinite array of multiple parallel strips

The transverse electric (TE) and transverse magnetic (TM) electromagnetic scattering solutions for an infinite array of multiple parallel strips are considered. The solution is found using the perturbational form of the modified residue calculus technique (MRCT). In particular, the solution is found from the canonical problem of an infinite periodic array of semi-infinite parallel plates. Numerical results are presented and discussed. In addition, numerical results are given for a polarizer application.     

Plane wave scattering by a material coated parabolic cylinder

An eigenfunction solution to the problem of transverse magnetic (TM) or transverse electric (TE) scattering by a coated parabolic cylinder is presented. Paralleling the well-known solution for the coated circular cylinder, eigenfunction expansions involving parabolic cylinder functions are obtained for the fields in the exterior and coating regions. Next, boundary conditions are enforced to obtain a pair of coupled equations for the unknown coefficients in the eigenfunction expansions for the fields. Unlike the corresponding solution for the coated circular cylinder, the eigenfunctions in the exterior and coating regions are not orthogonal, and an exact term-by-term solutions of these equations is not possible. Instead, the equations are solved by the method of moments. For thin coatings both an uncoupled-mode approximation and a surface-impedance model are described. In particular, for the TM polarization it is shown that a thin coating can be modeled by a specific nonuniform surface impedance for which an exact term-by-term solution is possible. Numerical data are presented, showing the convergence of the solution and comparing the solutions for the uncoupled-mode and surface-impedance models     

Scattering by a dielectric-loaded nonplanar slit-TM case

An exact series solution for the problem of transverse magnetic (TM) wave scattering by a dielectric-loaded nonplanar slit is presented. Some numerical results are shown and compared with those of exact solutions     

Mixed-domain Galerkin expansions in scattering problems

Entire-domain Galerkin expansions provide a computationally efficient representation in method-of-moments (MM) solutions for electrically extended surfaces forming part of a separable coordinate geometry. For surfaces not conforming to such geometries, such as those with discontinuities, subdomain representations have been used. For many classes of scattering problems involving electrically large two-dimensional scatterers with localized discontinuities, a mixed-domain Galerkin expansion is shown to lead to a computationally efficient formulation. Electromagnetic-scattering solutions are developed for such configurations. Convergence of these solutions is illustrated with choices of mixed-domain expansions as a function of surface discontinuity. The computed results are given for both transverse magnetic (TM) and transverse electric (TE) polarization and are compared with published results     

Electromagnetic scattering from extended wires and two- and three-dimensional surfaces

Efficient numerical solutions for the electromagnetic scattering for classes of electrically large one-, two-, and three-dimensional perfectly conducting scatterers are presented. The formulation is based on solution of the electric field integral equation (EFIE) using the method of moments (MM). An entire domain Galerkin representation is used for wires and two-dimensional surfaces and a combination of entire and subdomain representations is applied to surfaces in three dimensions. The analysis is extendable to corrugated surfaces formed from sections of surfaces of translation or rotation. Numerical results are presented for wires, infinite strips, and finite strips (or plates). The behavior of the solutions with the number of terms in the entire domain expansion is examined. The reconstruction of the traveling-wave contribution to the scattering cross section using various approximations is discussed, and representative examples are given.     

A waveguide transverse slot for array applications

The characteristics of a radiating rectangular transverse slot in a rectangular waveguide have been studied. A moment method solution is used with entire basis expansion and testing functions (Galerkin) including the effect of wall thickness. The results are presented in terms of normalized resistance and reactance versus slot length and frequency. Excellent agreement with a previous pulse basis solution is found, as well as with measured data. An array of resonantly spaced transverse slots radiates large grating lobes. A spatial filter using baffles to suppress the grating lobes is described, suppressed. The effect of the baffles on the transverse slot impedance is analyzed for the case of baffles with infinite height     

A method of moments analysis of electromagnetic coupling throughslots using a Gaussian beam expansion

A moment solution is presented for the problem of transverse electric (to the slot axis) electromagnetic coupling through a slot in infinitesimally thin, perfectly conducting screen separating two identical or contrasting half-space regions. The moment solution uses sets of properly shifted and modulated Gaussian elementary beams to expand the unknown equivalent magnetic current and a simple point-matching procedure for testing. The Gaussian expansion offers a numerical advantage in subsequent field calculations. Instead of integrating over surface currents when computing the fields, the proposed expansion allows the evaluation of the fields by summations of analytic terms exploiting the simple and well-understood propagation features of Gaussian beams. Sample computations are given and compared with a standard pulse-pulse Galerkin solution     

时域非连续伽辽金法在谐振腔中的应用

给出了时域非连续伽辽金(Discontinuous Galerkin Time Domain, DGTD)法的基本思想, 从Maxwell方程出发得到弱解形式和矩阵方程, 进一步给出了DGTD步进计算式.计算了空腔和填充谐振腔的谐振频率, 并与解析结果相比较.算例表明在谐振腔计算中DGTD可以达到很高的精度.     

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     

Phased arrays of probe-fed stacked microstrip patches

This paper presents calculated and measured results for infinite phased arrays of probe-fed stacked rectangular and circular microstrip patches. A numerical model is described that is based on a rigorous Green's function/Galerkin solution. In this solution, the connection of one or more vertical probe feeds to each patch is accurately modeled using a special attachment mode basis function, which is derived from the corresponding cavity model solution. Numerical results for both linearly and circularly polarized arrays are obtained. Measured results from a waveguide simulator are also presented and used to validate the numerical model     

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.     

A multiresolution study of two-dimensional scattering by metalliccylinders

The application of wavelet transforms in method of moments (MoM) solutions for scattering problems is extended to cases involving metallic cylinders whose periphery contains a variety of length-scale features ranging from smoothly varying large-scale features (characterized by a radius of curvature of several wavelengths) to rapidly varying small scale ones (characterized by a radius of curvature that is small compared with the wavelength). The basic idea is to first consider a periodic extension of the equivalent current in the arc-length variable with a period identical to the scatterer circumference, and then to expand this representation using a set of periodic wavelets derived from a conventional basis of wavelets by a periodic extension. Using a Galerkin method and subsequently applying a threshold operation, a substantial reduction in the number of elements of the moment-method matrix is attained without virtually affecting the solution accuracy. The proposed extension is illustrated by a numerical analysis of TM (transverse magnetic) and TE (transverse electric) scattering from a cylinder of elliptic cross section. A thorough study is carried out showing how the solution accuracy improves with increasing resolution level, and how this accuracy is affected by a thresholding process which renders the moment matrix sparsely populated     

Wave tilt sounding of a linearly inhomogeneous layered half-space

The wave tilt of a transverse electric (TE) electromagnetic wave over a linearly inhomogeneous lossy layer overlying a homogeneous half-space is studied. Two approaches are used: an exact formulation using solutions of Airy's equation and an approximate numerical solution using a large number of homogeneous layers with a linearly increasing dielectric constant. The numerical results of both solutions are practically identical as long as the thickness of the layers in the approximate model are somewhat smaller than a quarter-wavelength.     

Galerkin solution for the thin circular iris in aTE11-mode circular waveguide

An integral equation for the transverse electric (TE) field in the aperture of a concentric circular iris in a transverse plane of a circular waveguide is approximately solved using Galerkin's method. The aperture field is represented by a finite sum of normal TE and TM (transverse magnetic) circular waveguide modes that fit the circular aperture. The numerical convergence of the Galerkin solution is demonstrated using the resultant aperture field distributions and equivalent shunt susceptance for the case of dominant TE₁₁-mode excitation. The resultant aperture electric field distribution closely resembles that of the TE₁₁ aperture mode alone, except for edge contribution behavior at the edge of the iris. A resonant or capacitive iris is possible over a restricted range of frequencies     

Plane wave scattering by a conducting elliptic cylinder coated by anonconfocal dielectric

The scattering properties of a dielectric-coated nonconfocal conducting elliptic cylinder are investigated. The theoretical treatment of such a problem is based on the boundary value solution, which is an exact treatment of the problem. Only the transverse magnetic (TM) case is considered, although the transverse electric (TE) case can be treated in the same way. It is shown that this solution is much more general than all previous solutions because it can handle a variety of scattering geometries. Numerical results are presented in graphical form for the echo width pattern of various geometries     

Hybrid solutions for large-impedance coated bodies of revolution

Electromagnetic scattering solutions are developed for coated perfectly conducting bodies of revolution (BOR) that satisfy the impedance boundary condition. The integral equation arising from the impedance (Leontovich) boundary condition is solved by use of the method of moments (MM) technique along with an Ansatz for the surface currents that is derived from physical optics (PO) and the Fock theory that is modified for imperfectly conducting surfaces. The MM solution is expressed in terms of two integral (Galerkin) operators. The form of the Galerkin expansion used results in a symmetric MM system matrix. The hybrid solution is specialized for BOR's although the approach is applicable to a broader class of scatterers as well. The results are compared with the Mie solution for penetrable spherical scatterers, which satisfy the impedance boundary condition, and with recently published MM solutions for nonspherical scatterers.     

A hybrid equation approach for the solution of electromagneticscattering problems involving two-dimensional inhomogeneous dielectriccylinders

A numerical procedure for the solution of electromagnetic scattering problems involving inhomogeneous dielectric cylinders of arbitrary cross section is discussed. The cases of illumination by both transverse magnetic (TM) and transverse electric (TE) plane waves are considered. The scattering problems are modeled via a hybrid integral-equation/partial-differential-equation approach. The method of moments is applied to obtain a system of simultaneous equations that can be solved for the unknown surface current densities and the interior electric field. The interior region partial differential equation and the exterior region surface integral equation are coupled in such a manner that many existing surface integral equation computer codes for treating problems involving scattering by homogeneous dielectric cylinders can be modified easily to generate the block of the matrix corresponding to the surface current interactions. The overall system matrix obtained using the method of moments is largely sparse. Numerical results are presented and compared with exact solutions for homogeneous and inhomogeneous circular cylinders     

Modeling of arbitrary wire antennas above ground

An efficient method for modeling wire antennas of arbitrary shapes and orientations above a lossy ground is presented by using Galerkin method. As opposed to the traditional point matching method, careful treatment is required for the electric-field integral equation (EFIE) and its numerical implementation. Comparing with the point matching method, only three simple Sommerfeld integrals are needed in the new method, and the convergence is much faster. To test the validity of this method, numerous numerical examples are given. Numerical results show that, for equivalent-accuracy solutions, the cell number used in this method is much fewer than that in the point matching method     

A reflection factors oriented spectral domain approach for pole-free integrals and its application to multilayered microstrip line

An alternative formulation of the spectral domain approach (SDA) method is presented for multilayered microstrip line Green's function derivation. The method relies on reflection factors rather than the transverse impedance used in the immittance approach. The inner products involved in the Galerkin procedure are pole-free. The analysis is validated by comparing the results with a specific example in the literature.     

Scattering from conductors coated with materials of arbitrarythickness

Electromagnetic scattering from axisymmetric conducting bodies coated with thin materials of arbitrary thickness is considered and numerical results are obtained. The formulation presented for the coated conductor problem is based on existing E-PMCHW formulations for coated objects. This formulation is valid both for thick coatings and as the coating thickness approaches zero. Other existing surface integral equation implementations have been observed to fail for thin coatings. Two simple modifications are suggested for existing numerical codes to make them applicable for thin coatings. Several numerical examples are presented. The numerical solution is verified by comparison with the exact solution for a coated sphere