Resistive treatment to reduce edge diffraction from large wedge‐shaped objects and planar antennas

In the use of the time-domain integral equation (TDIE) method for the analysis of layered media, it is important to have the time-domain layered medium Green's function computed for many source-to-field distances /spl rho/ and time instants t. In this paper, a numerical method is used that computes the mixed potential Green's functions G/sub v/(/spl rho/,t) and G/sub A/(/spl rho/,t) for a multilayered medium for many /spl rho/'s and t's simultaneously. The method is applicable to multilayered media and for lossless or lossy dispersive media. Salient features of the method are: 1) the use of complex /spl omega/ so that the surface wave poles are lifted off the real k/sub /spl rho// axis such that pole extractions are not required; 2) the use of half-space extraction so that the integrand for the Sommerfeld integral decays exponentially along the k/sub /spl rho// axis to obtain fast convergence of the integral; and 3) the use of the fast Hankel transform so that the Green's function is calculated for many values of /spl rho/ simultaneously. For a four-layer medium, we illustrate the numerical results by a three-dimensional plot of /spl rho/G/sub v/(/spl rho/,t) versus /spl rho/ and t and demonstrate the space-time evolution of these Green's functions. For a maximum frequency range of 8 GHz, the method requires only a few CPU minutes to compute a table of 100 (points in /spl rho/) /spl times/ 168 (points in t) uniformly spaced values of G/sub v/(/spl rho/,t) on an 867-MHz Pentium PC.

Electromagnetic fields created in a homogeneous medium by a known distribution of electric current are determined by integral equations involving free space Green's functions. In actual situations, however, current distributions are not known beforehand and must be determined, in such a way that the total fields satisfy the boundary conditions on the conductors. The integral equation technique was extended to treat also heterogeneous structures, in order to analyze and design multilayer printed circuits and antennas, such as the broadband strip-slot-foam-inverted patch printed antenna. Sommerfeld integrals provide Green's functions for stratified media, which are evaluated by means of specifically developed, efficient computer algorithms. Structures including coaxial or line feeds and coupling through slots can now be easily analyzed with commercially available software packages.

In this paper, we present the multilevel Green's function interpolation method (MLGFIM) for analyses of three-dimensional doubly periodic structures consisting of dielectric media and conducting objects. The volume integral equation (VIE) and surface integral equation (SIE) are adopted, respectively, for the inhomogeneous dielectric and conducting objects in a unit cell. Conformal basis functions defined on curvilinear hexahedron and quadrilateral elements are used to solve the volume/surface integral equation (VSIE). Periodic boundary conditions are introduced at the boundaries of the unit cell. Computation of the space-domain Green's function is accelerated by means of Ewald's transformation. A periodic octary-cube-tree scheme is developed to allow adaptation of the MLGFIM for analyses of doubly periodic structures. The proposed algorithm is first validated by comparison with published data in the open literature. More complex periodic structures, such as dielectric coated conducting shells, folded dielectric structures, photonic bandgap structures, and split ring resonators (SRRs), are then simulated to illustrate that the MLGFIM has a computational complexity of O(N) when applied to periodic structures.

The analysis of the target’s broadband electromagnetic scattering characteristics plays an important role in radar stealth and recognition areas. The traditional method of moments (MoM) needs to calculate the currents at each frequency point when analyzing the target. With the increase of the target electrical size and complexity, the radar cross section (RCS) of the target changes drastically with frequency, it is necessary to calculate the accurate frequency response with a small frequency interval, which is very time-consuming in calculation and not feasible. This paper proposes to combine the subdomain method of moments (SMoM) with the Chebyshev approximation technique (CAT) to efficiently analyze the electromagnetic scattering of arbitrary shaped objects over a broad frequency band. In the SMoM technique, the whole object can be divided into several regions, each of which can be independently solved by the method of moments (MoM). The CAT technique is employed to expand the unknown current coefficients into a Chebyshev series for achieving fast frequency sweeping. Instead of direct point-by-point simulations, it is only necessary to calculate the currents by SMoM at several Chebyshev-Gauss frequency sample points. Furthermore, the Chebyshev series are matched via the Maehly approximation to a rational function to improve the accuracy. Numerical examples show that the hybrid technique can greatly reduce the computation time without loss of accuracy.

The spatial frequency technique (SFT) was developed for solving the integral equation (IE) in electromagnetic scattering and radiation problems and shown to work faster than many existing solution methods. In this paper, the new formulation, which is based on the efficient FFT algorithm, is analyzed further for analytically solving the IE for certain types scattering and radiation problems. It is shown that the SFT description of the symmetric matrix which represents the Green's function may be decomposed into an orthogonal basis using Takagi factorization. Transforming the Green's function into this orthogonal basis has the potential to invert the Green's function analytically. The SFT is also compared with the Fast Multipole Method (FMM) and shown to have similar underlying properties which may also be utilized to analytically invert the Green's function using FMM.

The transverse aperture‐integral equation method provides a means of computation for diffraction coefficients at blunt edges of a broad class of stratified layers, including sheet‐anisotropy models for conducting composites. In this paper we concentrate on the application of the method when the material profile comprises layers of homogeneous, potentially lossy material. The method proceeds from defining an artificial aperture perpendicular to a semi‐infinite, planar, stratified region and passing through the terminal edge of the region. An integral equation is formulated over this infinite‐extent aperture, and the solution to the integral equation represents the influence of the edge. The kernel in the integral equation is a weighted sum of the Green's functions for the respective half spaces lying on either side of the aperture plane. The vector wave equation is separable in each of these half spaces, resulting in Green's functions that are expressible analytically. The Green's function for the stratified half space is stated in terms of a Sommerfeld‐type integral.

The coupling–ray–theory tensor Green function for electromagnetic waves or elastic S waves is frequency dependent, and is usually calculated for many frequencies. This frequency dependence represents no problem in calculating the Green function, but may represent a great problem in storing the Green function at the nodes of dense grids, typical for applications such as the Born approximation. This paper is devoted to the approximation of the coupling–ray–theory tensor Green function, which practically eliminates this frequency dependence within a reasonably broad frequency band. In the vicinity of a given prevailing frequency, we approximate the frequency–dependent frequency–domain coupling–ray–theory tensor Green function by two dyadic Green functions corresponding to two waves described by their travel times and amplitudes calculated for the prevailing frequency. We refer to these travel times and amplitudes as the coupling–ray–theory travel times and the coupling–ray–theory amplitudes. This “prevailing–frequency approximation” of the coupling ray theory for electromagnetic waves or elastic S waves allows us to process the coupling–ray–theory wave field in the same way as the anisotropic–ray–theory wave field. This simplification may be decisive when storing the tensor Green function at the nodes of dense grids, which is typical for applications such as the Born approximation. We test the accuracy of the proposed prevailing–frequency approximation of the coupling ray theory numerically using elastic S waves in eight anisotropic velocity models. The additional inaccuracy introduced by the prevailing–frequency approximation is smaller than the inaccuracy of the standard frequency–domain coupling ray theory, and smaller than the additional inaccuracy introduced by many other approximations of the coupling ray theory.

A Complementary Electric Field Coupled (CELC) resonator, loaded in the ground plane of a conventional patch antenna to achieve dual band operation is presented here. Two antenna designs have been presented. In the first design, one CELC is etched out from the ground plane of patch antenna which leads to generation of a lower order mode in addition to the conventional patch mode. In order to achieve better impedance bandwidth for the lower order resonant mode two CELC resonators with closely spaced resonant frequencies are etched out from the ground plane of patch antenna in the second design. The proposed antennas can be used in WLAN (Wireless Local Area Network) and WiMAX (Worldwide Interoperability for Microwave Access) applications.

In this paper, we consider the Dirichlet and impedance boundary value problems for the Helmholtz equation in a non‐locally perturbed half‐plane. These boundary value problems arise in a study of time‐harmonic acoustic scattering of an incident field by a sound‐soft, infinite rough surface where the total field vanishes (the Dirichlet problem) or by an infinite, impedance rough surface where the total field satisfies a homogeneous impedance condition (the impedance problem). We propose a new boundary integral equation formulation for the Dirichlet problem, utilizing a combined double‐ and single‐layer potential and a Dirichlet half‐plane Green's function. For the impedance problem we propose two boundary integral equation formulations, both using a half‐plane impedance Green's function, the first derived from Green's representation theorem, and the second arising from seeking the solution as a single‐layer potential. We show that all the integral equations proposed are uniquely solvable in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including an incident plane wave, the impedance boundary value problem for the scattered field has a unique solution under certain constraints on the boundary impedance. Copyright © 2003 John Wiley & Sons, Ltd.

Wave propagation according to higher order field equations I

The array Green's function (AGF) represents the basic constituent for the full wave description of electromagnetic radiation from rectangular periodic arrays and scattering from periodic surfaces. In modeling the performance of such structures: one of the main objectives is the reduction of the often prohibitive numerical effort that accompanies the full-wave analysis based on an integral equation, which is structured around the ordinary individual element Green's function. For a periodic array, this array Green's function is composed of the sum of the individual dipole radiations. Under certain assumptions the integral equation can be restructured around the active Green's function, which is the field collectively radiated by an array of elementary dipoles. A series of papers have investigated the description of the AGF in terms of propagating and evanescent Floquet waves (FWs) together with corresponding FW-modulated diffracted fields which arise from FW scattering at the array edges and vertices. The above mentioned formulation, being based on an asymptotic evaluation of the constituent radiation integrals, fails when observing too close to the edge and vertices. The present work is intended to illustrate a complementary strategy for treating the observation point also close to the array contour, as implicated by a full-wave scheme.

We consider the method of evaluating matrix elements of electromagnetic volume integral equations with the help of suitably constructed Laplacian-type representations of singular kernels (Green functions) appearing in electromagnetic volume and surface integral equations. The method consists of representing the singular kernels (Green functions) in terms of a generalized Laplacian operator acting on some auxiliary functions. Such a representations allow us, by using Gauss divergence theorem, to convert volumetric and surface integrals representing matrix elements to integrals always involving only non-singular integrands. The task of of finding particular Laplacian representation of different kernels amounts to solving appropriate ordinary or partial inhomogeneous differential equations. We apply the Laplacian method to analytic evaluation of matrix elements of the volume integral equation by employing two different Laplacian representations of the integral equation kernels. The first representation allows us to reduce 6-dimensional volume integrals over tetrahedra to 2-dimensional surface integrals over tetrahedra faces. The second representation is subsequently used reducing surface integrals over tetrahedra faces to pairs of of 1-dimensional line integrals over tetrahedra edges. We also derive analytic expressions for the resulting line integrals given in terms of elementary functions.

Eliminating the electromagnetic interaction of a device with its background is a topic which attracts considerable attention both from a theoretical as well as from an experimental point of view. In this work, we analyze an infinite two‐dimensional planar microstrip antenna, excited by an incident plane wave, and propose its potential operation as a low‐profile receiving antenna, by suitably adjusting the parameters of its cloaking superstrate. We impose a semi‐analytic integral equation method to determine the scattering characteristics of the microstrip antenna. The method utilizes the explicit expressions of the Green's function of the strip‐free microstrip and yields the surface strip's current as the solution of a suitable linear system. Subsequently, the antenna's far‐field response is obtained. Numerical results are presented for the achieved low profile of the receiving antenna, by choosing suitably the cloaking superstrate parameters. It is demonstrated that for specific cloaking parameters the scattered field by the antenna is considerably reduced, while the received signal from the antenna is maintained at sensible levels. We point out that the material values achieving this reduction correspond to a superstrate filled with anϵ‐near‐zero or a low‐index metamaterial. Finally, the variations of the device reaction for various superstrates are depicted, concluding that for optimized superstrate's parameters, the reaction values are significantly reduced, while at distinct scattering angles even approach zero.

We consider the motion of a thin elastic plate with non-uniform thickness. The plate is either submerged and has some inclination with the vertical or is floating on the upper surface of the water. Green's function arising from the fourth-order boundary condition for the non-uniform plate (which we refer to as plate Green's function) is determined using two different methods in terms of the vibrating modes of the plate. These, in turn, are derived from the modes of a plate with constant thickness. The problem is finally reduced to a boundary integral equation involving the plate Green's function and the fundamental Green's function. This equation is hypersingular in the case of a submerged plate. A numerical solution to the integral equation is used to find results for elastic plates with variable thicknesses. The results are validated by comparing them with those of an elastic plate with uniform thickness. We also present simulations of the time-domain motion when the plate–fluid system is subject to an incident wave pulse using Fourier transform.

We consider the motion of a thin elastic plate with non-uniform thickness. The plate is either submerged and has some inclination with the vertical or is floating on the upper surface of the water. Green's function arising from the fourth-order boundary condition for the non-uniform plate (which we refer to as plate Green's function) is determined using two different methods in terms of the vibrating modes of the plate. These, in turn, are derived from the modes of a plate with constant thickness. The problem is finally reduced to a boundary integral equation involving the plate Green's function and the fundamental Green's function. This equation is hypersingular in the case of a submerged plate. A numerical solution to the integral equation is used to find results for elastic plates with variable thicknesses. The results are validated by comparing them with those of an elastic plate with uniform thickness. We also present simulations of the time-domain motion when the plate–fluid system is subject to an incident wave pulse using Fourier transform.