Study of different realizations and calculation models for softsurfaces by using a vertical monopole on a soft disk as a test bed

We study a vertical monopole on a circular metallic disk which is loaded in different ways to provide a soft boundary condition, e.g., by transverse corrugations or by dielectric or lossy material coatings. The different realizations are calculated by the uniform geometrical theory of diffraction (UTD), the incremental theory of diffraction, the moment method (MM) with an impedance boundary model, and MM using equivalent currents on all material interfaces. The calculated results are compared with measured results for specific geometries. Some general characteristics of the different realizations of the soft surfaces are extracted from the results. It is verified that the artificially soft boundary condition can be realized by different surface loadings. In particular, a nearly soft boundary condition can be realized over a large bandwidth by coating a conductor with a thin layer of lossy magnetic material. It is found that the surface impedance model works very well for modeling corrugations. It may also work for material coated surfaces provided the surface wave is prohibited from radiating. The bandwidth of the different soft surfaces are given, including corrugations with different cross-sectional shapes     

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     

Implementation and application of resistive sheet boundarycondition in the finite-difference time-domain method [EM scattering]

Use of a resistive sheet boundary condition in the finite-difference-time-domain (FDTD) analysis of scattering problems involving a resistively coated dielectric object is described. An algorithm is introduced through an analysis of E-polarized scattering from a thin resistive strip. For a given resistance, numerical experiments indicate that algorithm stability is ensured for time sampling intervals chosen according to a specific criterion. Validity of the resultant FDTD method is verified in a comparison of computed E-polarized scattering data for several resistive strips with existing data. Results on the E-polarized scattering behaviour of a resistively coated dielectric strip as a function of surface resistances and angle of incidence are also presented. Extension to the H-polarized case and application of the present method to pulsed problems are briefly discussed     

Extension of on-surface radiation condition theory to scattering bytwo-dimensional homogeneous dielectric objects

A recent analytical formulation by G.A. Kriegsmann et al. (see ibid., vol.AP-35, p.153-61, Feb. 1987) of electromagnetic wave scattering by perfectly conducting two-dimensional objects using the on-surface radiation boundary condition approach is extended to the case of two-dimensional homogeneous convex dielectric objects. It is shown that a substantial simplification in the analysis can be obtained by applying the outgoing radiation boundary condition on the surface of the object. The analysis procedure decouples the fields in the two regions to yield explicitly a differential equation relationship between the external incident field excitation and the corresponding field distribution in the interior of the dielectric object. The interior fields can be obtained by solving the differential equation using either an analytical approach or a suitable numerical method. Two-dimensional scattering examples along with validations are reported, showing the near-surface field distributions for a homogeneous circular dielectric cylinder and an elliptic dielectric cylinder, with with transverse magnetic plane-wave excitation     

Effective impedance boundary conditions for an inhomogeneous thinlayer on a curved metallic surface

Effective impedance boundary conditions for an inhomogeneous thin layer coated on a perfectly conducting object are considered. The permittivity of the thin layer is inhomogeneous along both the normal and tangential directions. Explicit forms of the first- and second-order approximate impedance boundary conditions are derived first for a two-dimensional (2D) thin layer for the TE and TM cases. Numerical results are presented. The case of Maxwell's equations for a three-dimensional inhomogeneous thin layer is also considered     

Diffraction of electromagnetic waves by the interface of two isotropic planar waveguides

The problem of excitation of the rectilinear interface of two semiinfinite planar waveguides by an eigenmode of one of these waveguides incident onto the interface at an arbitrary angle is considered. Planar waveguides shaped as a dielectric plate coated by thin isotropic films (e.g., gratings with spacings small as compared to the wavelength) are analyzed. A model of this structure in which films are described by means of two-sided impedance boundary conditions and parameters of the planar waveguide are varied by varying the film impedance is constructed. Solution to the electromagnetic problem by the Wiener-Hopf technique is presented. Closed-form expressions for scattering parameters of the analyzed structure are obtained. Results of the numerical solution are presented. Comparison with available results obtained for particular values of the film impedance is performed.     

High-order impedance boundary conditions for multilayer coated 3-Dobjects

The scattering problem by a multilayer coated three-dimensional (3-D) object where the coating is modeled by an impedance boundary condition (IBC) is considered. First, the exact boundary condition is obtained for an infinite planar coating with an arbitrary number of layers. Then, various approximations for the pseudodifferential operators involved in this exact condition are proposed. In the expressions of the resulting IBCs, all tangential derivatives of the fields of order higher than two are suppressed. These IBCs are compared, in terms of numerical efficiency, by computing either the reflection coefficients on an infinite planar metal-backed coating or the radar cross section (RCS) of a perfectly conducting coated sphere using the tangent plane approximation. In both cases, it is found that the highest order IBC models the coating with a good accuracy. Finally, some guidance is given on how this IBC may be numerically implemented in an integral equation or a finite-element formulation for an arbitrarily shaped object     

Electromagnetic scattering from a dielectric-coated sphere with anembedded impedance film

The electromagnetic scattering from a multilayered sphere modal solution of Wait (1963) is modified to allow the inclusion of infinitesimally thin impedance films at layer boundaries. The modified solution is implemented in a computer algorithm and the scattering from an aluminum sphere coated with a dielectric Delrin^TM layer containing an embedded impedance film is computed. This target was fabricated and laboratory measurements performed in the 2-18 GHz region are in good agreement with computations     

Resistive and conductive tube boundary condition models formaterial wire-shaped scatterers

An equivalent boundary condition model is introduced for computing the scattering by material wire-shaped scatterers which are either dielectric or magnetic, but not both simultaneously. While the methodology for numerically computing the scattering by perfectly conducting thin-wire scatterers has been developed for decades, no simple model for material scatterers with large length-to-radius ratios (wire shapes) has been available. This new model can be easily integrated into existing thin-wire computer codes while adding virtually no computational burden. Validating results are shown using comparisons of the full-wave scattering from a number of thin wire-shaped dielectric and magnetic structures with this new equivalent boundary condition model. It is demonstrated that this model is, in essence, an extension of the internal impedance expression for a conducting wire (developed over 50 years ago) to simple-material wire-shaped scatterers possessing a very wide range of material parameters     

Electromagnetic scattering by anisotropic impedance half and fullplanes illuminated at oblique incidence

The three-dimensional electromagnetic (EM) scattering from half and full plane configurations, both characterized by a perfectly conducting and an anisotropic impedance face, is analyzed. The anisotropic impedance boundary condition considered for the loaded face is suitable for modeling corrugated surfaces or strip-loaded grounded dielectric slabs used to realize artificially hard or soft surfaces, with a tensor surface impedance exhibiting a vanishing impedance along the corrugations or strips and a diverging impedance in the orthogonal direction. Previous rigorous solutions, valid when the vanishing impedance direction is either parallel or perpendicular to the edge, are generalized here to the case in which the direction of vanishing impedance is arbitrarily oriented     

Higher order impedance boundary conditions applied to scattering bycoated bodies of revolution

In this paper higher order impedance boundary conditions will be employed in the solution of scattering by coated conducting bodies of revolution. The higher order impedance solution reduces the total number of unknowns relative to the exact solution, and produces a system matrix which is less dense than that of the exact solution. The construction of the solution involves two distinct steps. In the first step the body of revolution is replaced by an equivalent set of electric and magnetic currents on its exterior surface which generate the true fields outside the body. An integral equation relating these currents through the free space Green's function is derived. Step two employs the higher order impedance boundary condition to relate the electric and magnetic currents on the surface of the body. This replaces the rigorous solution of the interior problem. The higher order impedance boundary conditions are derived by obtaining an exact impedance boundary condition in the spectral domain for the coated ground plane, approximating the impedances as ratios of polynomials in the transform variables, and employing the Fourier transform. The resulting spatial domain differential equations are solved in conjunction with the integral equation using the method of moments. Several examples of bistatic and monostatic radar cross section for coated bodies of revolution are used to illustrate the accuracy of the higher order impedance boundary condition solution relative to the standard impedance boundary condition solution and the exact solution. The effects of coating thickness, loss, and curvature on the accuracy of the solution are discussed     

Method of moments solution for a printed patch/slot antenna on a thin finite dielectric substrate using the volume Integral equation

In this paper, a volume integral equation (VIE)-based modeling method suitable for a patch or slot antenna on a thin finite dielectric substrate is developed and tested. Two new key features of the method are the use of proper dielectric basis functions and proper VIE conditioning, close to the metal surface, where the surface boundary condition of the zero tangential E -component must be extended into adjacent tetrahedra. The extended boundary condition is the exact result for the piecewise-constant dielectric basis functions. The latter operation allows one to achieve a good accuracy with one layer of tetrahedra for a thin dielectric substrate and thereby greatly reduces computational cost. The use of low-order basis functions also implies the use of low-order integration schemes and faster filling of the impedance matrix. For some common patch/slot antennas, the VIE-based modeling approach is found to give an error of about 1% or less in the resonant frequency for one-layer tetrahedral meshes with a relatively small number of unknowns. This error is obtained by comparison with fine finite-element method (FEM) simulations, or with measurements, or with the analytical mode matching approach. Hence it is competitive with both the method of moments surface integral equation approach and with the FEM approach for the printed antennas on thin dielectric substrates.     

基于FE-BI的介质粗糙面上方涂覆目标电磁散射特性研究

采用有限元-边界积分（finite element boundary integral,FE-BI）方法研究了介质粗糙面上方涂覆目标的复合电磁散射特性,推导了一维介质粗糙面上方二维涂覆目标电磁散射的FE-BI公式.在仿真中,采用功能强大的有限元方法模拟涂覆目标内部场,对于涂覆目标与粗糙面之间的多重耦合作用则通过边界积分方程方法进行考虑.结合Monte-Carlo方法,数值计算了介质高斯粗糙面上方涂覆圆柱目标的电磁散射,分析了涂层材料介电常数、粗糙面粗糙度以及介质粗糙面介电常数变化对复合模型双站散射系数的影响.数值结果表明,相比于传统矩量法（method of moment,MoM）,本文方法虽然在处理理想导体模型时效率略低,但可以处理MoM难以处理的复杂媒质电磁散射问题,且计算精度较高.     

Scattering of plane waves by an anisotropic dielectric half-plane

Scattering of plane waves by a semi-infinite anisotropic thin dielectric layer is investigated, which can be considered as an example for electromagnetic energy absorbing materials. A pair of second-order boundary conditions is used to simulate an anisotropic thin dielectric layer as an infinitesimally thin sheet. Formulation is based on the Fourier integral transform technique, which reduces the scattering problem to two decoupled scalar Wiener-Hopf equations. Diffracted, reflected, and transmitted field terms are evaluated by using the Wiener-Hopf solutions that is obtained by the standard method. The uniqueness of the solution is satisfied by imposing an edge constraint in addition to the classical edge condition     

On the Use of a Microstrip Three-Line System as a Six-Port Reflectometer

The scattering parameters for a coupled symmetrical three-Iine system in an inhomogeneous dielectric medium (e.g., microstrip) are derived directly in terms of a set of three orthogonal modes. The obtained results show that the condition for isolation of nonadjacent ports (e.g., ports 1 and 3 in Fig. 1) does not result from putting the corresponding per unit length immittance parameters equal to zero (i.e., z/sub 13/ =y/sub 13/ = 0). The use of such a three-line system as a six-port reflectometer is analyzed in terms of the derived scattering parameters. The reflectometer discussed in this paper allows an unknown impedance to be measured using a standard impedance.     

Scattering from dielectric structures above impedance surfaces andresistive sheets

Interest in understanding of electromagnetic interaction with rough surfaces has prompted the study of scattering from typical dielectric humps over impedance surfaces. It is shown that the Green's function of the problem for a resistive sheet resembles that of the impedance surface. Hence both problems are considered here. A numerical solution for the scattered field of a two-dimensional dielectric object, possibly inhomogeneous, with arbitrary cross section above the impedance surface or resistive sheet is sought. First the Green's function of the problem is derived based on the exact image theory. This form of the Green's function is amenable to numerical computation. Then the induced polarization currents are calculated by casting the integral equations into a matrix equation via the method of moments. Numerical problems in calculation of the Green's function when both source and observation points are close to the surface are discussed. Comparison of numerical results with a perturbation solution shows excellent agreement between the two methods     

Analysis of the effects of a resistively coated upper dielectriclayer on the propagation characteristics of hybrid modes in awaveguide-shielded microstrip using the method of lines

In this paper, propagation characteristics of even-symmetric hybrid modes in a waveguide-shielded microstrip in the presence of a resistively coated dielectric layer affixed to the top cover of the housing is analyzed with the method of lines. The resistive boundary condition is employed to model the resistive film. A shielded microstrip line having a unity strip-width-to-substrate-thickness ratio (i.e., w/h ₁=1) placed on top of a 0.635-mm-thick alumina substrate is considered. Based on a 10h₁×7h₁ reference housing, four different housing arrangements are obtained by varying the structural parameters of the resistively coated dielectric layer. Results obtained indicate that the effects of both the housing walls and the resistively coated upper dielectric layer on the dominant (quasi-TEM) mode are insignificant and may be ignored when frequency is above 15 GHz. For the higher order modes, the resistive film appears to be transparent when film resistance is greater than about 1 kΩ, it behaves as a good conductor when film resistance is much smaller than 100 Ω, and in between it results in nonlinear (and even oscillatory) higher order modal behaviors. Apparently, due to the increasing field concentration inside the upper dielectric (as suggested by the increasing ε_reff) for a given mode, both the maximum attenuation and the film resistance needed to achieve it increase with frequency and dielectric constant of the upper dielectric layer     

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     

Comprehensive understanding on the high dielectric constantinsulating layers for alternating-current thin-film electroluminescentdevices

We introduced thin-film electroluminescent cells (TFEL) with a new multilayered-BaTiO₃ layer for the low-voltage driven devices. We begin by simulating the basic parameters for TFEL devices in electrostatic boundary condition and point out how the insulator parameters influence the typical operating properties of the devices. Next, we performed the voltage accelerated breakdown testing of the multilayered-BaTiO₃ having both high dielectric constant and high breakdown strength. The time-zero-breakdown distribution is shown to be dependent on surface roughness, while the long-term failure studied by time-dependent-dielectric breakdown technique at high field is dependent on the bulk characteristics, i.e., transition layers within m-BT films. Thirdly, the TFEL devices were prepared using the multilayered-BaTiO₃ as dielectric materials. We observed a decrease of turn-on voltage with increasing thickness and the increase of the maximum overvoltage. Finally, typical symmetric capacitance-voltage (C-V) and internal charge-phosphor field characteristics were obtained for the device with thin m-BT layers. With increasing thickness of m-BT the significant asymmetry with respect to the applied voltage polarity was observed. This is a main difference as compared with the symmetric characteristics of conventional TFEL devices with low dielectric constant insulators. The experimental results indicate the fact that a selection of the thickness of upper m-BT and their deposition process would strongly affect the interfacial characteristics as well as bulk characteristics of an as-grown ZnS:Pr, Ce layer     

Reduction of forward scattering from cylindrical objects using hardsurfaces

We discuss how forward scattering can he characterized in terms of an equivalent blockage width, and a relation between this and the bistatic scattering width is derived. Then, we show how cylinders such as struts and masts can be constructed to reduce their blockage widths. Thereby, when the cylinders are mounted in front of an antenna, the sidelobes and losses caused by the blockage will be reduced. For thin metal cylinders the blockage width reduction is obtained by giving its cross section an oblong shape and, in addition (for the TM case), by coating the outer metal surface with dielectric material to obtain a hard boundary condition. For thick cylinders, the reduced scattering is obtained by designing them as dielectric-filled parallel plate waveguides with the outer surfaces of the plates coated in the same way as for the thin struts. Dual-polarized performance is obtained in both cases by strip loading the outer surfaces. The performance of both the thin and the thick struts have limited frequency bandwidth. Both computed and measured results are presented; the computations being done with the moment method. The designs are based on the concept of soft and hard surfaces in electromagnetics, and the results can be regarded as a proof of the existence of hard surfaces for electromagnetic waves. The study considers reduction of forward scattering which also will give a reduction of the total integrated power of the scattered field over all directions-even backward