Diffraction by an arbitrary-angled dielectric wedge. I. Physicaloptics approximation

A complete form is presented of the physical optics solution to diffraction by an arbitrary dielectric wedge angle with any relative dielectric constant in cases of both E- and H-polarized plane waves incident on one side of two dielectric interfaces. The solution, which is obtained by performing the physical optics (PO) approximation to the dual integral equation formulated in the spatial frequency domain, is constructed by the geometrical optics terms, including multiple reflection inside the wedge and the edge diffracted field. The diffraction coefficients of the edge diffracted field are represented in a simple form as two finite series of cotangent functions weighted by the Fresnel reflection coefficients. Far-field patterns of the PO solutions for a wedge angle of 45°, relative dielectric constants 2, 10, and 100, and an E-polarized incident angle of 150° are plotted in figures, revealing abrupt discontinuities at dielectric interfaces     

Diffraction by an arbitrary-angled dielectric wedge. II. Correctionto physical optics solution

For pt.I see ibid., vol.39, no.9, p.1272-81 (1991). The error of the physical optics solution for the E-polarized plane wave incidence in connection with diffraction by an arbitrary-angled dielectric wedge is corrected by calculating the nonuniform current distributed along the dielectric interfaces. Two kinds of series expansions to the nonuniform current are employed. One is an asymptotic expansion as the multipole line source located at the edge of the dielectric wedge, since the correction field seems to be a cylindrical wave emanating from the edge in the far-field region. The other is arbitrary electric and magnetic surface currents expanded by infinite series of the Bessel functions, i.e. the Neumann expansion, of which fractional order is chosen to satisfy the edge condition near the edge of the dielectric wedge in the static limit. Both of the two different expansion coefficients for a wedge angle of 45°, relative dielectric constants 2, 10, and 100, and the E-polarized incident angle of 150° are evaluated by solving the dual series equation numerically after finite truncation     

E-polarized scattering from a conducting rectangularcylinder with an infinite axial slot filled by a resistively coateddielectric strip

The potential use of resistive films for damping the resonance spikes observed in the radar cross section (RCS) spectrum of a partially open rectangular cavity is investigated using a recently developed finite-difference-time-domain (FDTD) method that utilizes the resistive-sheet boundary condition for the modeling of resistive films. Backscattering data obtained in the first resonant region for an E -polarized plane wave normally incident into the slotted side of the cavity are presented. It is shown that resonance behaviors can be eliminated completely with a low-resistance film that attenuates significantly the impinging wave. Poorer resonance damping performance is observed as the film resistance increases because more of the field is allowed to penetrate into the cavity. For the latter case, the presence of the resistive film lowers the Q-factor of the slotted cavity such that the resultant resonance spectrum is lower in strength and broader in bandwidth     

Scattering of H-polarized waves from conducting strips inthe presence of an electrically uniaxial half-space-a singularintegrodifferential equation approach

Electromagnetic scattering from perfectly conducting infinitely long strips in the presence of an electrically uniaxial half-space is treated analytically. A uniform H-polarized plane wave is incident from the isotropic region. As a prerequisite to this approach, the H-mode scalar Green's function of the structure is developed. Its use in connection with the reciprocity theorem leads to a singular integrodifferential equation for the current density induced on the scatterer surface. The equation is solved for strips parallel or perpendicular to the interface, located above or embedded in the anisotropic region, following a special technique based on the theory of singular integral equations that has been developed in connection with strips and slots and E- or H-polarized incident waves. Numerical results for the induced current density and for the scattered far field in a variety of cases are presented in graphical form. Whenever possible they are compared with existing results based on purely numerical procedures     

Importance of normal field continuity in inhomogeneous scatteringcalculations

The finite-element method with conventional scalar bases is coupled with the moment method to handle the three-dimensional scattering and/or absorption from inhomogeneous, arbitrarily shaped objects. The C⁰ finite-element basis enforces continuity of both normal and tangential E at element boundaries within homogeneous regions. At dielectric interfaces, the continuity of normal D and tangential E are enforced in a strong sense. Excellent agreement between the numerical solution and the Mie series is obtained for both internal and scattered fields for homogeneous and layered spheres under plane wave illumination. Compared to an alternative finite-element method using edge elements which lack strong enforcement of normal field continuity, the present method produces higher-order approximations, especially at dielectric interfaces, with no penalties in computational effort     

Dispersion characteristics of strip dielectric waveguides

A simple and accurate dispersion relation is derived for the guided mode of a strip dielectric waveguide. This relation shows explicitly the effect of the width of the waveguide and involves only the solution for a single three-layer slab waveguide. It is found that there always exist a strip waveguide with a specific aspect ratio in which the E_mn^x and E_mn^y modes propagate at the same phase velocity     

Electromagnetic scattering of finite strip array on a dielectricslab

A feast recursive algorithm is used to compute the scattering properties of a finite array of strip gratings on a dielectric slab. this algorithm has a computational complexity of O(N log² N) for one incident angle and O(N ² log N) for N incident angles. It uses plane wave basis for expanding the incident wave and the scattered wave. The scattered wave is expanded in terms of a Sommerfeld-type integral with spectral distribution along a vertical branch cut, rendering its expansion very efficient. To validate the scattering solution obtained using the recursive algorithm, comparisons with the method of moments are illustrated. The current distributions on the strips and scattering patterns are both presented. Since this algorithm has reduced computational complexity and is fast compared to other conventional methods, it can be used to analyze very large strip arrays. Scattering solution of a 50-wavelength wide strip is illustrated     

Application of hybrid finite element method to electromagneticscattering from coated cylinders

A hybrid finite-element method is applied to solve the electromagnetic scattering (for both E- and H-polarizations) from coated cylinders. The coating material can be nonhomogeneous and have permeabilities and permittivities different from their free-space values. Three numerical examples are presented to show the validity and versatility of the method: (1) bistatic scattering from a coated circular cylinder which verifies the formulation and the computer program, (2) backscattering from a coated rectangular cylinder, and (3) backscattering from an ogival cylinder with coated edges. Computations are compared with those obtained using moment-method codes and exact solutions when applicable     

TM scattering by conducting strips right on the planar interface ofa three-layered medium

Combining the Fourier transform with powerful singular integral equation methods, the authors investigate the scattering properties of a variety of two-dimensional, three-layered planar structures loaded by a strip or a couple of coplanar strips right on an interface. The primary excitation is the lowest-order incident TM (to strip axis) surface wave mode or an incident E-polarized plane wave. In the practical case where the entire space is magnetically homogeneous, the kernel of the integral equations is most conveniently decomposed into a singular closed-form term added to an exponentially convergent inverse Fourier integral. An efficient, accurate, and stable numerical code is obtained and used to determine the strip-induced current densities as well as any quantity of practical interest. Plotted results reveal that by a proper choice of certain geometrical parameters the structures may become very efficient radiators, which can be designed to exhibit either very wideband and high directivity or considerable frequency scanning     

A variational analysis of anisotropic, inhomogeneous dielectricwaveguides

The authors derive a variational formulation for anisotropic, dielectric waveguides using only the (E_x, E _y) or (H_x, H_y) components of the electromagnetic field. They show that the (E _x, E_y) formulation is completely equivalent to the (H_x, H_y) formulation. In fact, they are the transpose problems of each other. Given the variational formulation, one can derive the finite-element solution quite easily. The authors also show how to derive a variational expression where the natural boundary conditions are incorporated as an optimal solution of the variational expression. The theory is illustrated with a simple implementation of a finite-element solution. The solutions agree with previous results, and there is no occurrence of spurious modes     

Effects of a resistively coated dielectric strip on theTM-polarized resonant backscatter behavior of a slotted conductingrectangular shell

The performance of a resistively coated dielectric strip used to suppress the first TM-type resonant backscatter associated with a two-dimensional slotted conducting rectangular shell is analyzed using the moment method technique. Results obtained indicate that almost perfect resonance damping performances are attained when a finite-sized strip with dielectric constants ∈_r=4-j0.4 and film resistance R_s=188.5 Ω is placed: (1) at the slot (which directly faces the normally incident TM-polarized plane wave), (2) on the interior perimeter of the shell adjacent to the slot, or (3) at the center of the back wall of the shell. Poorer damping performances are observed, however, with the strip placed at other positions and/or with the same or higher film resistance. It is also shown that in general the knowledge of waveguide theory can be used advantageously in the placement of the strip for achieving best resonance damping performance     

A generalized recursive algorithm for wave-scattering solutions intwo dimensions

A generalized recursive algorithm valid for both the E _z and H_z wave scattering of densely packed scatterers in two dimensions is derived. This is unlike previously derived recursive algorithms which have been found to be valid only for E_z polarized waves. In this generalized recursive algorithm, a scatterer is first divided into N subscatterers. The n-subscatterer solution is then used to solve the (n+n')-subscatterer solution. The computational complexity of such an algorithm is found to be of O (N²) in two dimensions while providing a solution valid for all angles of incidence. This is better than the method of moments with Gaussian elimination, which has an O(N³) complexity     

Computer-aided design of evanescent-mode waveguide filter withnontouching E-plane fins

The authors present a computer-aided design algorithm for the analysis and design of an evanescent-mode bandpass filter with nontouching E-plane fins. The theoretical analysis is based on the generalized scattering matrix technique in conjunction with the spectral-domain approach and mode-matching method. The technique used takes into account the dominant as well as the higher-order effects. The measured filter responses in the Ka-band are in good agreement with those obtained by this analysis     

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     

A complete E-plane analysis of waveguide junctions usingthe finite element method

A complete finite-element analysis of inhomogeneous E-plane waveguide junctions is presented. It is shown that at least two field components are needed for the analysis. This method solves for the three components of the magnetic field in two dimensions and calculates the scattering parameters of the junction. Precalculated matrices are used for fast matrix assembly. Results for a metallic post agree very well with earlier published values. A dielectric post was also analyzed     

Continuous potential Maxwell solutions on nodal-based finiteelements

A nodal-based finite-element approach for computing electric fields in heterogeneous media is presented. The primary calculation is formulated in terms of continuous potentials, so that no special care is required on element assembly at dielectric interfaces. The resulting Galerkin weak-form matrices exhibit the special Helmholtz structure, which guarantees the absence of parasitic solutions in driven problems with physically well-posed boundary conditions. The enhanced sparsity of the Helmholtz form mitigates the extra coupling effort associated with introduction of a fourth degree of freedom relative to direct E solution. E can be extracted from the computed potentials as a postprocessing step either at nodal positions or element centroids. Solutions obtained with this approach for several benchmark and practical problems are shown to be parasite-free and essentially indistinguishable from previously reported direct E computations     

Computer-aided design of evanescent mode waveguide bandpass filterwith nontouching E-plane fins

The authors present an efficient computer-aided-design procedure that systematically utilizes a lookup table containing scattering parameters from variously dimensioned E-plane fins. The main idea is to achieve an optimal combination of filter parameters by proper selection of the E-plane fins from the table and appropriate determination of the other filter elements in order to satisfy the given filter specifications. The technique of selecting the proper fin from the table is explained. The relationship between the desired center frequency of the filter and the approximate resonant frequency of the single fin in the table is shown. The relationship between each design parameter and the filter characteristic is presented. The algorithm is applied to the design of a bandpass filter with two E-plane fins operating in the Ka-band. The algorithm is verified by comparing the characteristics of the designed filter with the experimental results     

Numerical analysis of waveguide discontinuity problems using thenetwork model decomposition method

The use of the network model decomposition method for analyzing arbitrarily shaped H- and E-plane waveguide junctions is discussed. By using the polygon discretization technique previously introduced by the author (1990), the waveguide discontinuity region, which is surrounded by a metallic wall and the reference planes chosen, is first discretized; the topological model and the corresponding network model for the waveguide discontinuity are then established. In the formulation, equivalent current sources connected to the nodes on the boundary of the region are introduced to replace the effect of the field external to the region. The field internal to the region is approximated by the nodal voltage distribution of the network model, which can then be used to determine the scattering parameters of the waveguide junction. A diakoptic algorithm for the solution of the network model is also developed. Numerical results for various H- and E-plane junctions are given, and it is shown that the method compares favorably compares with other theories