Showing papers in "Electromagnetics in 1996"

An Anisotropic PML Absorbing Media for the FDTD Simulation of Fields in Lossy and Dispersive Media

Abstract: A uniaxial anisotropic perfectly matched layer (PML) absorbing material is presented for the truncation of finite-difference time-domain (FDTD) lattices for the simulation of electromagnetic fields in lossy and dispersive material media. It is shown that by properly choosing the constitutive parameters of the uniaxial media both propagating and evanescent waves can be highly attenuated within the PML medium. This resolves the concern that the original Berenger's formulation for a PML medium does not attenuate evanescent waves. FDTD formulations for the uniaxial PML method are presented for lossy and dispersive medium. Based on this formulation an equivalent modified representation of Berenger's split equations is also derived. Through numerical examples, it is demonstrated that the uniaxial PML method provides a nearly reflectionless absorbing boundary for the FDTD simulation of evanescent and propagating waves encountered in highly dispersive and lossy medium.

Perfectly Matched Layers in the Discretized Space: An Analysis and Optimization

Abstract: The perfectly matched layer (PML) has recently been introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. Recently, it has been pointed out that this absorbing boundary condition is the same as coordinate stretching in the complex space. In this paper, the corresponding coordinate stretching is analyzed in the discretized space of Maxwell's equations as described by the Yee algorithm. The corresponding dispersion relationship is derived for a PML medium and then the problem of reflection from a single interface is solved. A perfectly matched interface is shown not to exist in the discretized space, even though it exists in the continuum space. Numerical simulations both using finite difference method and finite element method confirm that such discretization error exists. A numerical scheme using the finite element method is then developed to optimize the PML with respect to its parameters. Examples are given to demonstrate the performance of the optim...

Nonredundant Representation of the Electromagnetic Fields Over a Cylinder with Application to the Near-Field Far-Field Transformation

Abstract: An innovative sampling representation to efficiently reconstruct the electromagnetic field over a cylinder from a non-redundant and always finite number of samples is proposed. It is based on the recent results concerning the analytical properties of the fields radiated by finite sources and, in particular, on the proper choice of the phase factor extracted from the field expression and of the coordinates used to parameterize the cylinder. Such a sampling representation is properly employed to develop a fast and accurate near-field-far-field transformation technique with cylindrical scanning, which allows to evaluate the antenna far-field directly from the non-redundant near-field data without interpolating them. Accordingly, the measurement time is significantly reduced without losing the computational efficiency of the classical approach. Moreover, some numerical tests assessing the effectiveness and the stability of the above procedures are reported.

Influence of Chiral Shapes of Individual Inclusions on the Absorption in Chiral Composite Coatings

Abstract: This paper presents a theoretical investigation of reflection properties of planar layers of chiral composite materials. The goal of the study is to clarify the influence of inclusion shape on reflection and absorption in chiral mixtures. It is explained why the slabs of low-density isotropic chiral and racemic mixtures of chiral panicles of conventional shapes (helices. wire-and-loop elements) possess very similar reflective properties for waves coming from tin5 normal direction. In particular, we consider certain “asymmetric” chiral shapes, such that the chirality factor of single individual particles modifies the effective permittivity and permeability of mixtures with many inclusions. Numerical examples demonstrate typical properties of lossy chiralslabs.

How to design the imperfect berenger pml

Abstract: In contrast to the previously popular second order Miir absorbing boundary condition (ABC), the recently introduced Berenger Perfectly Matched Layer (PML) ABC can be designed to lower the numerical reflection coefficient associated with mesh truncation by several orders in magnitude. Nonetheless the PML ABC is not perfect; it does have a numerical reflection coefficient. This reflection coefficient is characterized in the time and frequency domains for narrow and broad bandwidth pulses from several points of view including specifically its behavior in terms of the magnitude of the loss tangent in the PML and the thickness of the PML. It is demonstrated that for broad bandwidth pulses the PML ABC exhibits a low frequency increase in its reflection coefficient that is associated with the actual thickness of the PML layer in terms of the longest wavelengths contained in the signal incident upon it. Moreover, it is shown that the effectiveness of the PML ABC saturates when the loss parameters of the ...

The alternating rotated transmission line matrix (artlm) scheme

Abstract: Combining the ATLM scheme with rotation of the polarization states of the mesh lines by 45° the computational effort can be reduced compared with conventional TLM by up to 75 %. It is shown that by this way the conventional TLM scheme degenerates into four independent computational schemes, each of which contains the full information. Besides the reduction of the computational effort and storage requirements, also spurious modes and nonphysical solutions are eliminated.

Stability Analysis for Perfectly Matched Layered Absorbers

Abstract: Stability issues involved with using a time domain formulation of the perfectly matched layer (PML) absorbers are considered. We consider one time domain form of the anisotropic PML and show that it is dynamically unstable. Numerical stability of Berenger's formulation is next considered. This formulation is shown to be conditionally stable. The stability condition is shown to be independent of the coordinate stretch variables σx, σy, and σz

Optimization of Aperture Distributions for Sum patterns

Abstract: This paper presents a method of synthesizing sum patterns yielding aperture distributions with minimal edge brightening. The method produces patterns in which the infinitely deep nulls are replaced by less deep nulls. This provides a multiplicity of solutions, some of which may be easier to achieve physically than the conventional solution possessing deep nulls. The results in the cases of linear and planar array synthesis show a significant improvement in the distributions, with a very small loss in directivity for the resulting pattern.

Mutual Coupling Between Waveguide-Fed Longitudinal Broad Wall Slots Radiating Between Baffles

Abstract: This paper presents an analysis of the mutual coupling effect in waveguide-fed longitudinal slots radiating between baffles. The region exterior to the waveguide-fed slots is assumed to be cylindrical, a parallel plate waveguide opening into an outer half-space region bounded by an infinite ground plane with an aperture in the middle. The field problem in the exterior region is solved in spectral domain. Mutual admittance characteristics are presented for a range of values of the physical parameters, including the special case of an infinitely long parallel plate waveguide. These results should be useful in the analysis and synthesis of slot arrays for applications such as dual polarization systems and for suppressing the off-axis grating lobes resulting from alternating slot offsets.

Comparison of Two-Dimensional Conformal Local Adiation Boundary Conditions

Abstract: Numerical solutions for openndash;region electromagnetic problems based on differential equations require some means of truncating the computational domain. A number of local Radiation Boundary Conditions (RBCs) for general boundary shapes have been proposed during the past decade. Many are generalizations of the Baylissndash;Turkel RBC for circular truncation boundaries. Tbis paper reviews several twondash;dimensional RBCs for general truncation boundaries. The RBCs are evaluated on the basis of their performance on two separate numerical tests: the annihilation of terms in the Hankel series and the comparison of nearndash;field and radar cross sections for finite element solutions to scattering problems. These tests suggest that the simpler RBCs can be very competitive with RBCs based on more sophisticated derivations.

Design of Planar Absorbing Layers for Domain Truncation in FEM Applications

Abstract: A metal-backed layer of absorbing material offers a number of advantages for truncating the computational domain in a finite element simulation. In this paper we present design curves for the optimal selection of the parameters of the layer to achieve a specified reflection coefficient. The curves are based on one-dimensional finite element simulations of the absorbers, and the optimization is therefore a function of the sampling rate. Three types of material are considered, including the recently introduced perfectly matched uniaxial material, either homogeneous or with a quadratic material profile. Two three-dimensional applications are also presented and used to examine the validity of the design curves.

3D FEM/BEM-Hybrid Approach for Planar Layered Media

Abstract: A finite element method (FEM)/boundary element method (BEM)-hybrid approach is presented which allows electromagnetic field calculations in planar layered media including three-dimensional inhomogeneous regions. The fields within the inhomogeneities are modeled by the FEM in terms of the electric field strength Ē with edge elements on tetrahedral meshes. Based on Huygens’ principle the BEM is formulated with equivalent electric and magnetic surface currents on a surface completely enclosing the inhomogeneous regions. Additionally, ideal conducting objects can be included into the BEM-model. The electric field integral equation (EFIE) for the BEM is formulated as a mixed potential integral equation (MPIE). Applications of the method to field calculations in a microstrip resonator with finite metallization thickness and to the coupling of a cylindrical dielectric resonator to a microstrip line are presented.

Duality in Electromagnetics: Application to Tellegen Media

Abstract: This article discusses the generalized duality transformation in electromagnetics. The duality transformation affects material parameters in the bi-anisotropic constitutive relations. It will be shown that the two magnetoelectric phenomena, chirality and nonrecipro city, behave differently in the duality transformation. The analysis of the duality transformation is shown to be relevant to the question about the existence of non-reciprocal Tellegen media.

Radar Cross Section Prediction Using Boundary Integral Equation Methods with Isoparametric Quadratic Surface Modeling and Iterative Solvers

Abstract: A boundary integral equation formulation for frequency domain near scattered field and radar cross section scattering is presented. It employs smooth, curved isoparametric quadratic elements for the modelling of both the geometry and field, along with high order gaussian quadrature for the integrations required to evaluate the matrix coefficients. The resulting matrix equations are solved using the complex biconjugate gradient approach. It is shown that this representation is efficient, allowing solutions to sizeable problems to be obtained, with accurate solutions with nodal separations as high as 1/5 of a wavelength. It is demonstrated that realistic geometries can require accurate integration, such as is provided by high order gaussian quadrature, for converged solutions to be obtained. Example results presented, all obtained on modest workstations, include a resonant cavity, the ∼ six wavelength NASA almond, and a dipole 20 wavelengths long.

Absorbing boundary conditions for time-domain tlm and fdtd analysis of electromagnetic structures

Abstract: In this paper, the absorbing boundary conditions (ABCs) most commonly used in time-domain numerical methods such as the Transmission Line Matrix (TLM) method and the Finite Difference Time Domain (FDTD) method are reviewed. Such boundary conditions are required to simulate matched loads and open surfaces. We discuss and compare ABCs based on single impulse reflection coefficients, one-way equations, diakoptics or Johns matrices, and Berenger‘s perfectly matched layer (PML). Even though the emphasis is on applications in the TLM method, the major differences in the performances of these ABCs in TLM and FDTD are pointed out. Two ways of applying ABCs in TLM (voltage impulses and node voltages) are discussed. It has been observed that an ABC applied directly to the TLM voltage impulses absorbs better than the same ABC applied to the TLM total node voltages or FDTD field values. Furthermore, different ways of stabilizing one–way equation ABCs, such as adding damping factors, choosing proper discretiz...

Cross Polarization and Beam Squint in Single and Dual Offset Reflector Antennas

Abstract: Cross polarization (XPOL) and beam squint phenomena of reflector antennas are examined in detail. Emphasis is on the explanation of the absence of XPOL and the presence of beam squint in offset parabolic reflectors illuminated by a circularly polarized feed. Linearly polarized feeds are also considered for both the offset and axisymmetric configurations. Although many of these results are known, they are presented in a single coherent treatment. In addition, the results for polarization and beam squint characteristics of prime-focus offset parabolic reflector antennas are extended to dual offset configurations based on computed data using the physical optics code, GRASP7 (TICRA, 1988).

Application of the PML Absorbing Boundary Condition to the Analysis of Patch Antennas

Abstract: The Berenger Perfectly Matched Layer (PML) absorbing boundary condition is applied to a Finite-Difference Time-Domain analysis of rectangular patch antennas. Both microstrip line and probe-fed patch antennas are analyzed. The effects of the proximity of the PML regions on the resonant characteristics of the antennas and the mutual coupling between antennas are examined. The computational overhead associated with the use of the PML is also considered. Numerical results are validated by comparisons with measured data.

Edge-Based Finite Element Analysis of Singly-and Doubly-Periodic Scatterers Using Absorging and Periodic Boundary Conditions

Abstract: This paper presents a simple but accurate Finite Element Method (FEM) technique which is based on hexahedral parallelepiped finite elements and Whitney's edge basis functions. The technique is useful for the analysis of scattering from 1-D, 2-D, or from isolated 3-D scatterers. Numerical results are presented for a variety of such scatterers to show the usefulness of the method. The results also point to the need for the use of improved absorbing boundary conditions (ABCs) as well as of higher order basis functions when more accurate results are required. The emphasis in the proposed method is on its simplicity and versatility.

Arbitrarily-Shaped Slot-Coupled Microstrips and Their Applications in Microwave Integrated Circuits and Antennas

Abstract: The mixed-potential integral equation (MPIE) is solved by the method of moments in order to investigate arbitrarily-shaped slot-coupled microstrip discontinuity problems. A concise expression of the mutual coupling matrix element is utilized to assure numerical efficiency and accuracy. Comparison between this MPIE and other moment methods (such as MFIE and EFIE) is also carried out and discussed. In order to validate this modeling tool, a circularly polarized dual slot-coupled patch antenna and a single slot-coupled directional coupler arc investigated. Good agreement between numerical results and measurement is achieved. Two examples of dual slot-coupled patch antenna and annular ring slot antenna with microstrip line feed arc designed to provide desired circularly polarized radiation. In addition, a weak coupling slot-coupled directional coupler is designed by utilizing a pair of circular slots. Good performance for directivity, isolation, and return loss is obtained.

Modeling of highly conducting boundaries with tlm

Abstract: Time–domain methods have the advantage to easily model media or boundaries which can be described or characterized in time–domain. However, constitutive parameters or impedance for instance are usually frequency–domain concepts and cannot be readily modeled with time–domain methods. Some investigation regarding the TLM modeling of a class of dispersive media, namely conducting media which have high conductivity, is proposed. Starting with a review of different techniques for modeling reflected signals from highly conducting boundaries, a procedure which uses an analytical formulation via Laplace transform is described in details. The interface with the TLM algorithm is discussed for transmitted as well as reflected signals. Asymptotic behavior of solutions is investigated and simplified formulae proposed. Some examples are given and compared to analytical solutions for validation.

EM Scattering Using Nonuniform Mesh FDTD, PML and Mur's ABC

Abstract: In this paper, techniques are presented to extend FDTD, PML and Mur's second order ABC to the non-uniform mesh case for scattering problems from a consideration of improving the efficiency of computer codes to run on parallel computers. An alternative method to obtain the space derivatives in non-uniform mesh FDTD and non-uniform mesh PML ABC is presented which provides a second order accuracy. Mur's second order ABC has also been extended to the non-uniform mesh case with a First order accuracy which is an improvement over an existing method. A method of extending the pure scattered-field formulation to the PML medium is described. The electric fields inside a single layer dielectric sphere as well as a three layer dielectric sphere illuminated by a sinusoidal uniform plane wave have been computed which compare well with the results from an exact formulation.

On the Efficient Interpolation of Stochastic Band-Limited Signals*

Abstract: Interpolation of stochastic band-limited signals is of relevance both from the theoretical point of view and application purposes. It is well-known that the classical interpolation method for band-limited signals, which follows from the Whittaker-Kotel'nikov- Shannon sampling theorem, provides the appropriate answer to exactly reconstruct them. Unfortunately, whenever an open domain is in question, only truncated versions of cardinal series expansions can be employed and this generates artifacts on the interpolated data. In particular, the quality of the interpolation scheme affects the data statistics and is a relevant issue which must be carefully examined. An interpolation scheme, which minimizes statistical artifacts, is therefore of great interest. In this paper we propose the use of two efficient interpolation schemes and demonstrate that they provide much better results than the truncated cardinal series expansion.

Primary Shadow Radiation and Classical Models of Black Bodies

Abstract: The notion of primary shadow radiation is introduced. This is a wave field created by the transverse diffusion in the vicinity of the geometrical optics boundary behind a black screen with a special property. This special screen is located on the boundary between two neighboring Rieman spaces and consists of two faces. These faces together are not transparent to the wave field; but, each separately is transparent. We call this screen the Riemann black screen. The well known classical models of black screens are interpreted as special sets of Rieniann screens.

Via Hole and Parasitically Coupled Microstrip Antennas of Arbitrary Shape in Multi-Layered Substrates

Abstract: Microwave antenna performance optimization may be achieved by shaping the antenna properly, as well as with the correct antenna excitation design. This article presents the theoretical development of an algorithm which is very suitable for the design of microstrip antennas of arbitrary shape in multi-layered substrates. It includes the design of the antenna excitation either through parasitic coupling, or through a via hole transition from a microstrip line. The algorithm is applied for the design of a circularly polarized notched ring microstrip antenna coupled parasitically to a microstrip transmission line. The performance of via hole excitation of a rectangular patch antenna is also discussed.

Numerically Efficient Computation of a Complete Set of Eigenfunctions in Complex Cavities

Abstract: It is demonstrated, that both the divergence-free resonance modes and the irrotational electric and magnetic eigenfunctions are necessary for a rigorous modal expansion in complex cavities. A numerically efficient computation of the irrotational eigenfunctions based on the generalized scattering matrix technique is presented. A systematic searching strategy for the cavity eigenfunctions which is based on Foster's theorem is discussed. Finally two improvements of the modal expansion are suggested which significantly increase the accuracy and the numerical efficiency of this method, namely, the removal of the non-uniform convergence of some field series at the coupling apertures and the estimation of the asymptotic values of some slowly converging series related to the modal expansion.

On the Reconstruction of Dielectric Objects from Scattered Field Data Using the Heitler Equation

Abstract: The problem of determining a scattering potential from scattered field data is addressed within the Heitler equation. This equation relates the on shell components of the T matrix directly to the scattering potential. This relationship leads to a novel iterative reconstruction algorithm for recovering the distribution of the possibly complex index of refraction of the scattering potential from measurements of the scattered field outside the potential at, a single frequency. Reconstructions of cylindrical objects from data obtained in a suite of scattering experiments show that the method can handle relatively large objects compared to the wavelength whose index of refraction is close to the index of refraction of the surrounding medium.

Closed-Form Evaluation of Flux Integrals Appearing in a Fem Solution of the 2D Poisson Equation with Dipole Sources

Abstract: The finite element method (FEM) is a versatile method for numerically solving the 2-D Poisson equation with arbitrary inhomogeneity. In many applications, the sources that appear in the Poisson equation are dipole sources. For this important class of problems, an accurate solution may be obtained by using a subtraction formulation, in which the unknown is the original potential function minus the potential of the dipole in infinite homogeneous space. This formulation requires the evaluation of certain flux integrals that appear at the boundaries of the elements. Computing these flux integrals numerically requires considerable computation time, especially for element edges that are very close to the dipole, because the field is rapidly varying near the dipole. Furthermore, numerical errors in the computation may produce large errors in the solution for the potential, since the FEM matrix may often be ill-conditioned. A closed-form evaluation of these flux integrals for first- and second-order tria...

Advanced simulation techniques in emc based on the tlm method

Abstract: The application of the TLM method to electromagnetic compatibility (EMC) problems is described. The essential modelling principles of TLM are presented and the manner in which it is adapted to model problems involving electromagnetic interactions in complex practical configurations is outlined. Specific problems addressed are multiwire-coupling, field-to-wire coupling and penetration through shields and apertures. In order to deal with large problems accurately and efficiently, it is necessary to carefully examine meshing and to consider strategies which minimise Storage and run-time requirements. A brief description of the issues involved and of recent developments in TLM to enhance efficiency is given, together with a review of current capabilities and future developments which will meet practical needs.

Plane Wave Propagation in a Class of Knotted Media

Abstract: We consider media with complex polarizability properties. For linear reciprocal media with arbitrary dyadic permittivity and permeability for the field components in a certain plane, analytical solution for plane eigenwaves is constructed. Such media can be modeled or practically realized as knotted media, i.e., as composite structures with inclusions in form of simple knots. Basic properties of knotted media are discussed, a simple model for the frequency dispersion of the material parameters is suggested.

Important Considerations in the Evaluation of Absorbing Boundary Conditions

Abstract: In this paper, we study the interaction of an absorbing boundary condition (ABC) with the discretization error. In many cases the major source of error is due to the discretization error and how it couples to the ABC. In order to study the ABC, we consider three methods to solve the problem. Two of these are finite element methods with either nodal elements or the recently proposed solenoidal elements. The third is based on analytical methods. The effect of electrical size of the geometry as well as the excitation on the error is studied within the context of the interaction between numerical dispersion and the ABC errors.