Three-dimensional finite-element method with edge elements forelectromagnetic waveguide discontinuities

When three-dimensional electromagnetic problems are solved by the finite-element method based on a functional with three components of electric or magnetic field, spurious solutions appear if the traditional tetrahedral elements are used. It is shown in the present work that the finite-element method using edge elements succeeds in suppressing spurious solutions and that it succeeds in analyzing three-dimensional electromagnetic waveguide problems in the case of metal wedges     

The finite-element modeling of three-dimensional electromagneticfields using edge and nodal elements

An efficient and accurate finite-element method is presented for computing transient as well as time-harmonic electromagnetic fields in three-dimensional configurations containing arbitrarily inhomogeneous media that may be anisotropic. To obtain accurate results with an optimum computational efficiency, both consistently linear edge and consistently linear nodal elements are used for approximating the spatial distribution of the field. Compared with earlier work, the formulation is generalized by adding a method for explicitly modeling the normal continuity along interfaces that are free of surface charge. In addition, the conditions for efficiently solving time-harmonic problems using a code designed for solving transient problems are discussed. A general and simple method for implementing arbitrary inhomogeneous absorbing boundary conditions for modeling arbitrary incident fields is introduced     

The advantages of triangular and tetrahedral edge elements forelectromagnetic modeling with the finite-element method

In this paper, we examine the numerical dispersion properties of the tetrahedral edge element in comparison to other edge and nodal elements. For all nodal elements as well as hexahedral edge elements, the phase error is always either positive or negative for waves propagating at any incidence angle, which means that the error accumulates as the wave propagates from element to element. This effect can produce large errors for electrically large geometries. On the other hand, the tetrahedral edge elements can produce either a negative or positive phase error, depending on the direction of propagation through the element. For an unstructured mesh, phase cancellation occurs since the orientation of the tetrahedral elements are arbitrary. Because of the cancellation, the numerical dispersion error is very low for meshes composed of well-shaped tetrahedral edge elements. Numerical results are presented to demonstrate this point     

Analysis of lossy inhomogeneous planar layers using Taylor's series expansion

A general method is introduced to frequency domain analysis of arbitrary lossy inhomogeneous planar layers. In this method, all electric and magnetic parameters and also all components of the electric and magnetic fields are expanded in a Taylor's series. The field solutions are obtained after finding unknown coefficients of the series. The validity of the method is verified using analysis of some special types of planar layers.     

Thin sheet modeling using shell elements in the finite-element time-domain method

The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In this paper, the focus is on modeling of thin material sheets and coatings in the finite-element time-domain method. The proposed method is based on degenerated prism elements, so-called shell elements. For a dielectric sheet the thickness is assumed small compared to the wavelength for all frequencies of interest. An important characteristic of the method is that it takes the discontinuity of the normal electric field component at a dielectric interface into account. The accuracy of the method is demonstrated for three different scattering cases. Comparisons are made with analytical data and results obtained on grids for which the thickness of the sheets is resolved. Good agreement is observed in all cases.     

Modeling lossy anisotropic dielectric waveguides with the method oflines

This paper presents a new formulation useful for modeling waveguides constructed from lossy inhomogeneous anisotropic media. Our approach is based on a pair of Sturm-Liouville type wave equations that have been derived to handle inhomogeneous, diagonalized complex permittivity and permeability tensors. The method of lines is then applied to these wave equations, and related field equations, creating an indirect eigenvalue problem that correctly models this class of structure. Some refinements to the method of lines are also proposed, particularly, regarding the construction of the modal matrices found in the eigenvalue problem. Using our approach, modal dispersion curves have been computed for millimeter-wave and optical structures. Comparisons made with results available from the literature validate our approach     

A simplified formulation to analyze inhomogeneous waveguides withlossy chiral media using the finite-element method

In this paper, an efficient finite-clement formulation is presented for the analysis of the propagation characteristics in arbitrarily shaped lossy inhomogeneous waveguides loaded with chiral media. It is a simplified form of the one proposed for the bi-anisotropic media. In this formulation, showing no spurious modes, the frequency or the propagation constants may be treated as eigenvalues of a resulting sparse quadratic eigenproblem. However, in order to handle losses easily and to facilitate computation of complex modes, the frequency is specified as an input parameter and the eigensystem is solved for the complex propagation constant as the eigenvalue. This sparse eigensystem is further transformed into a generalized one, thus maintaining the sparse properties of the matrices. New numerical finite-element results are presented     

Analysis of lossy dielectric guides by transverse magnetic fieldfinite elements method

Recently a transverse magnetic field formulation of the finite element method for solving lightwave propagation in lossless optical waveguides was demonstrated using only two components of the magnetic field. We extend this formulation to include loss in the waveguides, and compare the results from this formulation with those of other formulations for three different types of waveguides. Our results from the new approach show good agreement with those from previously published data. No perturbation technique is needed to arrive at these results     

Unrelated illumination method for electromagnetic inversescattering of inhomogeneous lossy dielectric bodies

A method aimed at reconstructing the complex permittivities of inhomogeneous lossy dielectric bodies is proposed. The method is based on the principle that sufficient information about a dielectric body can be obtained from the scattered field when the body is illuminated by an incident field composed of unrelated components. The derivations of the formulas are presented, and some numerical examples are given. The accuracy of the results show that the method has great potential in electromagnetic inverse scattering and microwave imaging     

A quasi-wave method for determination of a general solution to the complex maxwell equations in an inhomogeneous anisotropic absorbing medium

A formal general solution to the homogeneous Maxwell equations is obtained in the form of a matrix asymptotic series for the case of a quasi-plane-layered medium in which complex tensors \(\hat \varepsilon \) and \(\hat \mu \) arbitrarily depend on Cartesian coordinate zand slowly change in the planes z=const. A recurrent system of matrix first-order linear ordinary differential equations for the coefficients of this series is derived. In contrast to the method of geometric optics, this solution, even in the first approximation, takes into account the wave polarization and has a wider range of application.     

Analysis of lossy planar transmission lines by using a vectorfinite element method

The vector finite element method with hybrid edge/nodal triangular elements is extended for the analysis of lossy planar transmission lines. In order to handle lossy conductor transmission lines, the present approach includes the effect of finite conductivity of a lossy area, and the dissipations in metallic conductors and dielectrics are calculated directly by considering a complex permittivity for the lossy region of interest. A propagation constant formulation is used in the FEM, which avoids spurious solutions absolutely and can handle sharp metal edges in inhomogeneous electromagnetic waveguides. Numerical examples are computed for microstrip lines, finlines, and triplate strip lines. The results obtained agree well with the earlier theoretical and experimental results, and thus show the validity of the method. Also, the current distributions on the lossy microstrip lines with finite strip thickness and isotropic substrates are presented     

Analysis of waveguide discontinuities using edge elements in ahybrid mode matching/finite elements approach

A mode matching (MM)/finite element method (FEM) for the analysis of waveguide discontinuities is presented. The hybrid approach described combines the computational efficiency of the modal analysis with the versatility and flexibility of FEM and enables us to accurately model arbitrary cross section waveguides, where modal expansions cannot be derived analytically. The proposed procedure is based on the edge element expansion of the transverse field components for the direct calculation of the coupling integrals involved in the MM formulation. Numerical and experimental results are presented to show the validity and the accuracy of the method     

有限元法与UTD结合计算机载天线方向图

为了计算机载天线的方向图,近区矢量场可以作为有限元法(FEM)与UTD(一致性几何绕射理论)的结合点,将二者结合以解决类似的工程问题.首先利用基于有限元法的软件HFSS计算相控阵天线的近区矢量场,然后将此结果作为UTD方法的源进一步计算以预测该相控阵天线的受扰特性.结果表明这种方法可有效用于分析机载相控阵天线的辐射特性.     

Inverse scattering using the finite-element method and a nonlinearoptimization technique

A new spatial-domain technique for the reconstruction of the complex permittivity profile of unknown scatterers is proposed in this paper. The technique is based on a combination of the finite-element method (FEM) and the Polak-Ribiere nonlinear conjugate gradient optimization algorithm. The direct scattering problem is explicitly dealt with by means of the differential formulation and it is solved by applying the FEM. The inversion methodology is oriented to minimizing a cost function, which consists of a standard error term and regularization term. A sensitivity analysis, which is carried out by an elaborate finite-element procedure, results in the determination of the direction required for correcting the profile. Significant reduction of the computation time is obtained by introducing the adjoint state vector methodology. The efficiency of the presented inversion technique is validated by applying it to the inversion of synthetic scattered far-field measurements, which are corrupted by additive noise     

用2.5维的边缘元法分析屏蔽导波结构中含非匀质基片的微带线

微波单片集成电路（MMIC）的优化设计已受到工业界的关注，而MMIC元件广为采用含非匀质基片的微带线。用2．5维的边缘元法研究了这类屏蔽导波结构的色散特征，所导出的公式适用于各种复杂形状的导波结构。对某些简单结构，该结果与用其它解析和数值方法得出的数据相符；对某些复杂结构，提供的新结果预示了扩展应用的可能性。     

Generation of lossy mode resonances (LMR) using perovskite nanofilms

The results presented here show for the first time the experimental demonstration of the fabrication of lossy mode resonance(LMR) devices based on perovskite coatings deposited on planar waveguides. Perovskite thin films have been obtained by means of the spin coating technique and their presence was confirmed by ellipsometry, scanning electron microscopy, and X-ray diffraction testing. The LMRs can be generated in a wide wavelength range and the experimental results agree with the theoretical s...     

Microwave imaging using the finite-element method and a sensitivity analysis approach

A method for reconstructing the constitutive parameters of two-dimensional (2-D) penetrable scatterers from scattered field measurements is presented. This method is based on the differential formulation of the forward scattering problem, which is solved by applying the finite-element method (FEM). Given a set of scattered field measurements, the objective is to minimize a cost function which consists of two terms. The first is the standard error term, which is related to the measurements and their estimates, while the second term, which is related to the Tikhonov regularization, is used to heal the ill posedness of the inverse problem. The iterative Polak-Ribière nonlinear conjugate gradient algorithm is applied to the minimization of the cost function. During each iteration of the algorithm, the direction of correction is computed by using a sensitivity analysis approach, which is carried out by an elaborate finite-element scheme. The adoption of the finite-element method results in sparse systems of equations, while the computational burden is further reduced by applying the adjoint state vector methodology. Finally, a microwave medical imaging application, which is related to the detection of proliferated bone marrow, is examined, while the robustness of the proposed technique in the presence of noise and for different regularization levels is investigated.     

A comparison of anisotropic PML to Berenger's PML and itsapplication to the finite-element method for EM scattering

The use of an anisotropic material for the boundary truncation of the finite-element method is considered. The anisotropic material properties can be chosen such that a plane-wave incident from free space into the anisotropic halfspace has no reflection. Because there is no reflection, the material is referred to as a perfectly matched layer (PML). The relationship between the anisotropic PML and the original PML proposed by Berenger (see J. Comp. Phys., vol.114, p.185-200, October 1994) is considered. The anisotropic PML is applied to the finite-element solution of electromagnetic (EM) scattering from three-dimensional (3-D) objects. Numerical results are presented to demonstrate the accuracy of the PML     

Time-domain analysis of lossy active transmission lines using FDTD method

In this paper, an accurate and efficient method for analysis of a GaAs MESFET including frequency-dependent losses of the electrodes in the time domain is presented. The time domain analysis is obtained based on the fully distributed model using finite-difference time-domain (FDTD) technique, with the assumption of the skin effect losses. The time-domain results are verified using the conventional time-domain to frequency-domain (TDFD) solution technique.     

Generation of accurate rational models of lossy systems using the Cauchy method

A method to generate an accurate rational model of lossy systems from either measurements or an electromagnetic analysis is presented. The Cauchy method has been used to achieve this goal. This formulation is valid either for lossless or lossy system responses. Thus, it provides an improvement over the conventional Cauchy method and takes into account the relationship between the transmission and reflection coefficients of the system which in our case is a filter. The resulting model can be used to extract the coupling structure of the filter. Two examples have been presented. One deals with measured data and the other one uses numerical simulation data from an electromagnetic analysis.