Equivalent Magnetic Surface Currents Research Articles

Huygens' surface excitation for the finite element method applied to Maxwell's equations – A construction based on Nitsche's method

We present a Huygens' surface for the finite element method applied to Maxwell's equations, where the equivalent electric and magnetic surface currents are incorporated in the weak form by means of Nitsche's method. The proposed method preserves the reciprocity of Maxwell's equations and it allows for the computation of the total field inside the Huygens' surface, whereas on its outside only the scattered field is computed. The equivalent magnetic surface current at the Huygens' surface requires a double representation of the discontinuous tangential component of the electric field and we demonstrate that it can be efficiently combined with a previously presented higher-order brick-tetrahedron hybridization. Also, it is demonstrated that the near-to-far-field transformation can be evaluated in an accurate manner if collocated with the Huygens' surface, which allows for a compact computational domain and a reduction in the required computational resources. The proposed Huygens' surface is tested on two scattering problems with perfect electric conductor scatterers: (i) a sphere that demonstrates second-order convergence towards the analytical result for a piecewise linear approximation of the electric field; and (ii) a double ogive with two sharp tips which gives a computed monostatic radar cross section that compares well with measurements and computations in the open literature for both polarizations.

Discontinuous Galerkin integral equation method for light scattering from complex nanoparticle assemblies.

This paper presents a discontinuous Galerkin (DG) integral equation (IE) method for the electromagnetic analysis of arbitrarily-shaped plasmonic assemblies. The use of nonconformal meshes provides improved flexibility for CAD prototyping and tessellation of the input geometry. The formulation can readily address nonconformal multi-material junctions (where three or more material regions meet), allowing to set very different mesh sizes depending on the material properties of the different subsystems. It also enables the use of h-refinement techniques to improve accuracy without burdening the computational cost. The continuity of the equivalent electric and magnetic surface currents across the junction contours is enforced by a combination of boundary conditions and local, weakly imposed, interior penalties within the junction regions. A comprehensive study is made to compare the performance of different IE-DG alternatives applied to plasmonics. The numerical experiments conducted validate the accuracy and versatility of this formulation for the resolution of complex nanoparticle assemblies.

Efficient $2\times2$ Printed Circuit Band-Gap Cavity-Backed Slot Antenna

In this article, a novel structure is proposed for the realization of cavity section in the printed gap waveguide (PGW) technology. For the proof of the concept, a multilayer cavity-backed slot antenna element is designed and fabricated so that its performance can be compared to the devices in the literature made by printed circuit board (PCB) technology and also by metal parts using the CNC machine. The proposed structure benefits from the advantages of efficient, low cost, simplified fabrication process, lightweight, and high aperture efficiency compared to common cavity-backed antennas. To manage the available space, the feed is connected to the antenna cavity from the underneath using a coupling aperture. The proposed configuration simplifies the integration of accessory devices in antenna arrays, such as feed networks, phase shifters, and amplifiers. Also, the separation of feed network from the radiation slot section prevents any unwanted radiation. Using the mode analysis, four slots were implemented in the proposed cavity to achieve four equivalent magnetic surface currents with identical phase and magnitude. The antenna operating frequency is 16 GHz, the realized antenna radiation and aperture efficiencies are over 92% and 81.6%, respectively, and its achieved gain is 12 dBi.

MoM Analysis of Cavity-Backed Annular Spherical Antennas

This paper presents a full-wave solution for cavity-backed annular spherical antennas. The formulation is based on the equivalence principle and the application of method of moments, for modeling the equivalent surface magnetic currents. Results are presented for input impedance and radiation patterns.

Multilevel adaptive cross approximation for efficient modeling of 3D arbitrary shaped eddy current NDE problems

In this article, the multilevel adaptive cross approximation (MLACA) algorithm is presented to accelerate the boundary element method (BEM) for eddy current nondestructive evaluation (NDE) 3D problems involving arbitrary shapes. The Stratton-Chu formula, which does not have the low frequency breakdown issue, has been selected for modeling. The equivalent electric and magnetic surface currents are expanded with Rao-Wilton-Glisson (RWG) vector basis functions while the normal component of the magnetic field is expanded with pulse basis functions. The MLACA compresses the rank deficient matrices with the ACA and the butterfly algorithm. We improve the efficiency of MLACA by truncating the integral kernels after a certain distance and applying the multi-stage (level) algorithm adaptively based on the criteria for different operators to further decrease the memory and CPU time requirements while keeping almost the same accuracy comparing with the traditional MLACA. The proposed method is especially helpful to deal with the large solution domain issue of the BEM for eddy current problems. Numerical predictions are compared with the analytical, the semi-analytical predictions and the experimental results for 3D eddy current NDE problems of practical interest to demonstrate the robustness and efficiency of the proposed method.

Plane Wave Diffraction by Arbitrary-Angled Lossless Wedges: High-Frequency and Time-Domain Solutions

This paper concerns the diffraction phenomenon originated by a uniform plane wave impacting an arbitrary-angled lossless dielectric wedge with planar surfaces. The high-frequency diffraction coefficients are obtained by performing uniform asymptotic evaluations of the radiation integrals resulting from the physical optics approximation of the electric and magnetic equivalent surface currents located on the inner and outer faces of the wedge. The final expressions are in closed form and contain the standard transition function of the uniform theory of diffraction and the Fresnel reflection and transmission coefficients related to the geometrical optics propagation mechanisms. Moreover, they allow a simple physical interpretation of each contribution and they are easy to use and to implement in a computer code. The knowledge of such diffraction coefficients in the frequency domain permits to apply the inverse Laplace transform to obtain the time-domain counterparts, which enable the evaluation of the transient diffracted field originated by an arbitrary function plane wave.

Radiation from a Cavity-Backed Circular Aperture Array Antenna Enclosed by an FSS Radome

Radiation from a cavity-backed circular aperture array antenna enclosed by a frequency selective surface (FSS) radome is studied using the hybrid analysis method, by combining the mode matching method, the ray tracing technique, and Huygens’s principle. The equivalent magnetic surface currents on the apertures are derived from the aperture electromagnetic fields, which are calculated based on the mode matching method. The rays are generated from the equivalent magnetic surface currents and used to analyze the FSS radome based on the ray tracing technique. After being obtained from both the mode matching method and the ray tracing technique, electromagnetic fields on an outermost radome are transformed into the equivalent electric and magnetic surface currents using Huygens’s principle. The radiated fields are computed from the equivalent surface currents and compared with the measured data.

Novel Spatial Domain Integral Equation Formulation for the Analysis of Rectangular Waveguide Steps Close to Arbitrarily Shaped Dielectric and/or Conducting Posts

AbstractIn this paper, a novel integral equation formulation expressed in the spatial domain is proposed for the analysis of rectangular waveguide step discontinuities. The important novelty of the proposed formulation is that which allows to easily take into account the electrical influence of a given number of arbitrarily shaped conducting and dielectric posts placed close to the waveguide discontinuity. For the sake of simplicity, and without loss of generality, the presented integral equation has been particularized and solved for inductive rectangular waveguide geometry. In this case, the integral equation mixed‐potentials kernel is written in terms of parallel plate Green's functions with an additional ground plane located on the waveguide step. Therefore, the unknowns of the problem are reduced to an equivalent magnetic surface current on the step aperture and equivalent magnetic and electric surface currents on the dielectric and conducting posts close to the discontinuity. The numerical solution of the final integral equation is efficiently computed after the application of acceleration techniques for the slowly convergent series representing the Green's functions of the problem. The numerical method has been validated through several simulation examples of practical microwave devices, including compact size band‐pass cavity filters and coupled dielectric resonators filters. The results have been compared to those provided by commercial full‐wave electromagnetic simulation software packages, showing in all cases a very good agreement, and with substantially enhanced numerical efficiencies.

Fast Electromagnetic Analysis of Emissions From Printed Circuit Board Using Broadband Green's Function Method

In this paper, we apply the broadband Green's function with low wavenumber extraction (BBGFL) to fast modeling of the radiated emissions from printed circuit boards (PCBs). We study power bus structures for electromagnetic interference/compatibility (EMI/EMC). We use the BBGFL to compute the Green's function over broadband frequencies along the boundary walls of arbitrarily shaped power/ground planes. The broadband Green's function is calculated by using modal expansions and low wavenumber extraction. Because the modal expressions are independent of frequencies, they are computed once and used for all frequencies. The radiated fields are derived from the equivalent magnetic surface currents on boundary walls using Huygen's equivalent principle. Results are illustrated up to 10 GHz and for arbitrary shaped PCB up to 5 inches in size. The accuracy and computational efficiency of the present method are compared with the method of moments (MoM) and the commercial tool HFSS. The BBGFL results are in good agreement with MoM and HFSS. The BBGFL is several hundred times faster than MoM and HFSS for broadband simulations. The significant improvement in computational efficiency makes this technique useful for electronic design automation to EMI/EMC applications.

Cavity-excited Huygens' metasurface antennas for near-unity aperture illumination efficiency from arbitrarily large apertures.

One of the long-standing problems in antenna engineering is the realization of highly directive beams using low-profile devices. In this paper, we provide a solution to this problem by means of Huygens' metasurfaces (HMSs), based on the equivalence principle. This principle states that a given excitation can be transformed to a desirable aperture field by inducing suitable electric and (equivalent) magnetic surface currents. Building on this concept, we propose and demonstrate cavity-excited HMS antennas, where the single-source-fed cavity is designed to optimize aperture illumination, while the HMS facilitates the current distribution that ensures phase purity of aperture fields. The HMS breaks the coupling between the excitation and radiation spectra typical to standard partially reflecting surfaces, allowing tailoring of the aperture properties to produce a desirable radiation pattern, without incurring edge-taper losses. The proposed low-profile design yields near-unity aperture illumination efficiencies from arbitrarily large apertures, offering new capabilities for microwave, terahertz and optical radiators.

High-Frequency Evaluation of the Field Inside and Outside an Acute-Angled Dielectric Wedge

Explicit closed form solutions are presented for the high-frequency evaluation of the electromagnetic field produced inside and outside an acute-angled lossless penetrable wedge. Both cases of E- and H-polarized incident plane waves are addressed in the study. The problem is tackled and solved in the framework of the uniform theory of diffraction, so that the total field at the observation point is determined by adding the geometrical optics contributions and the diffraction one. This last is obtained by performing a uniform asymptotic evaluation of the radiation integrals arising from a physical optics approximation for the equivalent electric and magnetic surface currents lying on the infinite wedge boundaries. No limitation exists on the refractive index of the structure. The accuracy of the solution is assessed by comparisons with data produced by numerical tools. The physical optics approximation gives rise to inaccuracies when using the solution at grazing incidence and in correspondence of the dielectric interfaces.

Diakoptic Approach Combining Finite-Element Method and Method of Moments in Analysis of Inhomogeneous Anisotropic Dielectric and Magnetic Scatterers

A new diakoptic method combining the finite-element method and the method of moments is proposed for analysis of inhomogeneous anisotropic dielectric and magnetic scatterers. The method splits the original electromagnetic system into a number of closed-region finite-element method subsystems containing material complexities and an open-region method of moments subsystem, which are analyzed independently. The solution to the original problem is obtained from linear relations between coefficients in expansions of equivalent electric and magnetic surface currents on diakoptic boundary surfaces. Diakoptic electric sources and the magnetic field in finite-element method subsystems are connected using dual sets of higher-order hierarchical basis functions.

Quasioptical Theory of Relativistic Čerenkov Generators and Amplifiers

We study propagation of electromagnetic waves above periodically corrugated surfaces and excitation of such waves by rectilinear relativistic electron flows within the framework of the quasioptical approach. Near a periodic structure, the electromagnetic field can be expanded into a sum of spatial harmonics, which in the case of a low corrugation depth are paraxial wave beams whose relationship is described within the framework of the method of equivalent surface magnetic currents. Under these assumptions, we obtain a dispersion relation for normal waves, and two extreme cases are singled out on its basis. In the first case, the radiation frequency is far from the Bragg resonance frequency, and wave propagation can be described within the framework of the impedance approximation, where the field is represented in the form of a fundamental slow wave and its spatial harmonics. In the case of interaction with the electron flow, this case corresponds to a convective instability, where the particles are synchronous with the fundamental (zeroth) or higher spatial harmonics (the traveling-wave tube regime), and an absolute instability, where the particles are synchronous with the spatial harmonic of the backward waves (the backward-wave oscillator regime). In the second extreme case, which is realized at frequencies close to the Bragg resonance, the field is represented as two counter-propagating quasioptical wave beams. This determines the absolute character of the instability, which is used in generators of the surface wave at the π-type modes. Basing on the developed theory, we determined the main characteristics of the amplifier and generator schemes including growth rates, energy exchange efficiency, and the formation of a spatial self-consistent structure of the radiated field. Good prospects for application of relativistic amplifiers and generators of surface waves in the submillimeter-wave band is demonstrated.

Diffraction by 90° penetrable wedges with finite conductivity

This study concerns the diffraction problem relevant to a plane wave normally incident with respect to a 90° wedge. A penetrable material with finite conductivity forms the structure. A high-frequency solution is here obtained by adopting a physical optics approximation for the equivalent electric and magnetic surface currents involved in the radiation integrals used to represent the fields scattered in the inner region of the wedge and the surrounding space. Uniform asymptotic evaluations of such integrals lead to closed form expressions for the diffraction coefficient in terms of the transition function of the uniform theory of diffraction and the Fresnel coefficients for the reflection and transmission mechanisms. No limitation exists on the loss tangent of the medium. Comparisons with numerical tools assess the effectiveness of the proposed solutions for the field diffracted in the inner and outer regions.

Time-Domain Electric Current Formulation for the Analysis of Arbitrarily Shaped Dielectric Bodies

In this paper, we present a novel stable time-domain procedure to analyze the transient electromagnetic response from 3-D dielectric bodies. The principal method is based on the application of electric- and magnetic-field boundary conditions on the surfaces of homogeneous structures while considering the electric currents as unknowns. Triangular patches as well as quadrangular patches model the surface of the composite body. The method of moments is implemented to solve the resultant integral equations. The scattered electromagnetic fields that are dependent only on the electric surface currents are computed with less effort compared with other methods, which use both equivalent electric and magnetic surface currents. Comparing these methods, also our innovative method reduces the number of the submatrix elements by considering them as zero, when dealing with more than one homogeneous body, or combined PEC and body structures.

Useful Solutions for Plane Wave Diffraction by Dielectric Slabs and Wedges

This work presents an overview of available uniform asymptotic physical optics solutions for evaluating the plane wave diffraction by some canonical geometries of large interest: dielectric slabs and wedges. Such solutions are based on a physical optics approximation of the electric and magnetic equivalent surface currents in the involved scattering integrals. The resulting diffraction coefficients are expressed in terms of the geometrical optics response of the considered structure and the standard transition function of the Uniform Geometrical Theory of Diffraction. Numerical tests and comparisons make evident the effectiveness and reliability of the presented solutions.

A current-matrix model for metallic and dielectric postwall waveguides

Waveguide structure integration in planar substrates for use in microwave components has received considerable attention in recent years. Waveguides with side walls consisting of cylindrical posts (postwall waveguides or PWWGs) are of interest, since they are compatible with standard PCB fabrication technology and exhibit low loss. In this paper we present an electromagnetic model for PWWG building blocks, whose characteristics are described entirely in terms of equivalent electric and magnetic surface currents at predefined port interfaces consistent with Lorentz’s reciprocity theorem. Introducing input and output surface currents, we determine the response of a block for a given port excitation. The expansion of the currents in terms of suitable bases results in a matrix that relates input and output currents. The scattering parameters of a building block are determined by expressing waveguide modes in terms of these bases. This facilitates the future integration of PWWG components in a microwave circuit simulator. We validate our model by comparing the results for simulated and measured uniform PWWGs implemented with metallic and dielectric posts.

Plane-wave diffraction by an obtuse-angled dielectric wedge

Uniform high-frequency solutions in closed form are derived for the diffraction of a plane wave normally impacting on a penetrable wedge having an obtuse apex angle and arbitrary dielectric permittivity. The approach used here takes advantage of a physical optics approximation for the electric and magnetic equivalent surface currents in the scattering integrals related to the inner region of the wedge and the surrounding space. Numerical tests and comparisons with finite-difference time-domain results demonstrate the accuracy and effectiveness of the proposed solutions.

A Uniform Asymptotic Solution for the Diffraction by a Right-Angled Dielectric Wedge

We propose a uniform asymptotic solution for the field diffracted by a lossless right-angled dielectric wedge illuminated by a plane wave at normal incidence. The diffraction problem is solved by splitting the observation domain in the inner region of the wedge and the surrounding free-space. The scattered electric field in each region is assumed to be originated by a set of equivalent electric and magnetic surface currents involved in the well-known radiation integral. Such currents are localized on the interior and exterior faces of the wedge, and expressed in terms of the corresponding geometrical optics field. Useful analytical manipulations and asymptotic evaluations of the resulting integrals allow one to obtain the diffraction coefficients in terms of the Fresnel's reflection and transmission coefficients of the structure and the transition function of the uniform geometrical theory of diffraction. The related diffracted field compensates the discontinuities of the geometrical optics field and gives total field levels in good agreement with finite difference time domain results.

Analysis of Electromagnetic Scattering and Radiation From Finite Microstrip Structures Using an EFIE-PMCHWT Formulation

An EFIE-PMCHWT formulation is obtained in an easy manner for finite microstrip structures when they are regarded as separate conducting and dielectric bodies. By simply eliminating equivalent magnetic surface currents on the dielectric interface where the conductor is attached to, the formulation is reduced to a formulation which is identical to that originally proposed for conductors with partial dielectric coatings. Using the resulting EFIE-PMCHWT formulation, electromagnetic radiation from a patch antenna due to a localized voltage source on the conducting patch is computed. Good agreement is observed between the calculated and measured radiation patterns.