Electric Field Integral Equation Research Articles

The free-space dyadic Green function is orthogonal to its curl

The free-space dyadic Green function in electromagnetics is orthogonal to its own curl on any spherical surface whose center is the source point.

Dipole-dipole interactions in the presence of a topological insulator stratified sphere: dyadic Green’s function method

Dyadic Green’s functions (DGFs) are developed for calculating electric fields induced by multiple sources in the presence of a topological insulator (TI) stratified sphere within the framework of axion electrodynamics. Generalizing our previous work, these sources can be placed at arbitrary locations rather than be limited outside the TI stratified sphere. Utilizing these DGFs, we explore the topological magneto-electric (TME) effect of the dipole–dipole interaction in the presence of composite structures of an alternating metal-TI stratified sphere, causing some modifications of the energy transfer (ET) enhancement spectrum. Furthermore, for the multipolar resonances of the metal shells, we find the TME-induced red-shifts of each bonding and antibonding mode in the ET enhancement spectrum are independent on the locations and orientations of the two dipoles but only depend on the configuration of these composite structures. These phenomenological findings provide some useful guidance with experimenters to design realistic experiments for exploring possible unique TME signatures via the energy transfer between molecules near/in TI multicoated nanoparticles in the near-infrared region.

Low-Frequency Stabilization for the B-Spline-Based Isogeometric Discretization of the Electric Field Integral Equation

Low-Frequency Stabilization for the B-Spline-Based Isogeometric Discretization of the Electric Field Integral Equation

Composite Scattering Study of Layered Rough Surface withTarget based on CCIA

In this paper, a fast Cross Coupling iterative Approach (CCIA) is proposed for studying the composite scattering of the layered rough surfaces with buried target, which uses forward backward method (FBM) to solve the electric field integral equations (EFIE) of the layered rough surface and bi-conjugate gradient method (BI-CG) to solve the EFIE of the target, and the interaction between the rough surface and the target is achieved by updating the excitation term. The algorithm is applied to calculate the composite scattering coefficients of the rough surface with a buried target, the results match with those of the traditional numerical algorithm MOM while the error can be reduced to 10−3 by 6 iterations, and the convergence speed and calculation accuracy meet the requirements. The composite scattering coefficients and Angular Correlation Function (ACF) amplitudes of layered rough surface and dielectric targets with different conditions are calculated, and the effects of various factors such as target size and burial depth on the composite scattering characteristics are discussed. It is found that the buried targets will have a great influence on the scattering characteristics, weakening or neglecting the coupling between them will lead to larger errors. Moreover, the results show that ACF can suppress scattering from rough surfaces well, making the scattering characteristics of the target more obvious, which is important for detecting underground targets.

Far-zone analytical expressions for electromagnetic waves produced by a uniform-current loop placed in a uniaxial dielectric-magnetic material

We investigate the radiation generated by a current loop situated within an unbounded uniaxial dielectric-magnetic material characterized by a uniform current distribution. We employ dyadic Green functions in the frequency domain to derive closed-form expressions for the far-field radiation. Our analytical findings distinguish between two scenarios: one in which the loop’s axis aligns parallel to the optic axis and another where it is perpendicular to the optic axis. In cases where the loop’s axis parallel’s the optic axis, only magnetically extraordinary wave is emitted as a consequence. However, when the loop’s axis is perpendicular to the optic axis, both electrically and magnetically extraordinary waves are emitted. Our results demonstrate a pronounced dependence of the radiation pattern on the loop’s size, as observed for various loop radii.

Solution of electromagnetic scattering field of adjacent transmission towers based on reciprocity theorem

Due to the large number of transmission towers being built, the dense distribution of transmission towers is inevitable in some areas. Densely distributed transmission towers will generate severe electromagnetic coupling, which will affect the setting of the passive interference protection distance between transmission towers and adjacent radio stations. Therefore, based on the traditional algorithm for solving the electromagnetic scattering field of a single electrically large target in wide area space, the electromagnetic coupling effect between multiple adjacent transmission towers within a range of 10 times the signal wavelength was considered. Based on the reciprocity relationship between the scattering electric field and the source and the introduced auxiliary field source as the intermediate variable, the electric field integral equation of the secondary scattering field generated by the electromagnetic coupling effect of adjacent transmission towers was derived, and the secondary scattering field is superimposed with the primary scattering field of the transmission generated by the electromagnetic wave excitation of the radio station, obtaining the electromagnetic scattering field at any point. In order to verify the accuracy of the algorithm proposed in this article, the scaled model experiments for the electromagnetic coupling effect between two transmission towers in an anechoic chamber were conducted. The average error of the algorithm proposed in this article is 6.73%, while the error of traditional algorithms is 20.18%. Compared with the traditional algorithm, the accuracy of the proposed algorithm is improved by 13.45%.

Research on Quasi-isotropic Radiation of Small Circular Arc Antenna

The radiation characteristics of circular arc antennas are studied by applying the method of moments (MoM) to solve the electric field integral equation (EFIE). Based on the triangular current distribution of small circular arc antennas, the analytical expression of radiation fields of circular arc antennas is derived. It is found that the circular arc antenna is equivalent to a superposition of an electric dipole and a magnetic dipole, resulting in near isotropic radiation pattern. Finally, both MoM and CST simulations show that the small arc antenna can realize the near isotropic radiation pattern.

Research on electromagnetic scattering characteristics of dipole clusters

AbstractThis paper equates chaff clouds to dipole clusters and studies the electromagnetic scattering problem of dipole clusters based on the linear method of moment (LMM) that solve the electric field Integral equation with the pulse basis function. Firstly, the radar cross section (RCS) of three dipole elements is calculated. The dipole element is divided into 11 segment line units using pulse basis functions. The actual chaff clouds are modeled as two nearest dipole cluster models, which are cubic dipole cluster with uniform distribution formed and spherical dipole cluster with Gaussian distribution formed. The total RCS and total E‐Field magnitude of two dipole cluster models were calculated. Finally, two physical models are constructed based on the simulation models and an experiment is designed. The electromagnetic scattering characteristics of the two models are measured, which verifies the accuracy of the simulation results and the operability of the experiment.

An efficient adaptive h‐refinement for the RWG‐based electric field integral equation applied to antennas with waveport

AbstractAn approximation scheme that combines approximate solutions with error estimators to accelerate the adaptive h‐refinement of the RWG‐based method of moments (MoM) with the electric field integral equation (EFIE) is presented. The scheme is effectively implemented by using the near‐field matrix to solve the approximate solution. Several conventional error estimators incorporated with the scheme are investigated. Compared to using the full MoM system, it significantly reduces the computational cost while maintaining the refinement effect. Numerical results indicate that the scheme could accelerate the adaptive refinement, yielding significant reductions in computational time and memory requirements.

A Low-Frequency Stable, Excitation Agnostic Discretization of the Right-Hand Side for the Electric Field Integral Equation on Multiply-Connected Geometries

In order to accurately compute scattered and radiated fields in the presence of arbitrary excitations, a low-frequency stable discretization of the right-hand side (RHS) of a quasi-Helmholtz preconditioned electric field integral equation (EFIE) on multiply-connected geometries is introduced, which avoids an ad-hoc extraction of the static contribution of the RHS when tested with solenoidal functions. To obtain an excitation agnostic approach, our approach generalizes a technique to multiply-connected geometries where the testing of the RHS with loop functions is replaced by a testing of the normal component of the magnetic field with a scalar function. To this end, we leverage orientable global loop functions that are formed by a chain of Rao-Wilton-Glisson (RWG) functions around the holes and handles of the geometry, for which we introduce cap surfaces that allow to uniquely define a suitable scalar function. We show that this approach works with open and closed, orientable and non-orientable geometries. The numerical results demonstrate the effectiveness of this approach.

Integral Equation Residuals for Error Estimation and Internal Resonance Detection

The performance of the four basic residual error estimators for perfectly conducting targets is evaluated in connection with the Rao-Wilton-Glisson method of moments numerical solutions of the electric field, magnetic field, and combined field integral equations. Results for 17 perfectly conducting test targets are used to evaluate the performance. Tangential-field residuals appear to be more reliable than normal-field residuals for assessing accuracy. Residual estimates are shown to be poor when used to assess an equation based on the same boundary condition as the residual. Residuals are sensitive to internal resonance modes associated with the complementary boundary condition and can be used to detect spurious solutions due to their presence.

Laplacian Filtered Loop-Star Decompositions and Quasi-Helmholtz Filters: Definitions, Analysis, and Efficient Algorithms

Quasi-Helmholtz decompositions are fundamental tools in integral equation modeling of electromagnetic problems because of their ability of rescaling solenoidal and non-solenoidal components of solutions, operator matrices, and radiated fields. These tools are however incapable, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">per se</i> , of modifying the refinement-dependent spectral behavior of the different operators and often need to be combined with other preconditioning strategies. This paper introduces the new concept of filtered quasi-Helmholtz decompositions proposing them in two incarnations: the filtered Loop-Star functions and the quasi-Helmholtz filters. Because they are capable of manipulating large parts of the operators’ spectra, new families of preconditioners and fast solvers can be derived from these new tools. A first application to the case of the frequency and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> -refinement preconditioning of the electric field integral equation is presented together with numerical results showing the practical effectiveness of the newly proposed decompositions.

Isogeometric Analysis of Electric Field Integral Equation on Multipatch NURBS Surfaces With Discontinuous Galerkin

Isogeometric Analysis of Electric Field Integral Equation on Multipatch NURBS Surfaces With Discontinuous Galerkin

An efficient dual-scale method for analysis of EMI problems resulted from radiation sources

An efficient dual-scale method, which integrates parabolic equation (PE) with electric field integral equation (EFIE) formulated via the Rao-Wilton-Glisson moment method (RWG-MOM), is proposed to analyze the electromagnetic interference (EMI) problems resulted from radiation sources. This method is implemented by decomposing the original intractable multi-scale problem domain into two sub-regions: (1) modeling of the complicated ambient electromagnetic fields by PE and (2) solution of the fields coupling to the exposed electronic devices by RWG-MOM. Frequency-sweep and Fourier synthesis techniques are applied to calculate the transient currents and voltages. The proposed method is able to fully model the disturbances of the electromagnetic fields by multi-path effects. Besides, it reduces the memory footprint and the CPU computing time effectively compared to the traditional full-wave electromagnetic methods. Numerical examples are presented, and the simulation results indicate that this method is well suitable for the EMI analysis of external radiation sources.

Analyzing electromagnetic scattering from complex multi-layer patch objects using a multi-trace domain decomposition method

The local-coupling multi-trace and domain decomposition method originally developed to analyze electromagnetic scattering from closed composite objects is extended to solve the scattering from complex multilayer patch objects. Different from the traditional global radiation coupling surface integral equation domain decomposition method and contact-region modeling method (CRM), the local-coupling property yields many excellent properties, highly sparse matrix, better computational performance, etc. In this novel proposed method, the multilayer patch objects are decomposed into many independent sub-domains, and each sub-domain is assumed as a homogeneous dielectric subdomain to formulate the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE) for dielectrics as the governing equations. The corresponding boundary condition of the perfect electric conducting (PEC) surface sheet is then achieved by adopting Robin transmission conditions (RTCs) to PEC surfaces, termed PEC-RTCs. The final resulting equation yield a better performance than the traditional method. Numerical examples validate the advantages of the proposed method.

Dual-band higher-order topological states and four-wave mixing in plasmonic valley-Hall metasurfaces

Higher-order topological states in plasmonic metasurfaces are of great importance in practice for their tight confinements and high field enhancements, providing many promising nonlinear applications such as robust quantum light source through four-wave mixing (FWM). However, previous works are limited to single-band modes and FWM processes based on second-order topological corner states have still not been revealed. In this work, we propose a plasmonic valley-Hall topological metasurface, which is modelled based on coupled dipole approximation with dyadic Green's functions containing retarded long-range interaction terms. Simultaneous lifting of Dirac degeneracies in two bandgaps due to inversion-symmetry breaking results in dual-band second-order topological states, which are robust against structural disorder. We present a theoretical approach for considering the nonlinear interaction in dipole arrays and numerically show nonlinear generation of corner mode at signal frequency via the FWM process by pumping with edge modes. The results presented in this work will pave a broad way towards the wide applications of topological plasmonic metasurfaces.

Multi-level Power Series Solution for Large Surface and Volume Electric Field Integral Equation

In this paper, we propose a new multi-level power series solution method for solving a large surface and volume electric field integral equation-based H-Matrix. The proposed solution method converges in a fixed number of iterations and is solved at each level of the H-Matrix computation. The solution method avoids the computation of a full matrix, as it can be solved independently at each level, starting from the leaf level. Solution at each level can be used as the final solution, thus saving the matrix computation time for full H-Matrix. The paper shows that the leaf level matrix computation and solution with power series gives as accurate results as the full H-Matrix iterative solver method. The method results in considerable savings time and memory savings compared to the H-Matrix iterative solver. Further, the proposed method retains the O(NlogN) solution complexity.

A new microwave nondestructive testing method of relative permittivity and conductivity for stratified media based on dyadic Green's function I: Theory

Stratified composite materials are employed in many industrial scenes, including bridge construction, vehicle, ship, aviation, etc. However, minor imperfections in composite materials can have significant effects and even result in disasters when used. In this work, a multi-parameter inversion method that can simultaneously reconstruct the conductivity and permittivity parameters of layered media is devised and presented for microwave nondestructive testing (NDT) of the minor imperfections in stratified composite materials. Firstly, the calculations for the electric field in the layered medium model with the emission source as the point source are provided. Secondly, the spatial electric field variations (the Fréchet derivative) caused by changes in conductivity and permittivity of arbitrary layers are calculated. Then the permittivity and conductivity are reconstructed using the Distorted Born iterative method (DBIM) technique. The numerical examples at microwave frequencies show that the inversion technique has a strong capacity to reconstruct for a single parameter (relative permittivity or conductivity) and multi-parameter (relative permittivity and conductivity). Our suggested multi-parameter inversion technique in this research has excellent potential for use in the identification of multilayer composites and subsurface inclusions.

Analysis and Application of a Surface Admittance Operator for Combined Magnetic and Dielectric Contrast in Emerging Interconnect Topologies

In state-of-the-art interconnect design, topologies including magnetic materials, such as the so-called superlattice conductors, are rapidly emerging as a novel strategy to handle the challenges associated with the evolution toward higher operating frequencies and integration densities. Consequently, it is imperative that the newly developed full-wave electromagnetic solvers rigorously model these innovative materials and still accurately capture phenomena such as the skin and proximity effect in good conductors. In this article, we propose such a method to rigorously characterize this important class of interconnects with arbitrary, possibly frequency-dependent, material properties, including combined dielectric and magnetic contrast. To that end, a 2-D differential surface admittance (DSA) operator is used, which invokes a single-source equivalence theorem to model both nonmagnetic and magnetic conductors efficiently. This operator is combined with the electric field integral equation (EFIE), yielding a comprehensive formalism to extract the pertinent per-unit-of-length (p.u.l.) resistance and inductance parameters of the modeled structures. The numerical properties of our technique are studied in detail, with particular attention to the influence of magnetic materials. Finally, various relevant application examples are considered to establish its correctness and versatility.

Noninvasive Absorbed Power Density Assessment From 5G Millimeter-Wave Mobile Phones Using Method of Moments

Absorbed power density (APD) is challenging to assess due to antenna-human body interactions since the antenna is close to the human body. This paper presents a novel technique for non-invasive APD assessment by considering antenna-human body coupling. The electric field integral equation based on spatial dyadic Green’s functions (DGFs) is solved inversely by the method of moments to reconstruct the equivalent currents using the electric field sampled on the surface of the hemisphere surrounding the antenna. Then, the APD is assessed by the equivalent currents beneath the air-phantom interface. The reconstruction errors are obtained using two types of placement of the antenna array, at the edge and corner of the handheld device, at frequencies of 15, 30, and 60 GHz. It was found that at 60 GHz, the errors did not exceed 8.75% and 11.1% for the edge- and corner-type antennas, respectively, for the maximum spatially averaged power density. The measurement requirements were investigated for an actual testing scenario, including angular resolution, E-field measurement uncertainty, and required phantom size. It is shown that the proposed technique paves the way for a new methodology to assess APD, including the antenna-human body coupling, for exposure to handheld devices operating above 6 GHz.