Electric Field Integral Equation Research Articles

Near-Field IPO for Analysis of EM Scattering from Multiple Hybrid Dielectric and Conductor Target and High Resolution Range Profiles

Aiming at improving the accuracy and efficiency of scattering information from multiple targets in near-field regions, this paper proposes a near-field iterative physical optics (IPO) method based on a modified near-field Green’s function for the composite electromagnetic scattering analysis of multiple hybrid dielectric and conductor targets. According to the electric field and magnetic field integral equation, the electric and magnetic current were updated utilizing the Jacobi iteration method. Then, by introducing an expansion center lying in the neighborhood of the source point, Green’s function was modified for near-field scattering between multiple hybrid dielectric and conductor targets. To accelerate the implementation of the procedure, the multilevel fast multipole method, the fast far-field approximation, and parallel multicore programming were introduced. Numerical results indicate that there is good agreement between the results calculated by the near-field IPO method and MLFMM solver in commercial software FEKO while significantly reducing the computational burden. To fully exploit the scattering information, the high resolution range profiles (HRRP) of different targets under different conditions were analyzed, which can be further applied for automatic target detection and recognition.

Examination of the effect of cell thickness on the performance of a tandem nano-gap thermophotovoltaic system

In this paper, a study about the influence of cell thickness on the performance of a tandem thermophotovoltaic (TPV) system is performed in the near-field thermal radiation regime. This system includes an emitter made up of tungsten and two TPV cells made up of Si and GaSb, respectively. The fluctuational electrodynamics accompanied by the dyadic Green's function are applied in order to calculate the near-field thermal radiation heat flux. The generated photocurrent and the conversion efficiency are computed by solving the charge transport equations. By examination of the effect of TPV cell thicknesses on the performance of both cells, the optimum thicknesses are obtained. Furthermore, it is observed that variation of the n- or p-region thicknesses of the TPV cells also affect the performance of the system. In this regard, the best thickness for n- and p-regions of the first and second cells is also calculated.

Performance investigation of tandem nano-gap thermophotovoltaic system considering the near-field thermal radiation

In this paper, a near-field thermophotovoltaic (TPV) system with a dual TPV cell design is considered and studied numerically. The fluctuational electrodynamics accompanied by the dyadic Green's function are utilized for calculating the radiation heat flux. The generated photocurrent and the conversion efficiency are obtained by solving the photon-coupled charge transport equations. It was discovered that the addition of the second TPV cell to the system, increases the generated photocurrent of the system due to the absorption of the low-energy photons and generation of the electron-hole pairs. By increasing the gap size between the emitter and Si TPV cell from 50 nm to 1 μm, the generated photocurrent decreases because of the reduction of the near-field thermal radiation effects. Finally, the tandem nano-gap TPV system shows higher conversion efficiency compared with the single Si TPV cell for different values of the vacuum gaps, and the gap size of d1 = 200 nm is the optimum gap size due to the improvement of the conversion efficiency of the system.

Fast Wide-Band RCS Analysis of the Coated Target Based on PBR Using EFIE-PMCHWT and the Chebyshev Approximation Technique

The Chebyshev approximation technique (CAT) combined with the MoM based on the electric-field integral equation (EFIE) and the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) integral equation is proposed to efficiently calculate the wide-band radar cross-section (RCS) based on passive bistatic radars (PBR). The EFIE-PMCHWT equations can be used to analyze the electromagnetic scattering of coated targets. The combination with CAT only requires computing the electric and magnetic currents at a few Chebyshev frequency points, which can be employed to obtain the electric and magnetic currents over the entire frequency band. In this study, the RCS values of a coated target calculated by the hybrid EFIE-PMCHWT-CAT based on passive bistatic radar (PBR) were found to be consistent with that calculated by the MoM based on the EFIE-PMCHWT. The validity of the hybrid method is verified by several numerical examples. Compared with the conventional MoM method, the hybrid method can greatly improve the efficiency for electromagnetic scattering problems over a wide frequency band.

A Fast Power Lines RCS Calculation Method Combining IEDG with CM-SMWA

The existing methods for calculating electromagnetic scattering can be used to obtain the RCS of power lines. However, these methods do not take advantage of the periodicity of power lines. We propose a fast electromagnetic scattering calculation method combining the integral equation discontinuous Galerkin (IEDG) method and the characteristic modes-Sherman–Morrison–Woodbury algorithm (CM-SMWA) exploiting the power lines with stranded structure. We adopt the IEDG to discretize the electric field integral equation (EFIE) so that the EFIE can deal with non-conformal grids and significantly increase the flexibility of the CM-SMWA. Combing with the periodic property of power lines, the modeling and grid generation shall be carried out within one cycle (stranding) of the power line, and the grids of the rest cycle of the power line can be spliced by translating the grid of the divided sections. The advantage of the proposed method lies in that only the CM of one segment needs to be calculated, and the result can be applied to other segments to avoid repeated calculation of the CMs. The simulation results of the RCS of power lines show that the calculation time of our method is cut down by 50% as compared to the conventional CM-SMWA.

Full-Wave 3-D Transient Analysis With Method of Moments and Numerical Laplace Transform Including Resistive Non-Linear Elements

Methods based on both time ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> )-domain and frequency ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> )-domain have been used for electromagnetic transient (EMT) analysis using both circuit-theory and field-theory approaches. Methods based on circuit theory are fast and convenient but may become inapplicable to many engineering problems due to simplifications such as the transverse electromagnetic assumptions. Moreover, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> -domain-based techniques rely on approximate methods to account for frequency dependence, which is an essential characteristic of electric conductors, equipment and soil environment. In this paper, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> -domain solutions obtained from the method of moments (MoM) discretization of the electric field integral equation (EFIE) are converted to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t-</i> domain using the numerical Laplace transform (NLT) by means of post-processing. This circumvents the need to formulate the EFIE and MoM based on the complex frequency which would be required for their application to conventional NLT. Hence, existing MoM implementations can be used to perform a full-wave 3-D EMT analysis for a wide range of power system applications. Examples include energizations of 3-D power system networks with fast and non-vanishing excitations such as step functions, as well as modeling non-linear elements using the piecewise linear approximation. Results from experimental measurements, finite-difference <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> -domain method, and EMT-type software confirm the validity of the proposed method for power system transients in the range of microseconds down to nanoseconds.

Fast and Accurate Transient Analysis of Thin-Wire Structure in Half-Space With PEEC Method

This article presents an efficient full-wave partial element equivalent circuit (PEEC) method of thin-wire structure in half-space for lightning transient analysis. In the framework of the PEEC formulation for thin-wire conductors, the partial elements are computed by double-folded line integrals. In layered media, the interaction integrals involve dyadic Green's functions, which contain a closed-form part and a Sommerfeld-integral part. The direct numerical computation of these integrals is very challenging and time-consuming, which hinders the practical application of the full-wave method. However, the efficient and accurate evaluation of partial elements has not been investigated in a comprehensive way so far. Accordingly, this article presents an efficient method for the evaluation of the partial elements between elementary segments in half space. The main novelty is that the interaction integrals are computed through a combination of the Taylor series expansion of the full-wave free space Green's function and the Sommerfeld-integral adaptive interpolation technique, which significantly reduces the computation time. The new method is systematically validated on examples from finite-difference time-domain (FDTD) method and method of moments and experimental results. The proposed method is validated with the NEC code in the frequency domain and the FDTD in the time domain.

Efficient Millimeter-Wave Imaging Algorithm for Layered Dielectrics Based on MIMO-SAR With Nonuniform Transmitting Array

In this letter, an efficient near-field millimeter-wave (MMW) imaging algorithm is presented for layered dielectrics based on multiple-input–multiple-output synthetic aperture radar (MIMO-SAR) with nonuniform transmitting array. First, the model of target echo under MIMO-SAR configuration is built by dyadic Green's function, and the precise spectral echo expression is obtained through fast Fourier transform (FFT) and spherical-wave decomposition. Then, the image reconstruction of sparse MIMO-SAR is divided into separate single-input–multiple-output (SIMO)-SAR imaging problems, and the target's subimage corresponding to different SIMO-SAR setup can be quickly solved by employing inverse FFT, multistep phase compensation and wavenumber integration. Finally, the fully focused MIMO-SAR reconstructed image will be obtained by coherently accumulating all the SIMO-SAR results. Simulation analysis and experimental results validate the effectiveness the proposed algorithm.

On the Numerical Solution of Diffraction Problem by Random Spheres Using Electric Field Integral Equation

The aim of this paper is to solve the two-dimensional acoustic scattering problems by random sphere using Electric field integral equation. Some approximations for the two-dimensional case are derived. These various approximations are next numerically validated in the case of high-frequency.

UTD-PO Solution for E-Plane Radiation Pattern Calculation of Rectangular Horn Antennas With Rectangular-Shaped Corrugations

Proposing a novel hybrid uniform theory of diffraction-physical optics (UTD-PO) formulation, we develop a method to calculate the E-plane radiation pattern of corrugated E-plane rectangular horn antennas with rectangular corrugations. We derive the technique from the estimation of the total field that reaches the emitting source (a magnetic current line), thereby assuming the impingement of a plane wave above the horn (reciprocity is applied). To validate our method, we compare the performance of the UTD-PO analysis with that of the electric field integral equation (EFIE) solved using the method of moments (MoM). Our method shows improved computational efficiency over EFIE and other numerical techniques that fully discretize the geometry.

Dyadic Green’s Function of Perfect Electromagnetic Conductor Rectangular Waveguides and Cavities

In this article, we present the dyadic Green’s functions (DGFs) for electric dipole excitation of perfect electromagnetic conductor (PEMC) rectangular waveguides and cavities. To derive the DGFs of a PEMC rectangular waveguide, we define two sets of orthogonal vector wave functions, that satisfy the boundary conditions at the waveguide walls. The theory of finding the DGF of this waveguide is based on the Ohm-Rayleigh method and orthogonal properties of the rectangular vector wave functions. By having the DGFs of this waveguide, one can derive the DGFs of a PEMC rectangular cavity using the scattering superposition (SSP) principle. The derived electric DGF of this waveguide is used to obtain the electric field propagated inside the waveguide due to an arbitrary current distribution. The distribution of the electric field inside the PEC, PMC, and PEMC waveguides will be obtained and compared with each other.

Performance of Inexpensive Local Error Estimation Techniques for Integral Equation Numerical Solutions

The performance of several inexpensive local error estimation techniques is evaluated in connection with the Rao-Wilton-Glisson method of moments numerical solutions of the electric field integral equation. Results for 18 perfectly conducting test targets are used to evaluate the performance of the estimators. Two of the estimators produce error maps that consistently exhibit high correlations with reference solutions. These estimators are also suitable for “goal-oriented” estimation of secondary quantities, such as identifying cells that contribute the most error to the radar cross section of the target.

Simulation of realistic speckle fields by using surface integral equation and multi-level fast multipole method

This report presents a speckle simulator which calculates rigorously speckle fields with full randomization from rough surfaces. To achieve this, surface integral equation (SIE) method accelerated via multilevel fast multipole method (MLFMM) is implemented. Among several linear formulations to combine the electric and magnetic field integral equations, we demonstrate that one is most suitable for dielectric rough surfaces and one for metallic rough surfaces. As examples, silver and silicon rough surfaces are simulated at a wavelength of 500 nm. To investigate speckles from extended areas, silicon rough surfaces with a size of 30×30 µm2 and two million unknowns are calculated. Based on the resultant speckle fields, speckle contrast, angular speckle-correlation and transverse autocorrelation function of intensity in the van Cittert-Zernike zone are further calculated and known relations versus surface roughness are manifested, indicating that sufficient statistic surface information is encoded in the speckle fields. The SIE-MLFMM method with the suitable formulation proves to be an efficient rigorous simulation tool for relatively large rough surface problems and would enable more profound numerical studies for speckle involved optical metrologies.

Macroscopic quantum electrodynamics approach to multichromophoric excitation energy transfer. II. Polariton-mediated population dynamics in a dimer system.

In this study, based on the theory developed in Paper I, we explore the combined effects of molecular fluorescence and excitation energy transfer in a minimal model-a pair of single-vibration-mode chromophores coupled to surface plasmon polaritons. For the chromophores with zero Huang-Rhys factors and strong couplings to surface plasmon polaritons, we find that the frequencies of Rabi oscillations (the strengths of strong light-matter couplings) are associated with the initial excitation conditions. On the other hand, for the chromophores weakly coupled to surface plasmon polaritons, our numerical calculations together with analytical analysis elaborate on the conditions for the superradiant and subradiant decay behaviors. Moreover, we show that the modified decay rate constants can be explicitly expressed in terms of generalized spectral densities (or dyadic Green's functions), revealing a relationship between photonic environments and the collective effects such as superradiance and subradiance. For the chromophores with nonzero Huang-Rhys factors and strong coupling to surface plasmon polaritons, the effects of molecular vibrations emerge. We demonstrate that the low-frequency vibrational modes do not affect the excited state population dynamics, while the high-frequency vibrational modes can modify either the period of Rabi oscillation (Franck-Condon Rabi oscillation) or the amplitude of excited state population. Our study shows that the collective effects, including superradiance and subradiance, can be controlled via dielectric environments and initial excitation conditions, providing new insights into polariton chemistry and the design of quantum optical devices.

Advanced Numerical and Experimental Analysis of Ultra-Miniature Surface Resonators

Many scientific and technological applications make use of strong microwave fields. These are often realized in conjunction with microwave resonators that have small geometric features in which such fields are generated. For example, in magnetic resonance, large microwave and RF magnetic fields make it possible to achieve fast control over the measured electron or nuclear spins in the sample and to detect them with high sensitivity. The numerical analysis of resonators with small geometric features can pose a significant challenge. This paper describes a general method of analysis and characterization of surface microresonators in the context of electron spin resonance (ESR) spectroscopy and spin-based quantum technology. Our analysis is based on the Electric Field Integral Equation (EFIE) and the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation. In particular, we focus on a class of resonator configurations that possesses extremely small subwavelength features, which normally would require an ultra-fine mesh. We present several efficient techniques to numerically model, solve, and analyze these types of configurations for both normal and superconducting structures. The validation of these techniques is established both numerically and experimentally by the S11 parameters as well as the provision of direct mapping of the resonator’s microwave magnetic field component using a unique electron spin resonance micro-imaging method.

Improving the Solution Accuracy of the Volume-Surface Integral Equation for the Open PEC Structures Embedded Within Dielectrics

In the solution of volume-surface integral equation (VSIE) for open perfect electric conductor (PEC) structures embedded within dielectric substrates, how to explicitly enforce the continuity condition (CC) of electric flux on the PEC–dielectric interfaces to improve the numerical accuracy is investigated. In the traditional VSIE formed by combining the surface electric field integral equation (EFIE) and volume integral equation (VIE), the fictitious surface charge, which does not exist physically, is accumulated on the PEC–dielectric interfaces. This will lead to the inaccuracy of numerical results, which can be eliminated by the CC. To correctly enforce the CC, the equivalent surface current distribution on both sides of open PEC should be distinguished. For this purpose, the combined field integral equation (CFIE) consisting of electric field and magnetic field integral equations is used to model the open PEC part. In the proposed approach, the number of surface unknowns needs to be doubled, which can be balanced by reducing the volumetric unknowns through the enforcement of CC. Furthermore, by fully considering the numerical symmetry between both sides of open PEC surface, the filling process of the matrix as well as the excitation vector in implementing the method of moments (MoMs) can be simplified. Numerical experiment demonstrates that the enforcement of CC can improve the VSIE accuracy obviously. For example, when calculating the frequency response of frequency selective surfaces (FSSs), the results obtained from the traditional VSIE often shift to higher frequencies, while the proposed approach gives reasonably good results.

A Marching-on-in-Time Method of Moments for Transient Modeling of a Vertical Electrode Buried in a Lossy Medium

This article proposes a full-wave time-domain method for analyzing the transient behavior of a grounding electrode buried vertically in a lossy soil. In this method, the electrode is first approximated by a thin wire, and the modified image theory is utilized to account for the soil–air interface. The governing electric field integral equation (EFIE) is then derived with the current distribution along the electrode being the unknown quantities. Finally, the EFIE is solved by the time-domain method of moments based on a marching-on-in-time (MOT) procedure. This is done by expanding the unknown currents in terms of a finite linear combination of products of appropriate spatial and temporal basis functions, and adopting the Galerkin method in space and the point matching method in time. The MOT procedure makes the proposed method more efficient computationally than its rival frequency-domain method of moments (FD-MoM). The efficiency of the proposed method is demonstrated by comparing the lightning ground potential rise of various grounding electrodes with those obtained using the FD-MoM and a commercial numerical code.

Surface Integral Equation With Multibranch RWG Basis Functions for Electromagnetic Scattering From Dielectric Objects

A surface integral equation method with multibranch Rao–Wilton–Glisson (MB-RWG) basis functions for scattering from dielectric objects is proposed based on the electric and magnetic current combined field integral equations (JMCFIE). The MB-RWGs are defined at the boundaries between dense and coarse meshes and can keep the current continuity. Thus, the JMCFIE with MB-RWGs allows different surfaces of the dielectric models to be independently discretized by triangles with different sizes. Compared with the conventional JMCFIE, the JMCFIE with MB-RWGs increases the flexibility of mesh generation, which is attractive for multiscale dielectric models. Furthermore, the iterative convergence of JMCFIE with MB-RWGs is similar to that of conventional JMCFIE. Numerical examples are presented to demonstrate the advantages of the proposed method.

Accelerated Adaptive Error Control and Refinement for SIE Scattering Problems

We present an application of adjoint-based adaptive error control and refinement for scattering problems solved using the method of moments (MoM) in the electric field integral equation (EFIE) and the coupled EFIE and magnetic field integral equation (MFIE) formulations. Specifically, we examine the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) formulation of the EFIE-MFIE. We first construct the adjoint problems of the EFIE and the EFIE-MFIE for estimating the error of radar cross section (RCS) quantities of interest (QoIs) directly. We then introduce an effective adaptive refinement algorithm based on an error prediction heuristic and a posteriori error estimation, which enables rapid and consistent convergence regardless of a chosen tolerance and the coarseness of the starting discretization. The approach, moreover, inherently promotes equilibration of the QoI error contributions and produces, therefore, consistently balanced meshes. Numerical examples with canonical scattering targets and adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -refinement confirm the strength of the proposed refinement method, demonstrating the ability to generate high-quality discretizations, both in terms of accuracy and efficiency, without expert user intervention.

Estimation of Equivalent Current Distribution Using Fourier Transform and Eigenmode Currents

The estimation of the equivalent current distribution is a challenge when the precise geometry of the real source is unknown. In this study, a novel estimation method for the equivalent current distribution is proposed. The proposed method is a hybrid of the Fourier transform and eigenmode currents of equivalent sources. The equivalent current distribution is estimated using the proposed method as follows. First, the Fourier transform is applied to an electric field integral equation, and the initial equivalent current distribution on a specific estimation plane is estimated from the near-field data of the real source. Utilizing the initial equivalent current distribution, the equivalent sources that are uniformly arranged over the estimation plane are thinned. Subsequently, the equivalent current distribution is estimated using a matrix equation and the eigenmode currents of the remaining equivalent sources. The advantages of the proposed method are as follows. First, the precise geometry of the real source is not needed during estimation. Second, the number of equivalent sources is reduced, and the estimation of the equivalent current distribution is well conditioned. The performance of the proposed method is validated both numerically and experimentally. Empirical guidelines for threshold values for thinning equivalent sources are provided.