Electric Surface Current Densities Research Articles

Efficient Calculation of the 3-D Rectangular Waveguide Green’s Functions Derivatives by the Ewald Method

In this contribution, the Ewald method has efficiently been applied to accelerate the computation of the rectangular waveguide Green’s functions (GFs) derivatives. Based on previous works, we have outlined new approximation formulae that avoid the evaluation of computationally expensive complementary error functions of complex argument, needed by the Ewald method. This is possible when the internal medium of the rectangular waveguide is homogeneous and lossless. On the other hand, different convergence numerical studies have been carried out, showing a similar convergence rate for computing the original GFs and their derivatives. Moreover, we have checked that the computational time is only slightly increased for obtaining the derivatives as compared to the original GFs, after the application of these new techniques. The newly derived expressions are useful for the evaluation of electromagnetic fields, the characterization of dielectric materials and step discontinuities between rectangular waveguides, and the analysis of rectangular cavities using integral equation formulations. For validation, the electric field produced by a surface electric current density with a rectangular pulse distribution has been evaluated, using the new proposed expressions. These results have been compared to simulations provided by full-wave finite elements commercial software to verify their correctness, exhibiting a good agreement.

Shielding Effectiveness of Magnetostatically-Biased Anisotropic Graphene by the Method of Auxiliary Sources With a Surface Current Boundary Condition

Extensive experimental data and numerical simulations show that graphene is an ideal shielding material in the RF/microwave region. In most cases, it is considered to be isotropic with its scalar surface conductivity given by the Kubo formula. However, when it is electrostatically- and magnetostatically-biased, it exhibits anisotropy described by a surface conductivity tensor. The main objective of this work is to evaluate the shielding effectiveness of anisotropic graphene in the RF/microwave region. Since graphene’s thickness is many orders of magnitude smaller than the shortest wavelength in the considered regime, it does not affect substantially the computation of the fields. For this reason, we replace the graphene layer with a Surface Current Boundary Condition (SCBC), hence its effect is equivalent to a surface electric current density. We employ the Method of Auxiliary Sources (MAS) to analyze a planar and a cylindrical shielding configuration. For the cylindrical shield, the derived MAS results are compared with the exact solutions, which are also extracted. For the planar shield, the results are compared to those obtained by FEM-based commercial software. In both cases, excellent agreement is observed.

Inverse Source Solutions With Huygens’ Surface Conforming Distributed Directive Spherical Harmonics Expansions

Time-harmonic inverse source solutions are commonly working with electric and magnetic surface current densities defined and discretized on appropriately chosen Huygens’ surfaces. An efficient meshless alternative are spherical harmonics expansions of low-order distributed along the chosen Huygens’ surface, which still possess pretty good spatial localization properties. Similar to expansions with electric and magnetic surface current densities, distributed expansions with Cartesian spherical harmonics (SHCs) or standard vector spherical harmonics (SHVs) are redundant when they are placed on Huygens’ surfaces. This redundancy is reduced by allowing only spherical harmonics, which can be excited by surface current density distributions in a specific plane, and by forming directive spherical harmonics. This results in a considerable reduction of the necessary number of unknowns for representing the sources and improved conditioning of the discretized integral equations. Inspired by the Huygens’ radiator concept, appropriate directive harmonics on the basis of SHCs and SHVs are derived, implemented, and compared in terms of their performances. The validity of the presented techniques is confirmed via inverse source solutions for synthetic and real measurement data.

Mechanism study of electropolishing from the perspective of etching isotropy

Electropolishing, as a damage-free and highly efficient surface finishing method, has been widely used for finishing of metal components. In this study, the electropolishing mechanism of tungsten in the electrolyte with H2SO4 and CH3OH was investigated from the perspective of etching isotropy. The anodic dissolution behavior of tungsten demonstrated that anisotropic and isotropic etching occurred under the activation polarization and mass transfer polarization, respectively. The evolution of surface morphology, roughness, and electric current density during electropolishing has been experimentally investigated and analyzed. According to the changes in surface morphology and current density, there was a transformation from anisotropic etching to isotropic etching during the electropolishing due to the time-consuming accumulation of reactive products. The application of a pulse power supply with a duty cycle of 10% resulted in a rough surface on tungsten due to the mass transfer polarization being inhibited. Similar results were also obtained in the electrolyte with 2 wt% NaOH. The presented findings experimentally demonstrate the importance of the isotropic etching mode for electropolishing, which is of great value for further revealing the electropolishing mechanism.

Entire-Domain Basis Function with Segmented Edge Condition Applied for Scattering Structures

This paper proposes the formulation of a sinusoidal basis function with a novel segmented edge condition to model the impulsive behavior of the surface electric current density at the edges of rectangular microstrip scatterers. In comparison to traditional basis functions, the one considered in this approach demands using very few modes to expand the induced current. The effectiveness of the proposed formulation is validated using the commercial electromagnetic simulator Ansys Designer. Good agreement between the results obtained with the proposed formulation and with the commercial software has been obtained.

Dual-band and polarization-independent metamaterial terahertz narrowband absorber.

A dual-band terahertz metamaterial narrowband absorber is investigated based on a single simple windmill-shaped structure. The proposed metamaterial absorber achieves near-perfect absorption at 0.371 THz and 0.464 THz. The full width at half-maximum is 0.76% and 0.31% relative to absorption frequency. The multireflection interference theory is used for analyzing the absorption mechanism at low absorption frequency. The theoretical predictions of the decoupled model have excellent agreement with simulation results. By investigating the absorber's distribution of electric field and surface current density at high absorption frequency, the absorber's near-perfect absorption at the high absorption frequency originating from the magnetic resonance formed between the top metal structure and the bottom metal plane is explained. Besides, the absorber proposed is independent of the polarization angle. It is significant to various applications such as narrowband thermal radiation, photoelectric detection, biological sensing, and other fields.

Towards a unified approach to electromagnetic analysis of objects embedded in multilayers

According to the surface equivalence theorem [1], any enclosed surface with electric and magnetic current densities enforced on it can generate exactly the same fields as the original problem. The problem is how to construct the current sources. In this paper, an efficient and accurate unified approach with an equivalent current density enforced on the outermost boundary is proposed to solve transverse magnetic (TM) scattering problems by objects embedded in multilayers. In the proposed approach, an equivalent current density is derived after the surface equivalence theorem is recursively applied on each boundary from innermost to outermost interfaces. Then, the objects are replaced by the background medium and the equivalent electric current density only on the outermost boundary is derived. The scattering problems by objects embedded in multilayers can be solved with the electric field integral equation (EFIE). Compared with the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) and other dual source formulations, the proposed approach shows significant benefits: only the surface electric current density instead of both the electric and magnetic current densities is required to model the complex objects in the equivalent problem. Furthermore, the electric current density is only enforced on the outermost boundary of objects. Therefore, the overall count of unknowns can be significantly reduced. At last, several numerical experiments are performed to validate its accuracy and efficiency. Although overhead is required to construct the intermediate matrices, the overall performance improvement is still significant as numerical results are shown. Therefore, it shows great potential useful in the practical engineering applications.

3-D BEM Formulations for Eddy-Current Problems With Multiply-Connected Domains and Circuit Coupling

Quasi-static linear problems can be solved efficiently with Boundary Element Method (BEM). This method is based on surface integral equations dealing with equivalent magnetic and electric surface current densities. Many works have shown the potentiality of BEM especially for the modeling of non-destructive testing devices. In this paper, after selecting formulations enabling the modeling of multiply-connected regions, an original coupling is proposed in order to take into account external electric circuit in the problem.

Five-Band Terahertz Perfect Absorber Based on Metal Layer–Coupled Dielectric Metamaterial

A five-band tunable ideal terahertz metamaterial absorber based on subwavelength range is proposed. It consists of a reflective layer, a dielectric layer, and an absorbing layer consisting of an internal closed square ring and an outer open square circle. We have found that the five absorption peaks can reach more than 97% on average. Meanwhile, in order to analyze the absorption mechanism, we studied the different structures and geometric parameters of the absorber and drew the electric field intensity diagram and surface current density diagram at different peaks. Moreover, we also studied the effect of similar opening structures based on this structure on absorption. Therefore, the designed absorber has good frequency selectivity and can be applied to terahertz imaging, detection, and so on.

The effects of surface elasticity on the thermal stress around a circular nano-hole in a thermoelectric material

We analyze the contribution of surface elasticity and electric current density on the thermal stress distribution around a circular nano-hole in a thermoelectric material. Using complex variable methods, we obtain closed-form solutions describing the corresponding thermoelastic fields in the vicinity of the nano-hole. Our results indicate that the effect of surface elasticity is to generate significant normal and shear stresses on the boundary of the hole, allowing for the ability to either suppress or enhance hoop stress depending on the sign of the corresponding surface material constant. In addition, we find that positive hoop stress generated on the boundary by the remote electric current density can be neutralized by the incorporation of positive surface elasticity. In the case of the remaining boundary stress components, both surface elasticity and electric current density are found to enhance normal stress, while the maximum shear stress depends largely on the contribution of surface elasticity.

$\mathcal {H}$-Matrix Accelerated Solution of Surface–Volume–Surface EFIE for Fast Electromagnetic Analysis on 3-D Composite Dielectric Objects

An efficient fast direct algorithm based on the hierarchical ( $\mathcal {H}$ -) matrices is presented for solution of the radiation problems on piecewise homogeneous dielectric objects using Method of Moment (MoM) discretization of the surface–volume–surface electric field integral equation (SVS-EFIE). The SVS-EFIE for the composite objects introduces independent surface electric current density on the boundary of each region. Therefore, different from the traditional Poggio–Miller–Chang–Harrington–Wu–Tsai formulation, in the SVS-EFIE, the object regions can be meshing independently according to their local properties which improves the flexibility and efficiency of the proposed method. It also makes the proposed algorithms appropriate for the analysis of both multiscale and large-scale composite structures. The numerical results from the proposed fast method are provided for the high-loss biological tissues from bioelectromagnetics applications and agree well with the analytical Mie series solution and commercial software. The CPU time and memory cost of the required $\mathcal {H}$ -matrix operations are analyzed in details and verified through several numerical experiments. The new computational framework allows for fast direct solution of 3-D radiation and scattering problems of moderate electrical size with $O(P^{\alpha } \log ^2 P)$ CPU time and $O(P^{\alpha } \log P)$ memory complexity, $P$ being the number of surface unknowns produced by the MoM discretization, and $1\leq \alpha \leq 1.5$ being a geometry-dependent parameter.

Electromagnetic resonance in the asymmetric terahertz metamaterials with triangle microstructure

We investigate terahertz transmission properties and electromagnetic resonance modes in the asymmetric triangle structures with the change of asymmetric distance and the direction of electric field. When the THz electric field is perpendicular to the split gap of triangle, the electric field can better excite the THz absorption in the triangle structures. Importantly, electromagnetically induced transparency (EIT) characteristics are observed in the triangle structures due to the destructive interference of the different excited modes. The distributions of electric field and surface current density simulated by finite difference time domain indicate that the bright mode is excited by the side of triangle structures and dark mode is excited by the gap-side of triangle. The present study is helpful to understand the electromagnetic resonance in the asymmetric triangular metamaterials.

An ultra-broadband metamaterial absorber based on the hybrid materials in the visible region

In this paper, an ultra-broadband metamaterial absorber is successfully designed in the visible region. The structure of the absorber is just obtained by the two-dimensional plane structure which rotate 90° along x-axis. Furthermore, the formation of the structure for the hybrid materials is based on the four U-shaped structure of the metal titanium is embedded in the semiconductor (indium antimonide). The simulated results show that the proposed metamaterial absorber can achieve an ultra-broadband absorption with greater than 90% from 252.2 to 822.3 THz, and the relative absorption bandwidth gets to 106.1%. Finally, the simulated electric field, surface current and power loss density distributions further illustrate the absorption mechanism of the metamaterial absorber. And we believe the metamaterial absorber will have many potential applications in energy harvesting and stealth devices.

New Single-Source Surface Integral Equation for Magneto-Quasi-Static Characterization of Transmission Lines Situated in Multilayered Media

We recently proposed a novel single-source integral equation (SSIE) for accurate broadband resistance and inductance extraction and current flow modeling in 2-D conductors. The new surface integral equation is advantageous compared with the traditional volume electric field integral equation (V-EFIE) used for the inductance extraction, since the unknown function is defined on the surface of conductors as opposed to the volumetric unknown current density in V-EFIE. The new SSIE is also more suitable for the solution of inductance extraction problems than the traditional surface integral equation formulations, as it features only a single unknown surface function as opposed to having the unknown equivalent electric and magnetic surface current densities. The new equation also features only the electric field Green’s functions unlike the previously known SSIE formulations. The latter property makes the new SSIE equation particularly suitable to the inclusion of the multilayered substrate effect into the inductance extraction model. This paper describes the generalization of the new SSIE formulation to the case of transmission line models embedded into the multilayered lossy substrates. This paper also shows how the matrix sparsity in the method of moments discretization of the novel integral equation can be exploited to accelerate its numerical solution and reduce associated memory use. This sparsity arises due to the skin-effect-based attenuation of the fields in conductors’ cross sections leading to vanishing levels of the matrix elements corresponding to the distant interactions. Typical examples of inductance extraction in complex interconnects situated in lossy substrate are considered to validate the proposed techniques against traditional approaches.

Fast Inverse Equivalent Source Solutions With Directive Sources

A fast inverse equivalent source technique is presented for the fully probe-corrected transformation of measured radiation or scattering fields utilizing directive sources. The directivity of the expansion sources is either obtained by combining electric and magnetic surface current densities in a directive Huygens radiator or by shifting the source locations into complex space. The latter approach is known to generate Gaussian-beam-like directive radiators. These two techniques can be used separately or in combination to obtain three different solutions that approximately satisfy the null-field condition (also known as the Love condition) outside the solution domain, i.e., inside the volume of the original device under test. The directive sources lead to a better conditioning of the inverse problem and especially the Huygens radiator concept leads to good conditioning for a small number of unknowns. Thus, considerable reduction in computation times and better solution accuracies are achieved. Moreover, antenna diagnostics is promoted by the improved localization of the directive equivalent sources. The directive sources are implemented together with Rao–Wilton–Glisson basis functions and the new concepts are utilized within the fast irregular antenna field transformation algorithm with its hierarchical propagating plane wave-based radiation operator representation. This algorithm has recently been augmented with Gaussian beam-based translation operators which lead to considerably reduced computation times and lower memory requirements. The algorithmic capabilities are demonstrated with synthetically generated near-field data as well as with real spherical measurements of a double-ridged waveguide antenna.

Current recovery for the RWG‐based method of moments

Derivative recovery through local smoothing, is a well-known approach to obtain an estimate of a solution field's derivative, to one polynomial order higher than its direct representation. In the finite element method context, this is often referred to as ‘gradient recovery’. The method of moments (MoM) is routinely used to solve electromagnetic field integral equations in terms of the electric surface current density, which is often represented by mixed first-order, Rao–Wilton–Glisson (RWG) basis functions upon a mesh of triangle elements. A procedure for recovering a mixed second-order, approximate solution from an RWG-based MoM solution is presented. Recovery of the solution itself rather than its derivative, is made possible by exploiting specific properties of the mixed-order, surface divergence-conforming function spaces. The procedure is not strictly local, however, only sparse, positive-definite global linear systems must be solved. The procedure is independent of the integral operator. Computational complexity is lower than that of existing residual-based MoM error estimators. Results are shown with the recovered solution being a better approximation than the original solution. The procedure is useful for post-processing and for local or global a posteriori error estimation. It can be incorporated into any RWG-based MoM code.

An air core pulse transformer with a linearly integrated primary capacitor bank to achieve ultrafast charging

An air core transformer that linearly integrates a capacitor bank as well as a selfclosing switch into the primary winding (LIP) was designed to achieve ultrafast charging. Limiting stray inductance and maximizing the uncoupled dual resonance of the primary and secondary windings were the primary design criteria. To show this concept, two transformers with an uncoupled resonant frequency of approximately 8 MHz were designed for a low voltage output (several kV) and a high voltage output (>100 kV). The design was simulated in a Multisim discrete circuit model and a CST hybrid model which includes the transformer's 3-D structure as well as discrete circuit components. The discrete output (voltage and current) as well as the distributed parameters (electric field distribution and surface current density distribution) for the transformer were obtained. These designs were validated by experimental results. We show that their respective resonance characteristic and voltage gain are accurately predicted by the simulated values, demonstrating the design procedure is valid for both low voltage and high voltage applications. For the high voltage transformer, it has a voltage gain of 3-4. The maximum output voltage was tested up to 120 kV. A charging pulse with a rise time of less than 100 ns was obtained.

Design and Performance Evaluation of Microstrip Antenna for Ultra-Wideband Applications Using Microstrip Feed

In the modern days the development in communication systems engineering requires the development of low profile antennas that are capable of maintaining high performance over a wide spectrum of frequencies. In this review, we have designed an elementary Microstrip patch Antenna for ultra-wideband application. This technological trend has focused much effort on the basic concepts, characteristics and design of a Microstrip patch antenna. This paper explains the pattern of designs of the Microstrip patch antenna along with detailed study. A thorough analysis and observations of the problem begins with the application of the equivalence principle that introduces the unknown electric and magnetic surface current densities on the dielectric surface. Here in this technical review, our main goal is to design an elementary Microstrip antenna, which will work in the ultra-wide band range and also it should work in the desired operating frequency. Ansoft High Frequency Structured Simulations (HFSS) software is used for the elementary design of a rectangular patch Microstrip antenna and also some of the basic calculations has been done by using MATLAB. This review paper also comprises of basic parameters, types of antenna, working, fundamental concepts and characteristics as well as feeding techniques and simulation, results of Microstrip patch antenna.

Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.

ADAMANT: A surface and volume integral-equation solver for the analysis and design of helicon plasma sources

We present a full-wave numerical tool, dubbed ADAMANT (Advanced coDe for Anisotropic Media and ANTennas), devised for the analysis and design of radiofrequency antennas which drive the discharge in helicon plasma sources. ADAMANT relies on a set of coupled surface and volume integral equations in which the unknowns are the surface electric current density on the antenna conductors and the volume polarization current within the plasma. The latter can be inhomogeneous and anisotropic whereas the antenna can have arbitrary shape. The set of integral equations is solved numerically through the Method of Moments with sub-sectional surface and volume vector basis functions. This approach allows the accurate evaluation of the current distribution on the antenna and in the plasma as well as the antenna input impedance, a parameter crucial for the design of the feeding and matching network. We report several numerical examples which serve to validate ADAMANT against other well-established numerical approaches as well as experimental data. The numerical accuracy of the computed solution versus the number of basis functions in the plasma is also assessed. Finally, we employ ADAMANT to characterize the antenna of a real-life helicon plasma source.