Full-wave Finite Element Method Research Articles

Frequency-Dependent Grounding Impedance of a Pair of Hemispherical Electrodes: Inductive or Capacitive Behavior?

This article is the authors’ last contribution to a trilogy of research papers submitted to Energies’ Special Issue on Electromagnetic Field Computation, aimed at the theoretical analysis and numerical computation of the frequency-dependent complex impedance of hemispherical electrodes. In this work, we consider a pair of distant identical hemispherical electrodes buried in the ground, whose constitutive parameters (conductivity and permittivity) are assigned diverse values. Simulation experiments carried out using a full-wave finite element method, considering different combinations of the earth’s constitutive parameters, reveal that the grounding impedance of the electrode system can exhibit surprisingly varied frequency behavior. For frequencies close to zero, the impedance can start out inductive or capacitive, then go through a number of resonant transitions between inductive and capacitive states, finally tending towards purely resistive behavior. The results are interpreted using theoretical approximations valid for low- and high-frequency regimes.

Simulation of GHz ultrasonic wave piezoelectric instrumentation for Fourier transform computation

The recent emerging alternative to classic numerical Fast Fourier transform (FFT) computation, based on GHz ultrasonic waves generated from and detected by piezoelectric transducers for wavefront computing (WFC), is more efficient and energy-saving. In this paper, we present comprehensive studies on the modeling and simulation methods for ultrasonic WFC computation. We validate the design of the WFC system using ray-tracing, Fresnel diffraction (FD), and the full-wave finite element method (FEM). To effectively simulate the WFC system for inputs of 1-D signals and 2-D images, we verified the design parameters and focal length of an ideal plano-concave lens using the ray-tracing method. We also compared the analytical FFT solution with our Fourier transform (FT) results from 3-D and 2-D FD and novel 2-D full wave FEM simulations of a multi-level Fresnel lens with 1-D signals and 2-D images as inputs. Unlike the previously reported WFC system which catered only for 2-D images, our proposed method also can solve the 1-D FFT effectively. We validate our proposed 2-D full wave FEM simulation method by comparing our results with the theoretical FFT and Fresnel diffraction method. The FFT results from FD and FEM agree well with the digitally computed FFT, with computational complexity reduced from O(N^2 logN) to O(N) for 2-D FFT, and from O(NlogN) to O(N) for 1-D FFT with a large number of signal sampling points N.

Laser coupling in waterjets subject to jet instabilities, laser parameters, and alignment errors.

High coupling accuracy and efficiency attract wide attention in waterjet-guided laser technology due to the requirements for high processing performance in hard-to-cut material and diamond industries. The behaviors of axisymmetric waterjets injected into the atmosphere through different types of orifices are investigated by adopting a two-phase flow k-epsilon algorithm. The water-gas interface is tracked with Coupled Level Set and Volume of Fluid method. The electric field distributions of laser radiation inside the coupling unit are modeled by wave equations and numerically solved with the full-wave Finite Element Method. The coupling efficiency of the laser beam affected by waterjet hydrodynamics is studied by considering the profiles of the waterjet shaped at transient stages, namely vena contracta, cavitation, and hydraulic flip. The growth of the cavity leads to a larger water-air interface and increases the coupling efficiency. Eventually, two types of fully developed laminar waterjets, i.e. constricted waterjets and non-constricted waterjets, are formed. Constricted waterjets that are detached from the wall throughout the nozzle are preferable to guide laser beams since they significantly increase the coupling efficiency compared to non-constricted waterjets. Furthermore, the trends of coupling efficiency affected by Numerical Aperture (NA), wavelengths, and alignments errors are analyzed to optimize the physical design of the coupling unit and develop the alignment strategies.

Coupled-Mode Theory for Graphene-Based Metasurfaces

In this article, a temporal coupled-mode theory (CMT) formalism is proposed to design graphene-based metasurface (MTS) structures. Such structures may be nonuniform and synthesized by numerous graphene resonators. To obtain a desired functionality, such MTSs may be designed, by performing multiple parametric analyses of the structure's geometric parameters. An accurate calculation of their response may be attained by a full-wave vectorial finite-element method (VFEM), by modeling graphene as a surface boundary condition; however, it requires high computational resources, especially for larger configurations. CMT offers an appealing time- and memory-efficient alternative, by solving a sparse system of equations, of particularly small size, fed by the results of simpler and smaller simulations, with the ability to take into account graphene dispersion. CMT may be used to design more complex MTS structures, by providing approximate and preliminary results, which shall be used as a starting point for the final FEM fine-tuning.

Определение LC-параметров корпусов ИМС с помощью электромагнитного моделирования

At the IC design phase it is required to consider all possible factors to ensure the produced device’s compliance with specified requirements. For instance, it is necessary to select an optimum package and to lower its impact on IC’s final characteristics. Electromagnetic simula-tion is widely used to calculate electrical parameters of the electric motors, printed circuit boards, and microcircuits. In this work, full-wave three-dimensional finite element method simulation in frequency domain was used to characterize LGA package. S-parameters matrix obtained by modeling was converted to an equivalent RLGC transmission line model to determine the electrical parameters of the package – self-capacitance and inductance of the leads, mutual capa-citance of the adjacent leads, – on which the package bandwidth and crosstalk depend. Correct-ness of the obtained results was confirmed by comparison with the measurements results. It has been found that discrepancy between the results of modeled and measured capacitance was less than 5 %. The inductance modeling results turned out to be less accurate, which, however, is not significant for low and medium frequency applications.

The Research for Approaches to Increase Power of the Compact THz Emitters Based on Low-Temperature Gallium Arsenide Heterostructures

The design and technological conditions for the manufacture of photoconductive antennas based on low-temperature gallium arsenide (LT-GaAs) have been developed. The optimized photoconductive THz antenna is made based on LT-GaAs with the flag geometry of the contacts and with the interdigitated structure including metal closing through the dielectric of each second period. LT-GaAs samples were obtained by molecular beam epitaxy at temperatures of 210 °C, 230 °C, 240 °C on GaAs substrates (100). Dark and photocurrent were measured depending on the bias voltage of the LT-GaAs heterostructure at the EP6 probe station. Full wave finite element method solver has been used to investigate the proposed plasmon PCA electrical and optical behavior by combining the Maxwell's wave equation with the drift-diffusion/Poisson equations.

Fast Analysis of Metasurfaces Through Temporal Coupled-Mode Theory

In this article, a rigorous temporal coupled-mode theory (CMT) formalism is developed, to analyze metasurface (MTS)-based structures. Such MTSs are generally rather complex, requiring extensive, full-wave simulations. To facilitate their design and minimize the associated computational demand, the CMT solves a small linear system of equations, fed by the results of certain much simpler and less time- and memory-consuming eigenvalue problems. The proposed method is versatile and offers an initial, valuable estimation of the structure's frequency response, which may be used as a guideline for the final MTS fine tuning. As proof of concept, split-ring resonator (SRR) MTSs coupled to microstrip lines are analyzed, and their response is compared with the full-wave finite-element method (FEM) results.

Low-index-contrast waveguide bend based on truncated Eaton lens implemented by graded photonic crystals

Low-index contrast waveguides such as silica waveguides are indispensable part of passive integrated optical components. Reducing the bending radius of silica waveguides with low bend loss is vital in miniaturizing silica planar lightwave circuits. The Eaton lens is a gradient index lens that can bend parallel light rays by 90{\deg}, 180{\deg}, or 360{\deg}. We present a low-loss and compact 90{\deg} waveguide bend with a radius of 9 $\mu$m designed by truncating the Eaton lens. The performance of the designed bend, implemented by graded photonic crystal, was evaluated by full-wave two-dimensional finite element method. The average bend loss in the C-band is 0.9dB while the average bend loss for the wavelength range of 1260-1675nm is 1.05dB. The proposed design strategy can be applied to other low-index contrast waveguides.

Parametrized Local Reduced-Order Models With Compressed Projection Basis for Fast Parameter-Dependent Finite-Element Analysis

This paper proposes an automated parametric local model-order reduction scheme for the expedited design of microwave devices using the full-wave finite-element method (FEM). The approach proposed here results in parameterized reduced-order models (ROMs) that account for the geometry and material variation in the selected subregion of the structure. In each subregion, a parameter-dependent projection basis is generated by concatenating several local bases that correspond to different parameter values, yielding a small, dense ROM. The process is automated and uses an adaptive scheme guided by a local goal-oriented error estimator to select points in the parameter space at which a local basis needs to be computed. A two-stage basis compression technique is also proposed to remove the redundancy from the projection basis and yields compact macromodels. Numerical examples, including FE analysis of a fifth-order filter with seven geometric variables as parameters, demonstrate that the approach provides a significant reduction in computational time while preserving the accuracy of the simulations.

Modeling Effective Anisotropy of Substrate Integrated Dielectric Waveguides for Polarization Diversity

A field-based analytical procedure is presented and developed for accurate modeling of the effective parameters of substrate integrated nonradiative dielectric (SINRD) waveguide. This modeling strategy is based on the eigenmode analysis of a dielectric substrate material perforated with air holes and enclosed between two horizontal metallic plates. From this model, it is found that the resulting effective dielectric constant of the periodic geometry of the SINRD waveguide is dependent on the direction of an electric field vector with respect to the material periodicity. In other words, the guiding parts of the SINRD waveguides act as anisotropic materials. A full demonstration for the proposed analysis is supported with simulation results using a full-wave finite-element method. The proposed model provides a scheme for the isotropization of anisotropic substrates. This is in addition to clarifying the exact regimes of operation inside the SINRD waveguide based on the guiding mechanism. Validation examples are studied based on polarization-selective coupling and effective polarization-independent coupling. A prototype is realized and measured where good agreement is achieved between simulation and measurement results.

A Short–Open Calibration Method for Accurate De-Embedding of 3-D Nonplanar Microstrip Line Structures in Finite-Element Method

This paper presents the numerical short–open calibration (SOC) method in the full-wave finite-element method (FEM) algorithm for accurate de-embedding of equivalent circuit parameters of a variety of 3-D nonplanar periodic guided-wave and discontinuity structures. It holds its attractive features in high efficiency and good accuracy as demonstrated in the method of moments algorithm, and further allows itself to be capable of characterization of 3-D nonplanar structures. By setting the reference plane along each feeding line as the perfect electric and magnetic conductors, i.e., PEC and PMC, the entire error box involved in each feeding line and impressed source can be characterized by using these two calibration standards, namely, short- and open-ended circuits. Formulation of ABCD matrix of this error box is described under the introduction of an impressed voltage at each port. Then, ABCD matrix of the core circuit structure can be effectively de-embedded or extracted. Finally, a few numerical examples are given to demonstrate the efficiency and accuracy of our proposed full-wave 3-D FEM-SOC approach in numerical de-embedding of 3-D nonplaner structures.

Numerical Modeling and De-Embedding of Non-Planar Periodic Guided-Wave Structures via Short-Open Calibration in 3-D FEM Algorithm

In this paper, a numerical short-open calibration (SOC) technique is presented to numerically model and de-embed a variety of non-planar periodic guided-wave structures based on the 3-D full-wave finite element method (FEM). A simple current source or lumped-port model is introduced in formulation of a determinant FEM algorithm. By incorporating the SOC in the FEM solver, the intrinsic port discontinuity caused by this port model is then fully removed or calibrated out of the core non-planar periodic guided-wave structure during the calibration process. Because of the 3-D nature of FEM, the effective per-unit-length parameters of the core periodic guided-wave structure, i.e., effective propagation constant and effective characteristic impedance, are extracted successfully. Two numerical examples, including microstrip line with periodical loading of shorting pins and metal–insulator–metal composite right/left handed structure, are numerically modeled for demonstration and verification. Extracted results have validated the feasibility and accuracy of the presented FEM-SOC, thereby exhibiting its advanced capability in numerical modeling and de-embedding of non-planar structures with complicated configurations.

Effective media properties of hyperuniform disordered composite materials.

The design challenge of new functional composite materials consisting of multiphase materials has attracted an increasing interest in recent years. In particular, understanding the role of distributions of ordered and disordered particles in a host media is scientifically and technologically important for designing novel materials and devices with superior spectral and angular properties. In this work, the effective medium property of disordered composite materials consisting of hyperuniformly distributed hard particles at different filling fractions is investigated. To accurately extract effective permittivity of a disordered composite material, a full-wave finite element method and the transmission line theory are used. Numerical results show that the theory of hyperuniformity can be conveniently used to design disordered composite materials with good accuracy compared with those materials with randomly dispersed particles. Furthermore, we demonstrate that a Luneburg lens based on the proposed hyperuniform media has superior radiation properties in comparison with previously reported metamaterial designs and it may open up a new avenue in electromagnetic materials-by-design.

Shielding Effectiveness Simulation of SMT EMI Gaskets Utilizing ANSYS HFSS

Abstract As more components populate smaller board areas, the risk of unwanted coupling between components increases. Shielding and radiated emissions tests outlined by IEEE standards such as IEC 61000-4-21 and ASTM4935D identify measurement techniques to quantify shielding effectiveness. In a PCB topology, shields enclose components to create a Faraday cage, but necessitate a method to ground and fasten the shield to the PCB. Typical methods include the use of gaskets, sealants and clips. This paper reviews a gasket methodology and validates a parameterized ANSYS HFSS simulation with the measured relationship between gasket configuration and shielding effectiveness. Surface mount, rectangular, compressible gaskets manufactured by W.L. Gore & Associates, Inc. are used in several configurations to shield a PCB radiator. Radiated emissions measurements are performed in an ETS-Lindgren reverberation chamber to evaluate shielding effectiveness for each configuration. ANSYS HFSS, a full wave Finite Element Method (FEM) electromagnetic simulation solver, is used to simulate each geometric configuration and is verified with measured results.

Topological edge states in acoustic Kagome lattices

We demonstrate that an acoustic Kagome lattice formed by an array of interconnected resonant cavities exhibits a new class of topological states protected by C3 symmetry, and it is characterised by a topological invariant in the form of a winding number in Pauli vector space. This acoustic topological metamaterial can be considered as the two-dimensional analogue of the Su–Schrieffer–Heeger model, exhibiting a topological transition when a detuning is introduced between the inter-cell and intra-cell hopping amplitudes. The topological transition caused by such detuning is accompanied by the opening of a complete topological band gap, which may host edge states. The edge states emerge on either truncated ends of the lattice terminated by a cladding layer or at the domain walls between topologically nontrivial and trivial domains. First-principles simulations based on full-wave finite element method are used to design the lattice and confirm our analytical predictions.

Improving $B_{1}$ Efficiency and Signal-to-Noise-Ratio of a Surface Coil by a High-Impedance-Surface RF Shield for 7-T Magnetic Resonance Imaging

In this paper, we present a fundamental investigation to improve the $B_{1}$ efficiency and the signal-to-noise ratio (SNR) of a radio frequency (RF) surface coil for ultrahigh-field magnetic resonance imaging (MRI) by utilizing a high-impedance surface (HIS) as the RF shield. An analytical investigation indicates that a circular loop backed by a perfect magnetic conductor (PMC), which is the ideal case of an HIS, suggests an improved magnetic field compared with the case of a perfect electric conductor (PEC) and the case without any shield. This improvement is verified by a full-wave simulation, where the surface coil is modeled by an ideal impressed current model with azimuthal component ( $J_{\text {surf}, \alpha }= 1$ A/m). The electromagnetic field is effectively shielded out behind the PEC and PMC shields compared with the case without any shield. Furthermore, the surface coil with uniform current distribution and the PMC shield is realized by a series resonant loop structure and a 2-D HIS structure, respectively. Since the normal component of the magnetic field is supported at the surface of an HIS, whereas suppressed by a conventional PEC, the ${\boldsymbol{B}}_{1}$ field in the vicinity of the HIS shield is enhanced compared with the case with a PEC shield. Hence, an improvement on SNR and ${\boldsymbol{B}}_{1}$ efficiency is achieved by utilizing an HIS shield, especially in the regions adjacent to the surface coil. It has been found that the improvement of $B_{1}$ efficiency is more prominent than the improvement of SNR due to different normalizations. The difference of peak SAR between considered shields, which is used for $B_{1}$ efficiency normalization, is considerably larger than the difference of the power loss within the phantom, which is used for the SNR normalization. The proposed approach is validated by full-wave finite-element method simulations and near-field measurements, which reveal good agreement with each other.

Accurate theoretical and experimental characterization of optical grating coupler.

Periodic structures, acting as reflectors, filters, and couplers, are a fundamental building block section in many optical devices. In this paper, a three-dimensional simulation of a grating coupler, a well-known periodic structure, is conducted. Guided waves and leakage characteristics of an out-of-plane grating coupler are studied in detail, and its coupling efficiency is examined. Furthermore, a numerical calibration analysis is applied through a commercial software package on the basis of a full-wave finite-element method to calculate the complex propagation constant of the structure and to evaluate the radiation pattern. For experimental evaluation, an optimized grating coupler is fabricated using electron-beam lithography technique and plasma etching. An excellent agreement between simulations and measurements is observed, thereby validating the demonstrated method.

A Rigorous Approach for the Modeling of Through-Silicon-Via Pairs Using Multipole Expansions

This paper presents a novel multipole expansion method for the rigorous analysis of wave propagation along a through-silicon-via (TSV) pair. TSV models are often constructed using equivalent circuits under the assumption that the interfaces between different media are equipotential. In comparison with that, the proposed method is a rigorous full-wave solution of the propagation mode. It takes advantage of cylindrical wave expansion functions and matches the boundary conditions at both the metal-to-insulator and insulator-to-silicon interfaces exactly. The method is validated against a full-wave finite-element method solver, and analysis examples using the method are demonstrated in a frequency range up to 100 GHz.

Surface-plasmon enhanced photodetection at communication band based on hot electrons

Surface plasmons can squeeze light into a deep-subwavelength space and generate abundant hot electrons in the nearby metallic regions, enabling a new paradigm of photoconversion by the way of hot electron collection. Unlike the visible spectral range concerned in previous literatures, we focus on the communication band and design the infrared hot-electron photodetectors with plasmonic metal-insulator-metal configuration by using full-wave finite-element method. Titanium dioxide-silver Schottky interface is employed to boost the low-energy infrared photodetection. The photodetection sensitivity is strongly improved by enhancing the plasmonic excitation from a rationally engineered metallic grating, which enables a strong unidirectional photocurrent. With a five-step electrical simulation, the optimized device exhibits an unbiased responsivity of ∼0.1 mA/W and an ultra-narrow response band (FWHM = 4.66 meV), which promises to be a candidate as the compact photodetector operating in communication band.

Cylindrical radial superlattice conductors for low loss microwave components

Theory and experimental demonstration of a cylindrical radial superlattice (CRS) conductor composed of alternating nanoscopic non-ferromagnetic/ferromagnetic metal layers are presented with focus on low conductor loss in a K-band microwave spectrum. The dynamic frequency response of the ferromagnetic thin films has been extracted using the Landau-Lifshitz-Gilbert equation which shows a negative magnetic permeability value in the frequencies above its ferromagnetic resonance. The reduction of the conductor loss results from the eddy current canceling (ECC) effect in the CRS conductors, where the negative-permeability ferromagnetic and positive-permeability non-ferromagnetic metal layers produce a zero effective permeability, resulting in virtually infinite skin depth at the targeted frequency. The closed and uniform boundary conditions inherent in the radial shape conductors preclude discontinuity effects occurring at the edges of the planar superlattice conductor and end up with a more effective ECC effect in practice. The design aspects with regards to the CRS materials and structural configuration are discussed. Simulations using a full-wave finite element method high frequency structure simulator are performed to show the ECC effect inside the CRS conductors. An air-lifted inductor made of the CRS conductor has been implemented to prove the effectiveness of the conductor loss reduction with the CRS conductor. The inductor shows an inductance value of 1–2 nH and a Q-factor of 45 at 18 GHz, which is the highest value reported at the frequency by now.