Full-wave Formulation Research Articles

Numerical Stability of Dual Full-Wave Formulations With Electric Circuit Element Boundary Conditions

Numerical Stability of Dual Full-Wave Formulations With Electric Circuit Element Boundary Conditions

Dual full-wave formulations with Radiant Electric Circuit Element boundary conditions — Application to monopole antenna modeling

Electric Circuit Element (ECE) are special boundary conditions that enable a natural coupling between electromagnetic devices and circuits. ECE can be generalized to allow for parts on the domain boundary where absorbing boundary conditions can be set, to model the unbounded space. This paper illustrates the implementation of radiant ECE in the 2D and 3D-finite element method, for a full-wave time-harmonic field in dual frequency-domain E and H formulations. The weak formulations are implemented in the free environment Open Numerical Engineering LABoratory (onelab). The formulations are proven to be well-posed (existence, uniqueness and stability of the weak solution are proven) and validated for a monopole antenna.

Eddy Current Modeling in Multiply Connected Regions via a Full-Wave Solver Based on the Quasi-Helmholtz Projectors

Eddy currents are central to several industrial applications and there is a strong need for their efficient modeling. Existing eddy current solution strategies are based on a quasi-static approximation of Maxwell’s equations for lossy conducting objects and thus their applicability is restricted to low frequencies. On the other hand, available full-wave solvers such as the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equation become highly ill-conditioned and inaccurate in eddy current settings. This work presents a new well-conditioned and stable full-wave formulation which encompasses the simulation of eddy currents. Our method is built upon the PMCHWT equation and thus remains valid over the entire frequency range. Moreover, our scheme is also compatible with structures containing holes and handles (multiply connected geometries). The effectiveness of quasi-Helmholtz projectors is leveraged to obtain a versatile solver, which is computationally efficient and allows for a seamless transition between low and high frequencies. The stability and accuracy of the new method are demonstrated both theoretically and through numerical experiments on canonical and realistic structures.

Inhomogeneous lossy waveguide mode analysis

This paper discusses electromagnetic numerical mode analysis in waveguides with materially inhomogeneous cross-sections and material dissipation. A full-wave formulation of Maxwell’s homogeneous equations including Gauss electric law, stable at vanishing propagation constant is implemented and verified in terms of the hp-adaptive version of the finite element method. It provides the possibility to use high order polynomial enrichments combined with strongly graded meshes. It is considered most efficient in resolving the loss of solution regularity at material interfaces with large contrast. Numerical examples including materially lossless homogeneous and inhomogeneous cross sections with and without losses are analysed to corroborate the implementation. The efficiency of using higher order polynomial enrichments is shown. The approach is anticipated to have a broad application, from modern on-chip interconnect and antenna technologies to the design of low observable aerial vehicles.

Excitation of whistler waves below the lower hybrid frequency by a loop antenna located in an enhanced density duct

Whistler wave radiation from a loop antenna located in a cylindrical duct with enhanced plasma density is considered in the case where the wave frequency is less than the lower hybrid frequency. Using the full-wave formulation, the total radiation resistance and the partial radiation resistances corresponding to guided eigenmodes of such a duct and unguided waves radiating to the background magnetoplasma are calculated and analyzed as functions of the plasma and source parameters. The emphasis is placed on the radiation characteristics of the considered source in the presence of an artificial near-antenna duct that can be created during active experiments in the ionosphere. Conditions are revealed under which the total radiation resistance is predominantly determined by the excitation of the eigenmodes of the duct. It is shown that the presence of an enhanced density duct can lead to a notable increase in the radiation resistance of a loop antenna in the discussed frequency range even if the duct is rather narrow and capable of guiding only a single low-order eigenmode. The results obtained can be helpful in understanding the basic features of excitation of the ducted whistlers and planning the related ionospheric and laboratory experiments.

Modeling of Resonant Wireless Power Transfer With Integral Formulations in Heterogeneous Media

A full-wave integral formulation has recently been proposed for the simulation of magnetically coupled resonant wireless power transfer (WPT) arrangements in homogeneous medium. In this paper, the formulation is extended to the case where two different types of dielectrics are separated by a planar interface. This configuration has extensive practical interest nowadays, especially for modeling biomedical WPT applications. The new formulation is based on a stationary approximation, which is valid at the typical operating frequencies. The proposed scheme requires much less computational resources compared with standard finite-element simulations. The results are validated against alternative simulations and measured data as well.

Analytical Circuit Model for 1-D Periodic T-Shaped Corrugated Surfaces

An analytical circuit model is obtained to study the reflection of TM polarized electromagnetic waves that impinge obliquely on a 1-D periodic corrugated surface consisting of dielectric-loaded T-shaped planar corrugations backed by an infinite ground plane. The model is based on transmission line theory and equivalent lumped-element circuits. For the case of perfect conductors, the topology of the circuit is directly inferred from a rigorous full-wave formulation of the periodic problem without using any heuristic argument. This procedure leads to fully analytical expressions for all the circuit parameters. Ohmic losses are further incorporated in the model under the assumption of strong skin effect. The results thus obtained are compared with those given by an accurate Method of Moments numerical code and HFSS software showing a very good agreement. The strong numerical efficiency as well as the good physical insight provided by the present equivalent circuit model can be advantageously employed for the analysis and/or design of a variety of devices. As examples of the latter, the circuit model is used for the first-stage design of an electrically thin hard impedance surface, a corrugated surface that prevents specular reflection, and an absorber.

A New Volume Integral Formulation for Broadband 3-D Circuit Extraction in Inhomogeneous Materials With and Without External Electromagnetic Fields

A new first-principles-based volume integral equation (VIE) formulation is developed for the broadband full-wave extraction of general 3-D circuits, containing arbitrarily shaped lossy conductors with inhomogeneous dielectrics. The proposed formulation accentuates all the advantages of the VIE formulation traditionally developed for solving wave-related problems, while allowing for the extraction of multiport circuit parameters such as impedance Z-, admittance Y-, and scattering S-parameters at ports located anywhere in the physical structure of a circuit. Its first-principles-based formulation without circuit-based simplifications and approximations can also be utilized to analyze the performance of a circuit in adverse ambient conditions, such as the exposure to strong external electromagnetic fields. In addition, the magneto-quasi-static and electro-magneto-quasi-static counterparts of the proposed full-wave formulation are also given for low-frequency applications. Numerical experiments have validated the accuracy and capability of the proposed new VIE formulation.

Charge Polarization and Current Distribution in a Conductive Particle in the Rayleigh Region

An investigation of the interaction of a conductive sphere with an electromagnetic wave with attention given to space-charge effects would appear timely, as there is much current interest in the electromagnetic properties of mesoscopic structures. In this study, the polarization of a small semiconductor sphere immersed in a dynamic electric field is explored analytically and numerically. In one approach, suitable for a sphere with low to moderate charge carrier concentration, the Poisson's equation is coupled with the transport equations of the carriers, leading to a quasi-static formulation under the weak-field approximation. Screening effects of the charges on the interior field are revealed, along with a current distribution that is essentially uniform over much of the volume of the sphere. Frequency dependence of the total induced dipole moment of the sphere displays strong dispersion and absorption near the bulk plasma frequency. Validity of the quasi-static assumption is assessed by comparison to results of calculations based on a full-wave formulation. As the nominal carrier concentration exceeds 1020 cm-3, the quasi-static solutions for interior field and current distribution begin to deviate from the full-wave solution and the latter must be employed to provide a realistic account of the charge-wave interaction within the sphere.

Calculation of Multiconductor Underground Cables High-Frequency Per-Unit-Length Parameters Using Electromagnetic Modal Analysis

A new method is proposed for calculating the frequency-dependent parameters of underground cables at high frequencies where commonly used quasistationary formulations may not be valid. The method uses full-wave formulation for calculating the modal electromagnetic fields and corresponding modal voltages and currents. The proposed method can be used for any cross-sectional shape of cables. Multiconductor coaxial cables and sector-shaped cables are studied in this paper and the calculated per-unit-length parameters are compared with those obtained from commonly used formulations and other methods available in the literature.

Open-Ended Waveguide Measurement and Numerical Simulation of the Reflectivity of Petri Dish Supported Skin Cell Monolayers in the mm-wave Range

Open-ended waveguide reflectometry is a promising tool for permittivity and other material properties calculation at mm-waves (30–300 GHz). Measurement of the reflection coefficient does not require sample manipulation, allowing in vivo and in vitro non destructive studies on cells. Here we used this technique for measuring the power reflection coefficient (reflectivity) of water and Petri dish supported human skin melanoma and keratinocyte cell cultures, in the 53–72 GHz frequency range. The dependence of the reflectivity on polystyrene or glass thickness of the Petri base plate and on the cell layer thickness was analyzed. Permittivity data were then easily retrieved by using a plane wave-dominant mode approach for formulating the reflectivity at the aperture of the flange-mounted open-ended rectangular waveguide probe. Limits and validity of such an approximate approach were analyzed and compared with full-wave near field formulations for which magnitude and phase of the reflection coefficient must be measured and solved using complicated systems of integral equations and extensive numerical calculation. Finally, Petri dish reflectivity measured by the open-ended waveguide method was compared with that numerically simulated under far-field exposure conditions used in a large number of in vitro studies. Such an analysis showed that, under certain conditions, open-ended reflectivity values approach the far field ones.

Gap Discontinuity in Microstrip Lines: An Accurate Semianalytical Formulation

A semianalytical full-wave formulation is used to analyze a narrow gap in a microstrip line. The analysis assumes that the length of the gap is small compared to the strip width, but allows for an arbitrarily high frequency. The formulation accounts for radiation from the gap into space and into surface waves. Based on this formulation, the scattering parameters of the gap are obtained along with the complete equivalent circuit of the gap. The percentage of power lost due to gap radiation from an incident mode on the microstrip line is found, and the physics of the gap radiation are examined.

Numerical modeling for plasmonics

This contribution is a review paper, concerning mainly the research work made by the authors, about the numerical modeling, in the frequency domain, of both surface and bulk plasmon oscillations induced in metallic nanoparticles wit h arbitrary shapes by an external electromagnetic field. Surf ace plasmons are governed by a local constitutive relation, whereas bulk plasmons are governed by a constitutive relation that is expressed by a partial differential equation. The electro magnetic field scattered by the nanoparticles is evaluated using an in tegral formulation. In nanoparticles with maximum linear dimensions much smaller than the vacuum wavelength the plasmon dynamic may be studied approximately by using the electro quasi- stationary approximation of the Maxwell equations. The paper discusses both a full-wave integral formulation, where t he unknown is the induced current density, and an electro quasi-stationary integral formulation, where the unknown is the surface charge density.

Space-Charge Plane-Wave Interaction at Semiconductor Substrate Boundary

A theoretical investigation of space-charge plane-wave interaction at dielectric-semiconductor interfaces is presented. A full-wave and charge transport formulation is applied to the analysis of the fundamental mode of propagation in a semiconductor substrate backed with a ground plane. Closed-form expressions for the field components, charge carrier density, and current density are obtained. The reflection coefficients for both H- and E-polarized incident waves were then derived from the field solutions. The interaction between the fields and charge carriers causes a charge accumulation at the semiconductor surface in the case of H-polarization. The effects of the charge accumulation on the reflection coefficient are accounted for. Results indicate that the space charge exerts a weak effect on the reflection coefficient and a strong screening effect on the normal component of the electric field. The tangential component, however, is mainly governed by energy dissipation effect resulting from the conduction current.

Numerical Modeling for the Analysis of Plasmon Oscillations in Metallic Nanoparticles

This work is focused on the numerical modeling, in the frequency domain, of the plasmon oscillations induced in metallic nanoparticles of arbitrary shapes by an external electromagnetic field. The electromagnetic response of the nanoparticles is modeled through a proper frequency dependent dielectric constant. The electromagnetic field scattered by the nanoparticles is evaluated by a full-wave integral formulation where the unknown is the induced current density. The integral equations are solved numerically by the finite element method, by decomposing the current density in the solenoidal and non-solenoidal components and using the edge-elements. Particular care has been devoted to treat, within such numerical method, arbitrary topologies. A detailed analysis is carried out to understand the limit of applicability of the electro-quasi-stationary model and a characteristic length lm of the metal, together with the wavelength of the electromagnetic field, are found to provide a constraint on the maximum nanoparticle size that can be treated within such approximation.

Interface wave-modes in comb transducers

An elastic body with periodic teeth of finite height (a comb), insonified by incident ultrasonic wave and applied, with sliding contact, to the surface of another elastic body (a substrate), constitutes a typical arrangement of ultrasonic nondestructive testing system exploiting comb transducers. The arising scattering problem of incident wave on periodic voids between the teeth and the sliding teeth-substrate contact is considered in the full-wave formulation. In physical interpretation, the vibrating teeth generate surface Rayleigh wave in the substrate by the incident wave pressure exerted on the substrate. In fact, the interface waves are generated which differ from the Rayleigh wave in both the propagation velocity and the wave-mode shape. These interface waves, their velocity and modal shape are the main subject of this paper; an approximated formula is presented for the relation between the most important Bloch components of interface modes in the considered periodic system.

A Unified Finite-Element Solution From Zero Frequency to Microwave Frequencies for Full-Wave Modeling of Large-Scale Three-Dimensional On-Chip Interconnect Structures

It has been observed that a full-wave finite-element-based solution breaks down at low frequencies. This hinders its application to on-chip problems in which broadband modeling from direct current to microwave frequencies is required. Although a static formulation and a full-wave formulation can be stitched together to solve this problem, it is cumbersome to implement both static and full-wave solvers and make transitions between these two when necessary. In this work, a unified finite-element solution from zero frequency to microwave frequencies is developed for full-wave modeling of large-scale three-dimensional on-chip interconnect structures. In this solution, a single full-wave formulation is used. No switching to a static formulation is needed at low frequencies. This is achieved by first identifying the reason why a full-wave eigenvalue-based solution breaks down at low frequencies, and then developing an approach to eliminate the reason. The low frequency breakdown problem was found to be attributed to the discrepant frequency dependence of the real part and the imaginary part of the eigenvalues, which leads to an ill-conditioned eigenvalue system at low frequencies. The discrepant frequency dependence of the real part and the imaginary part is further attributed to the different scaling of the transverse and longitudinal fields with respect to frequency in a transmission-line type structure. By extracting transverse and longitudinal fields separately in the framework of a full-wave formulation, we avoid the numerical difficulty of solving an ill-conditioned eigen-system at low frequencies. The validity of the proposed approach is demonstrated by numerical and experimental results.

A Transmission-Line Model for Full-Wave Analysis of Mixed-Mode Propagation

The paper presents a generalized transmission line model able to describe the high-frequency mixed-mode propagation along electrical interconnects. The model is derived from a full-wave formulation and extends the validity of the standard transmission line (TL) model to frequency ranges where the propagation is no longer of transmission electron microscopy (TEM)-type. This generalized TL model describes the high-frequency differential and common mode propagation and the mode conversion. Within its validity limits, the proposed model provides solutions in good agreement with those obtained through full-wave models. Case studies are carried out to evaluate the high-frequency mode conversion in asymmetric interconnects.

3-D Numerical Modeling and Circuit Extraction Techniques for the Analysis of Unshielded Twisted Pairs

A three-dimensional full-wave surface integral formulation is used to predict the terminal response of unshielded twisted pairs. The proposed approach allows taking into account the skin effect, proximity effect and radiation losses. The proposed full-wave simulation is validated by comparing the results with those obtained by a software tool based on the finite integration technique, discussing advantages and limitations. The surface integral formulation results obtained on a short length of the line are used to predict the behavior of a longer line. In addition, they are used to extract equivalent circuits suitable for the time domain analysis by any commercial circuit simulator

Impedance boundary conditions for finite planar or curved frequency selective surfaces embedded in dielectric Layers

We consider the time-harmonic electromagnetic scattering problem from a finite planar or curved structure made up of infinitesimally thin frequency-selective surfaces (FSSs) embedded in dielectric layers, with possibly nearby located objects. In order to avoid the meshing of the unit cells that constitute the FSSs, this problem is solved by employing an integral equation (IE) or finite-element (FE) formulation in conjunction with approximate impedance boundary conditions (IBCs) prescribed on the sheets that model the FSSs. The impedances in the IBCs are derived from the exact reflection and transmission coefficients calculated for the fundamental Floquet mode on the infinite planar structure illuminated by a planewave at a given incidence. When the structure is curved and/or the direction of the incident wave is unknown, higher order IBCs are proposed that are valid in a large angular range and can be implemented in a standard IE or FE formulation. Their numerical efficiencies are evaluated for finite planar or curved two-dimensional structures, or radomes, where the FSSs are strip gratings. As an example, for a curved radome surrounding a conducting plate, it is shown that, when the Floquet modes of the gratings are evanescent, these IBCs allow an accurate calculation of the radar cross section of the whole structure with far smaller computing resources than would have been required by a full-wave formulation.