Full-wave Solution Research Articles

Application of POD and PGD for Efficient Parameter Sweeping in Frequency-Domain Full-Wave Problems

Full-wave solutions of Maxwell’s equations defined on a wide-range parametric space can be necessary for modeling and design of high-frequency electronic systems. Model order reduction (MOR) techniques can be used to develop efficient solvers for accelerating the parameter sweeping process. In this article, we implement two MOR methods for solving parametric full-wave problems. One is the well-known proper orthogonal decomposition (POD) method and the other is a more recent and novel method, which is proper generalized decomposition (PGD). The two methods are applied on a wave propagation problem in both frequency domain and frequency-permittivity domain. Results show that both POD and PGD can model the field changes in the parametric space accurately. The efficiency and behavior of the reduction modes of both methods are compared and discussed.

Seismogram Synthesis for Multilayered Heterogeneous Media with Irregular Interfaces by the Global Generalized Reflection–Transmission Matrices Method

ABSTRACTWe present a semianalytical numerical method to simulate SH-wave propagation in heterogeneous multiple layers with smooth property variations. Wave propagation in such piecewise heterogeneous media will dominate the reflection and transmission at interfaces, whereas the scattered waves by volume heterogeneities inside each geological layer are superimposed on the boundary waves to cause fluctuations in amplitude and phase. The incident, boundary-scattering, and volume-scattering waves are accurately superposed through the generalized Lippmann–Schwinger integral (GLSI) equation. The multilayered heterogeneous media with irregular interfaces are sliced into horizontal and heterogeneous slabs, with each discretized into a series of volume elements. The traditional generalized reflection–transmission matrices (GRTMs) method is extended to solve the GLSI equation for each heterogeneous slab in the frequency–wavenumber domain by incorporating the boundary–volume integral equation numerical techniques. The global GRTM is obtained by integrating all the slab’s GRTMs in terms of the boundary condition across adjacent slabs. The wavefield at an arbitrary depth can be computed in a recursive relation from a source term. The accuracy of the method is tested by comparing it with other full-wave solutions to the SH problem. To show the applicability of the method, we calculate synthetic seismograms to demonstrate the significant impact of volume heterogeneities on seismic responses in layered heterogeneous media.

An Accurate Analytical Model to Calculate the Impedance Bandwidth of a Proximity Coupled Microstrip Patch Antenna (PC-MSPA)

This paper presents a new set of analytical equations to calculate the impedance bandwidth of electrically thin and thick proximity-coupled square microstrip patch antenna (PC-MSPA). The proposed mathematical model uses the relationship among different antenna parameters, material, and antenna dimensions to estimate the percentage impedance bandwidth with high accuracy. The proposed model was validated with rigorous full-wave solutions, and experimental antenna prototypes implemented for different thicknesses, patch dimensions, frequencies, and different substrates. The theoretical bandwidth results of S-, Cand X-band PC-MSPA antennas obtained using the new model are in very good agreement with simulations and the experimental results. Errors between the proposed analytical model and both simulation and measurement are less than 3.1%. These equations are mostly valid for permittivities between 2.2 and 6.15, and with feed substrate thickness less than 0.1λ r . The PC-MSPA is a candidate element for integration with MIMIC devices and wireless communication applications.

Characteristic Mode Analysis of Composite Metallic–Dielectric Structures Using Impedance Boundary Condition

In this article, an approach combining the electric field integral equation (EFIE) and impedance boundary condition (IBC) is presented for the characteristic mode analysis (CMA) of composite metallic–dielectric structures. Different from published works, only the electric currents are used in this approach and the computed eigencurrents are in a similar form as those of purely metallic structures. To ensure completeness and orthogonality of the eigencurrents, symmetry of the IBC-EFIE operator has been carefully examined. For lossy structures, a new formulation is deduced for CMA. The presented IBC-EFIE formulation is able to handle a variety of problems, e.g., lossy metals, thin dielectrics, thin dielectric-coated conductors, and metasurfaces. Several numerical examples are provided for those problems, and full-wave CMA solutions are used to verify the IBC-EFIE formulation. It is shown that this method is fairly accurate while computationally efficient, which makes CMA a promising tool for large scale or complex composite structures.

On the possible role of gravity waves in the ocean in T-phase excitation by earthquakes

Recent applications of a time-domain spectral-element method to obtain full-wave solutions of seismo-acoustic problems by Bottero et al. [J. Acoust. Soc. Am., 144, EL222–EL228 (2018)] and especially their investigation of T-phases in the Mediterranean [Bottero et al., J. Acoust. Soc. Am., 141, 4045 (2017)] challenge the existing understanding of the mechanisms of seismic energy conversion into T-waves, which propagate at the speed of sound in water. Motivated by these results, this paper aims to evaluate the contribution of scattering by hydrodynamic waves into T-phase generation. Ocean is modeled as a range-independent waveguide with superimposed volume inhomogeneities due to internal gravity waves and surface roughness due to wind waves and sea swell. Guided acoustic waves are excited by volume and surface scattering of ballistic body waves. The size of the effective source of T-waves and their amplitudes are calculated in the single scattering—multiple reflections approximation. Efficiency of the gravity wave-mediated conversion of seismic energy will be compared to that of the conversion that occurs on a seafloor slope.

From a reflectrometry code to a ‘standard’ EC code to investigate the impact of the edge density fluctuations on the EC waves propagation

In this work we employ and extend a 2D/3D code (FWR2D/FWR3D), originally developed for reflectrometer simulations, to study the impact of the edge density fluctuations on the electron cyclotron (EC) wave beam propagation. 2D and 3D simulations for DIII-D-like plasma are discussed with and without the presence of the edge density fluctuations in order to evaluate the impact on the EC wave beam broadening at the location of the EC resonance. Moreover, a comparison between the paraxial and the full-wave solution (which are both implemented in the code, making it very flexible) of the EC beam with and without edge density fluctuations is shown. The paraxial solution is numerically convenient and in very good agreement with the full-wave solution. A scan in the amplitude of edge density fluctuations is performed together with an average with 1000 different fluctuations realizations. For the case shown in this work, an ensemble larger than 100 independent edge density fluctuations shows to reasonably represent the impact of the fluctuations on the EC beam. Our simulations shown here demonstrate the importance of the edge density fluctuations to the EC propagation in agreement with previous work.

Lightning Propagation Analysis on Telecommunication Towers Above the Perfect Ground Using Full-Wave Time Domain PEEC Method

Lightning surge propagation on telecommunication towers is essential to lightning protection design. Analysis of very fast surges in a telecommunication tower requires a full-wave solution of Maxwell's equations. This paper proposes a full-wave time domain partial element equivalent circuit (PEEC) method considering the effect of ground to evaluate the surge currents and voltages on vertical structures. The PEEC of the formulation is provided by using the method of image. This method can take into account the attenuation of the lighting surges, and has the potential to be implemented as a new type of solution for general lightning surge analysis. The proposed method is validated numerically with the finite-difference time domain method, and is used to analyze the surge propagation on cables mounted on two typical grounded telecommunication towers. The simulation shows that both the location of cable installations and the type of towers have a significant influence on the lightning protection performance.

On the Use of the Antenna Theory Model of Lightning Return Stroke With Distributed Current Source for EMC Analysis

A full-wave solution method of Maxwell's equations is adopted for the electromagnetic analysis of the lightning return stroke channel. The method is based on a numerical solution of the electric field integral equation by the method of moments. The lightning channel is modeled as a wire monopole antenna with current sources distributed along its length. The method makes it possible to consider phase shift and amplitude decay between consecutive current sources in the frequency domain. The implementation of any engineering models of lightning in the integral form of Maxwell's equations is thus realizable. Special attention is devoted to the consequences of a limited channel length. Indeed, taking into account a finite channel length generates undesirable reflections from the top of the channel, which limits the use of the proposed method for electromagnetic compatibility analysis. Procedures are proposed to mitigate the effects of a limited channel length on the obtained results. Transient and frequency analyses of various lightning related problems demonstrate the applicability of the method to the analysis of complex electromagnetic problems.

Nonlinear response from optical bound states in the continuum

We consider nonlinear effects in scattering of light by a periodic structure supporting optical bound states in the continuum. In the spectral vicinity of the bound states the scattered electromagnetic field is resonantly enhanced triggering optical bistability. Using coupled mode approach we derive a nonlinear equation for the amplitude of the resonant mode associated with the bound state. We show that such an equation for the isolated resonance can be easily solved yielding bistable solutions which are in quantitative agreement with the full-wave solutions of Maxwell’s equations. The coupled mode approach allowed us to cast the the problem into the form of a driven nonlinear oscillator and analyze the onset of bistability under variation of the incident wave. The results presented drastically simplify the analysis nonlinear Maxwell’s equations and, thus, can be instrumental in engineering optical response via bound states in the continuum.

MoM Analysis of Cavity-Backed Annular Spherical Antennas

This paper presents a full-wave solution for cavity-backed annular spherical antennas. The formulation is based on the equivalence principle and the application of method of moments, for modeling the equivalent surface magnetic currents. Results are presented for input impedance and radiation patterns.

Microstructure-related Stoneley waves and their effect on the scattering properties of a 2D Cauchy/relaxed-micromorphic interface

In this paper we set up the full two-dimensional plane wave solution for scattering from an interface separating a classical Cauchy medium from a relaxed micromorphic medium. Both media are assumed to be isotropic and semi-infinite to ease the semi-analytical implementation of the associated boundary value problem.Generalized macroscopic boundary conditions are presented (continuity of macroscopic displacement, continuity of generalized tractions and, eventually, additional conditions involving purely microstructural constraints), which allow for the effective description of the scattering properties of an interface between a homogeneous solid and a mechanical metamaterial. The associated “generalized energy flux” is introduced so as to quantify the energy which is transmitted at the interface via a simple scalar, macroscopic quantity.Two cases are considered in which the left homogeneous medium is “stiffer” and “softer” than the right metamaterial and the transmission coefficient is obtained as a function of the frequency and of the direction of propagation of the incident wave. We show that the contrast of the macroscopic stiffnesses of the two media, together with the type of boundary conditions, strongly influence the onset of Stoneley (or evanescent) waves at the interface. This allows for the tailoring of the scattering properties of the interface at both low and high frequencies, ranging from zones of complete transmission to zones of zero transmission well beyond the band-gap region.

Numerical and Experimental Characterization of RF Waves Propagation in Ion Sources Magnetoplasmas

This paper describes three-dimensional numerical simulations and Radio Frequency (RF) measurements of wave propagation in microwave-heated magnetized plasmas of ion sources. Full-wave solution of Maxwell's equations has been addressed through the Finite Element Method (FEM) commercial software COMSOL. Our numerical model takes into account the strongly inhomogeneous and anisotropic magnetized "cold" plasma medium. The simulations reproduce the main features of the wave-plasma interaction of the Flexible Plasma Trap (FPT) that recently came into operations at INFN-LNS. A two-pins RF probe has been ad-hoc developed and used as a plasmaimmersed antenna for measuring local wave electric fields in the FPT device. The measurements of plasma electron density and RF electric field, performed for different external magnetic field configuration, allowed a direct comparison with the assumed simulation model.

Forward model for propagation-based x-ray phase contrast imaging in parallel- and cone-beam geometry

We demonstrate a fast, flexible, and accurate paraxial wave propagation model to serve as a forward model for propagation-based X-ray phase contrast imaging (XPCI) in parallel-beam or cone-beam geometry. This model incorporates geometric cone-beam effects into the multi-slice beam propagation method. It enables rapid prototyping and is well suited to serve as a forward model for propagation-based X-ray phase contrast tomographic reconstructions. Furthermore, it is capable of modeling arbitrary objects, including those that are strongly or multi-scattering. Simulation studies were conducted to compare our model to other forward models in the X-ray regime, such as the Mie and full-wave Rytov solutions.

On the Performance of Grounding, Bonding, and Shielding Systems for Direct and Indirect Lightning Strikes

A full-wave solution method of Maxwell's equations is adopted for the analysis of the performance of grounding, bonding, and shielding systems of a metallic enclosure subjected to direct and indirect lightning strikes. The method is based on a numerical solution of the electric field integral equation by the method of moments. An array of conducting wires and metallic surfaces is used to represent the lightning channel and structures in its proximity. An improved antenna theory model approach based on the concept of the distributed source is adopted for the electromagnetic analysis of indirect lightning. The methodology enables an efficient electromagnetic compatibility analysis of a combined network of metallic plates, wires, and cables exposed to direct and indirect lightning strikes. The effectiveness of most common protective schemes—namely grounding, shielding, and bonding—is examined for cables located inside a metallic enclosure with apertures. A safety assessment analysis is performed for the case of indirect lightning and is compared to the case where the lightning current is injected directly into the top of the enclosure.

Pole-zero analysis of scattering resonances of multilayered nanospheres

We demonstrate a general pole-zero method for the design of the scattering resonances of multilayered nanospheres, and we apply it to the relevant cases of strongly dispersive light scattering from metal-dielectric-metal and all-dielectric nanostructures. The pole-zero method is based on the full-wave iterative solution of the Mie scattering theory of multilayered spheres, which is valid beyond the conventional quasistatic limit. By investigating scattering resonances in the complex frequency plane, we show how to engineer anomalous Fano-like dipolar line shapes from complex pole-zero interactions controlled by the geometrical parameters of the structures. The pole-zero method is then applied to the design of the backscattering and forward-scattering efficiencies beyond the dipolar approximation. The engineering of scattering and absorption resonances with customized line shapes in metal-dielectric nanostructures provides unique opportunities for active devices including optical sensors, light emitters, and nonlinear elements.

An Accurate and Efficient 3-D Shooting-and- Bouncing-Polygon Ray Tracer for Radio Propagation Modeling

This paper describes two important improvements to a 3-D shooting-and-bouncing-polygon (SBP) ray tracer for radio propagation modeling. It introduces a way to trace diffracted-reflected (D-R) rays in the SBP framework and improves SBP accuracy when the D-R rays play an important role. It also introduces a better space partitioning scheme for the use with SBP and improves the SBP's computation efficiency by more than 10× in some applications. The numerical results are compared against published measurements and 3-D full-wave solutions. They show that the improved SBP ray tracer is a good multipurpose 3-D ray tracer which can be used to simulate urban street canyon (without double over-rooftop diffraction), indoor, and tunnel propagation environments.

Source Bearing of Extremely Low Frequency (ELF) Waves in the Earth‐Ionosphere Cavity With Day‐Night Nonuniformity

AbstractImpact is modeled of the day‐night nonuniformity of the Earth‐ionosphere cavity on the source bearing. The smooth day‐night interface is considered. The source is located at the 22.5° N; 0° E point, and the observer is positioned at 22.5° S; 0° E. Propagation path position corresponds to 4 hr UT (the night side) and to 8 hr UT (the dayside of morning terminator). We apply the full wave solution to determine the propagation parameters of extremely low frequency radio waves and solve the problem by using the 2‐D telegraph equations. The following results were obtained: Terminator impact is absent when the propagation path is at the center of night or day hemisphere. Deviation of source bearing varies with frequency similarly to Schumann resonance pattern and may reach 3–4° at certain frequencies. A weak elliptic polarization is observed for the monochromatic radiation; its sign changes when propagation path shifts from one side of the day‐night interface to the other. Temporal variations of the pulsed orthogonal components of horizontal magnetic field form a hodograph outlining complex loops, which obstructs the source bearing. Waveforms change noticeably due to frequency response of a receiver, but the maximum instantaneous deviations do not exceed 1–2°. Effect of the day‐night nonuniformity on the Schumann resonance fields does not exceed the level of natural fluctuations caused by the background lightning activity. Therefore, deviations in the source bearing caused by the day‐night nonuniformity might be detected exclusively for exceptionally great extremely low frequency transients.

Lightning-Induced Voltages on a Distribution Line With Surge Arresters Using a Hybrid FDTD–SPICE Method

Installing lightning arresters is an effective way to protect distribution lines from lightning-induced voltages. Spacing effectiveness of lightning arresters is one of the main concerns in the industry. Different separation distances of arresters have been proposed in the literature. In these studies, the simulations are made with simplified circuit models, which are not sufficient to support their conclusions. This paper presents a hybrid finite-difference time-domain (FDTD) SPICE method for analyzing lightning-induced overvoltages on a distribution line with arresters being installed. The FDTD method gives a full-wave solution of the induced voltages. To handle nonlinear lightning arresters, this FDTD method is integrated with a circuit solver SPICE. A diode-based model for the arrester is proposed using a SPICE subcircuit and is coupled to the FDTD domain as a connecting port. For the verification purpose, the method is compared with the results obtained in the rocket-triggered lightning experiment, in which no arresters were installed. Lightning-induced overvoltages on the distribution line with different arrester spacing arrangements are analyzed finally. Efficient arrester spacing under both first and subsequent strokes is investigated.

Impact of the Ionospheric Day–Night Non-Uniformity on the ELF Radio-Wave Propagation

The real structure of the lower ionosphere should be taken into account when propagation of extremely low frequency (ELF) radio waves is modeled and the global electromagnetic (Schumann) resonance in the Earth–ionosphere cavity is studied. In the present work, we use a 2D telegraph equation (2DTE) to estimate the effect of the ionospheric day–night non-uniformity on the electromagnetic field amplitude at the Schumann-resonance and higher frequencies. The properties of the cavity are accounted for by using the full wave solution technique through conductivity profiles in the daytime and night-time conditions. Electromagnetic fields in the non-uniform cavity are found by using a 2DTE. Both the sharp terminator model and the model of a smooth day–night transition were considered. The main attention was focused on effects arising on 5000-km paths that are perpendicular or parallel to the solar terminator line. The data were computed for a series of frequencies. A comparison of the calculated data with observation results is also performed and an interpretation of the observed effects is given.

Solution box: SOLBOX-12

In three-dimensional electromagnetic solvers, extreme values for electrical parameters typically lead to instability, inaccuracy, and/or inefficiency issues. Despite using the term “extreme,” such relatively large or small values of conductivity, permittivity, permeability, wavenumber, intrinsic impedance, and other electrical parameters are commonly observed in natural cases. Computational electromagnetic solvers adapt themselves to handle challenging cases by replacing exact models with approximate models, while minimizing the modeling error due to these transformations. For example, most metals with high conductivity values are assumed to be perfectly conducting, especially if the considered structure is comparable to the wavelength. This is very common for practical devices, such as antennas, metamaterials, filters, etc., at radio and microwave frequencies. In some cases — e.g., when the overall structure is small in terms of a wavelength — even a full-wave solver may not be required to analyze the underlying phenomena. Examples are circuit theory based on lumped elements and transmission-line modeling. On the other side, penetrable models are commonly used to represent dielectric and magnetic materials, when their electrical parameters (specifically, permittivity and permeability) have numerically “reasonable” values that facilitate their full-wave solutions without a fundamental issue. As the electrical parameters become extreme and other conditions (sizes, excitations, geometric properties) are satisfied, numerical approximations may again become useful, leading to the well-known implementations such as those based on impedance boundary conditions and physical optics.