Full-wave Theory Research Articles

On Wave Propagation Mechanisms in a Dielectric Rod Array

Wave propagation mechanisms in a lossy dielectric rod array are examined using full-wave simulation and homogenization theory. Both approaches show that a slab mode and an air mode propagate in the structure with different phase velocities. The propagation constants, attenuation constants, and field distributions of these two dominant mechanisms are extracted from simulation data and compared to those found from homogenization theory.

Controlling light scattering and polarization by spherical particles with radial anisotropy

Based on full-wave electromagnetic theory, we derive the zero-forward and zero-backward scattering conditions for radially anisotropic spheres within the quasi-static limit. We find that the near-field intensity can be tuned dramatically through the adjustment of the radial anisotropy, while the far-field light scattering diagrams are similar under the zero-forward or zero-backward scattering conditions. Generalized "Brewster's angle" for anisotropic spheres is also derived, at which the scattering light is totally polarized. In addition, the high-quality polarized scattering wave and the tunable polarization conversion can be achieved for the radially anisotropic spheres.

Analysis and Design of Two-Dimensional Resonant-Type Composite Right/Left-Handed Transmission Lines With Compact Gain-Enhanced Resonant Antennas

A two-dimensional (2-D) resonant-type composite right/left-handed transmission line (CRLH TL) is proposed consisting of complementary split-ring resonators (CSRRs) and series capacitive gaps. For characterization and design, the circuit parameters extraction procedure for the TL element is derived, and the unique 2-D dispersion characteristics (CRLH nature) are analytically investigated and further verified by eigenmode analysis performed in HFSS and phase analysis in ADS. A good agreement of dispersion diagram is obtained between full-wave simulation and theory. To demonstrate potential applications, two types of microstrip antennas have been designed, fabricated, and measured following the design procedures that are established. In the first design, a multifrequency antenna operating at three resonant modes of n = -1, n = 0, and n = + 1 is designed by arranging a 2×2 CRLH array in a conventional patch. The frequency ratios between these modes are 1.98 and 1.15, respectively, which can be arbitrarily modulated by controlling the proportion between the CRLH section and the patch. In the second design, zeroth-order resonant antennas are researched. These antennas exhibit simultaneously a leaky-wave characteristic and an omnidirectional radiation behavior, distinguishing them significantly from any previous designs. In both cases, the antenna gain is comparable, and the cell structure is uniplanar and electrically small.

Mono- and Bistatic Scattering Reduction by a Metamaterial Low Reflection Coating

Significant reduction of mono- and bistatic scattering cross sections of an electrically large metallic cube through the application of an electrically thin metamaterial low reflection coating operating in the Ka-band (30-40 GHz) is described. A coating composed of a metallic array of sub-wavelength sized capacitively loaded strip inclusions printed on top of a thin, slightly lossy and grounded substrate has been designed and fabricated to experimentally evaluate the performance of the coating in scattering reduction. The scattering reduction is estimated by comparing the mono- and bistatic scattering patterns of the coated and uncoated cube. The measurement results are compared with full wave and physical theory of diffraction simulations, and the possibility of accurately modeling the low reflection coatings with impedance boundary conditions is pointed out.

Anomalous high amplitude ratios of P5KP/PKPab and P4KP/P(S)cP observed globally around 1 Hz

Amplitude ratio of 30 short-period conspicuous P5KP and PKPab phases from five intermediate depth or deep events in Fiji-Tonga recorded at European stations around 150° distance shows a mean value two to three times the ratio of the synthetic amplitudes obtained by the normal-mode theory (and ak135 model) or by full-wave theory (and PREM). There is a large variance in the results, also observed in five amplitude ratios from one event in Argentina observed at temporary stations in China around 156°. Global recordings of three major deep earthquakes in Fiji, Bonin, and Western Brazil observed at ASAR, WRA, and ZRNK arrays, at 59 North America stations and at six South Pole stations displayed conspicuous P4KP and PcP (or ScP) phases. The amplitude ratio values of P4KP vs P(S)cP are sometimes almost one order of magnitude larger than the corresponding values of the synthetics. In both cases, arrival times and slowness values (corrected for ellipticity and station elevation) at the distances up to 23° beyond the A cutoff point predicted by ray theory match both the synthetics, suggesting the observations are the AB branch of PmKP (m = 4, 5) around 1 Hz. In disagreement to ray theory, no reliable BC branch is observed neither on the recordings nor on the normal-mode synthetics. The high amplitude ratio values cannot be explained by realistic perturbations of the velocity or attenuation values of the global models in the proximity of the core-to-mantle boundary (CMB). We speculate that the focusing effects and/or strong scattering most likely associated to some anomalous velocity areas of the lowermost mantle are responsible for that. The results suggest limitations of the previous evaluations of the short-period attenuation in the outer core from PmKP amplitudes (m ≥ 3), irrespective of the fact that they are obtained by using ray theory, normal-mode or full-wave synthetics. Attempts to use PmKP arrival times in order to refine velocity structure in the proximity of CMB should be also regarded with care if the propagation times have been computed with ray theory.

Comparison of Image and Transmission Line Models of Energized Horizontal Wire Above Two-Layer Soil

The paper presents comparison between two approximate models of energized horizontal thin-wire conductors above two-layer soil. The formulation is posed in frequency domain by using two approaches. The first one is based on quasi-static image theory within Mixed Potential Integral Equation. The second one is based on transmission line theory with approximation of per unit length parameters. The authors compare currents computed by the both approximate models of a center fed wire to establish the computation errors over a wide frequency range. The main objective is to validate the proposed image and transmission line models for various lengths of wire conductors, and various cases of low and high conductivities of two-layer soil. The verification of the results is done by comparison with exact model based on full-wave theory. Detailed parametric analysis clearly illustrate validity domain and problems when using both approximate models with respect to their use in practical EMC studies.

ANALYSIS OF ELECTROMAGNETIC PLANE WAVE SCATTERING FROM 2-D PERIODIC ARRANGEMENTS OF POSTS

In the paper, the analysis of electromagnetic wave scattering from frequency selective surface is presented. The surface is composed of periodically arranged posts. The multimodal scattering matrix of such structure is derived and the transmission and re∞ection characteristic for the structure with arbitrary plane wave illumination are calculated. The exact full-wave theory based on the mode-matching method is applied to develop an e-cient theory to analyze such structures. The validity and accuracy of the approach are verifled by comparing the results with those obtained from alternative methods. The analysis of plane wave scattering form the frequency selective surface (FSS) composed of periodic arrangements of scatterers is conducted in this paper. The constructive elements of this structure are comparable in size to the operation wavelength and are composed of conducting and dielectric material. FSSs when multilayered can be utilized as an electromagnetic band structure (EBG) in microwave wavelength range or photonic band structure (PBG) in optical range. Recently, EBGs and PBGs are of great interest due to their extraordinary properties and potential applications, e.g., fllters, polarizers, substrates for radiating elements, or optical switches (1{14). Many numerical techniques have been utilized to investigate band gap structures. The most popular are the cylindrical-harmonic expansion method (15), the flnite element method (16), the flnite difierence method (17), and Fourier modal method (18). FSSs can also flnd application in polarizers

Efficiency of Ultrasonic Comb Transducers

AbstractComb transducers are applied in ultrasonic testing for generation of Rayleigh or Lamb waves by scattering of the incident bulk waves onto surface waves at the periodic comb-substrate interface. Hence the transduction efficiency, although rarely discussed in literature, is an important factor for applications determining the quality of the measured ultrasonic signals. This paper presents the full-wave theory of comb transducers concluded by evaluation of their efficiency for a couple of examples of standard and certain novel configurations.

Focusing of surface waves by variable bathymetry

Abstract Scattering of a monochromatic train of surface gravity waves incident on a finite region of arbitrary three-dimensional smoothly varying bathymetry is considered in this paper. The full three-dimensional linear water wave theory is approximated by the depth-averaged modified mild-slope equations and a Greens function approach is used to derive domain a integral equation for the function relating to the unknown surface over the varying bed. A simple but robust and effective numerical scheme is described to approximate solutions to the integral equation. The method is applied to bathymetries which exhibit focusing in the high-frequency ray-theory limit and used to illustrate that focusing occurs at finite wavelengths where both refractive and diffractive effects are included. Specifically, examples of elliptical and bi-convex lens bathymetries are considered.

On the mechanisms of heat transport across vacuum gaps

Heat exchange between closely positioned bodies has become an important issue for many areas of modern technology including, but not limited to, integrated circuits, atomic force microscopy, and high-density magnetic recording, which deal with bodies separated by gaps as narrow as a few nanometers. It is now recognized that heat transport across a gap of sub-micron width does not follow the Stefan–Boltzmann law, which is based on a conventional theory developed for sufficiently wide gaps. This paper describes the structure of thermally excited electromagnetic fields in arbitrarily narrow gaps, and it also shows that heat can be carried across narrow vacuum gaps by acoustic waves. The structure of the acoustic wave fields is also described, and it is shown that they become the dominant heat carriers in gaps narrower than a certain critical width, which is estimated to be a few nanometers. For example, consider a vacuum gap between silicon half-spaces. When the gap’s width is below a critical value, which is about 7.5 nm, the contribution of acoustic waves must be taken into account. Assuming that the wavelength of thermally excited acoustic waves is of order 1 nm, it may be possible to estimate the contribution of acoustic waves to heat transport across gaps with 4 nm < h < 7.5 nm by the kinetic theory, but for narrower gaps with h < 4 nm, this approximation is not valid, and then the full wave theory must be used. Also for gaps narrower than about 2.5 nm, there is no need to take into account electromagnetic radiation because its contribution is negligible compared to that of acoustic waves.

Analysis of comb transducers with sliding teeth

Ultrasonic comb transducer generates surface acoustic waves on an elastic substrate by periodic traction exerted by its vibrating periodic teeth on the substrate surface . In this paper, the comb teeth are actually sliding elastic spacers between an acoustic buffer and the substrate. The incident wave in acoustic buffer scatters on periodic spacers producing interface waves in the system which transform into Rayleigh waves at the transducer edges. The full-wave theory of interface wave generation is presented, concluded by efficiency estimation of transformation of the incident wave into the surface wave in the substrate and of the surface waves back to bulk waves in the acoustic buffer. Numerical examples presented for all aluminum substrate , buffer and teeth show the 11-teeth comb combined efficiency for generation and detection on the level of −40 dB for optimized teeth height.

Multilayer Laue Lens: A Path Toward One Nanometer X-Ray Focusing

The multilayer Laue lens (MLL) is a novel diffractive optic for hard X-ray nanofocusing, which is fabricated by thin film deposition techniques and takes advantage of the dynamical diffraction effect to achieve a high numerical aperture and efficiency. It overcomes two difficulties encountered in diffractive optics fabrication for focusing hard X-rays: (1) small outmost zone width and (2) high aspect ratio. Here, we will give a review on types, modeling approaches, properties, fabrication, and characterization methods of MLL optics. We show that a full-wave dynamical diffraction theory has been developed to describe the dynamical diffraction property of the MLL and has been employed to design the optimal shapes for nanofocusing. We also show a 16 nm line focus obtained by a partial MLL and several characterization methods. Experimental results show a good agreement with the theoretical calculations. With the continuing development of MLL optics, we believe that an MLL-based hard x-ray microscope with true nanometer resolution is on the horizon.

High Frequency PKKPBC Around 2.5 Hz Recorded Globally

Anomalous high frequency PKKPBC signals (displaying a large amount of energy around 2.5 Hz), recorded globally for deep and intermediate depth earthquakes, are compared to PKKPAB signals. The attenuation difference $$ t_{\text{AB}}^{*} - t_{\text{BC}}^{*} $$ is evaluated from spectral amplitudes in the range 96–111°, being approximately twice the results provided by full-wave theory and PREM (with no low Qμ zone in the lowermost mantle and a nearly infinite QK in the outer core). Most ray paths for such recordings are piercing the D″ region in the proximity of regions where ultra-low velocity zones (ULVZ) have been previously reported beneath the North Atlantic Ocean, the Southwest Pacific and the southwestern part of South America. If BC amplitudes around 2.5 Hz and at low frequencies (0.5–1.5 Hz) are comparable, the observed attenuation difference (in the frequency range 0.2–2.5 Hz) is small (around 0.25 s) and close to the PREM value. The particle motion of the high-frequency PKKPBC at 2.5 Hz is quite similar to that of the raw recording, suggesting a deep source. An explanation for this might be scattering of the BC branch in some very restricted areas of the lowermost mantle. Alternately, the presence of a thin layer with high attenuation in the D″ region would most likely be associated with either the ultra-low velocity zone (ULVZ) or light sediments on the underside of the core-mantle boundary (CMB). Correlated to other methods to investigate the lowermost mantle, the high-frequency PKKPBC can be used to map lateral variations of attenuation above the CMB, possibly associated with the boundary of the superplumes, especially when PKKPAB is observed.

Achieving Invisibility of Homogeneous Cylindrically Anisotropic Cylinders

In this paper, we establish the full-wave electromagnetic scattering theory to study the electromagnetic scattering from infinitely long cylinders with cylindrically anisotropic coatings. We show that the total effective scattering width can be dramatically reduced by the suitable adjustment of the dielectric anisotropy of the shell, while it is not the case for tuning the dielectric anisotropy of the core. Furthermore, we could make the cylindrical objects invisible when both dielectric and magnetic anisotropies are adjusted. In the long wavelength limit, we develop effective medium theory to derive the effective isotropic permittivity and permeability for the anisotropic coated cylinders, and the invisibility radius ratio derived from the full-wave theory for small coated cylinders can be well described within the effective medium theory.

PLASMONIC RESONANT LIGHT SCATTERING BY A CYLINDER WITH RADIAL ANISOTROPY

We apply the full-wave electromagnetic theory to study electromagnetic scattering by a small cylindrical particle with radial anisotropy for normally incident light with transverse magnetic (TM) polarization. The scattering coe-cients are derived, when the radial anisotropies in both the permittivity and permeability tensors are taken into account. It is shown that the surface and volume plasmon resonances can be identifled by the sign of dt=dq, in which t is the permittivity element in a direction tangential to the local r-axis, and q is the size parameter. The near fleld distributions for surface and volume modes are illustrated by flnite element method. It is found that small changes of anisotropy can afiect the scattering e-ciencies signiflcantly. Moreover, the quadrupole and octupole resonant peaks may be much higher and sharper than those of dipole resonance in the scattering e-ciency spectra.

A Method to Solve the Forward Problem in Magnetic Induction Tomography Based on the Weakly Coupled Field Approximation

Magnetic induction tomography (MIT) is a noninvasive modality for imaging the complex conductivity (kappa = sigma + jomegaepsilon) or the magnetic permeability (mu) of a target under investigation. Because MIT employs noncontact coils for excitation and detection, MIT may be suitable for imaging biological tissues. In medical applications where high resolutions are sought, image reconstruction is a time and memory consuming task because the associated inverse problem is nonlinear and ill-posed. The time and memory constraints are mainly imposed by the solution of the forward problem within the iterative image reconstruction procedure. This paper investigates the application of a weakly coupled approximation to the solution of the forward problem and examines the accuracy against the computation time and memory gained in adopting this approximation. Initially, an analytical solution for mutual impedance change of a coil pair due to a large planar conductive object is presented based on a full wave theory and used to demonstrate a 10 MHz frequency excitation as an acceptable upper frequency limit under which the approximation is valid. Subsequently, a numerical impedance method adopting the approximation is presented. Here the impedance method is used to solve the forward problem, which employs electrical circuit analogues to mesh the target into a network that can be solved using circuit analysis and sparse matrix technique. The error due to the approximation is further estimated numerically with the impedance method against a commercial finite-element package (commercial FE solver, COMSOL) and results show at 10 MHz excitation a 0.4% of tolerance is achieved for conductivities in the range <0.5 S/m. The results also show the method can be applied for low conductivity medical applications and is computationally efficient compared to equivalent finite-element methods.

New Full Wave Theory for Plane Wave Scattering From Rough Dielectric Surfaces—The Correction Current Method: TE Polarization

A new full-wave theory for scattering from rough dielectric surfaces-called the correction current (CC) method-is presented. An iterative solution is developed leading to a first-order scatter pattern in the form of a single integral, making it computationally efficient and capable of showing surface parameter dependencies explicitly. The first-order CC-scatter solution is shown to satisfy reciprocity, to comply with a pattern symmetry relation, and to be accurate over a wide range of surface parameters. The theory is also shown to be capable of quantifying its field errors resulting in an error criterion that is derived from the theory itself (which is not generally available in other theories). Radar cross sections for random rough surfaces with Gaussian statistics are compared to data generated by solving the electric field integral equation using the method of moments. Good agreement was shown to result for a wide range of surface parameters.

The structure of the base of the outer core inferred from seismic waves diffracted around the inner core

We systematically searched for seismograms of waves diffracted around the inner core (PKPCdiff) from all the temporary seismic arrays with data currently available at the IRIS DMC, as well as some permanent regional seismic arrays including F‐NET in Japan and GRF in Germany, to assemble the largest high‐quality PKPCdiff database ever created. PKPCdiff waves preferentially sample the base of the outer core and so contain important clues about Earth structure in this region. We measured PKPDF–PKPCdiff differential traveltimes and PKPCdiff/PKPDF amplitude ratios in the distance range of 154°–160° and modeled the observations using grid searches and full wave theory synthetic seismograms. The optimum model found by fitting the differential traveltimes has relatively low velocity at the base of the outer core as in AK135, which is consistent with many previous traveltime studies. However, the optimum model found by fitting the amplitude ratios (PKPCdiff/PKPDF) does not exhibit this feature, and instead is closer to PREM. The discrepancy may be explained by two likely causes. One is that small‐scale topography or roughness on the ICB tends to scatter energy away from PKPCdiff waves by generating trailing coda waves. The other is that there exists a thin layer with relatively low Q at the base of the outer core. This might be expected if there are suspended solid particles at the base of the outer core, as proposed decades ago. Both mechanisms could generate smaller PKPCdiff amplitudes without significantly affecting PKPCdiff traveltimes.

Analysis and Design of a Polarizer Rotator System

A new analysis of an N-section polarizer composed of periodic arrays of wires is presented. The exact full-wave theory based on the mode-matching method is applied to analyze the structures. The validity and accuracy of the approach are verified by comparing the results with those obtained from an equivalent circuit model based on the transmission line theory and the authors' measurement of a manufactured prototype.

Analysis of Circular Cavity With Cylindrical Objects

This paper presents the analysis of electromagnetic wave scattering by cylindrical objects located arbitrarily in a circular cavity. The exact full-wave theory based on the mode-matching method is applied to analyze the structures. The resonance frequencies of the investigated resonators are accurately determined. The validity and accuracy of the approach are verified by comparing the results with those obtained from alternative numerical methods and the authors' experiment.