Surface Wave Modes Research Articles

Observation of Higher-Mode Surface Waves from an Active Source in the Hutubi Basin, Xinjiang, China

ABSTRACTBasins with thick sediments can amplify and prolong the incoming seismic waves, which may cause serious damage to surface facilities. The amplification of seismic energy depends on the shear-wave velocity of the uppermost layers, which is generally estimated through surface wave analysis. Surface waves may propagate in different modes, and the mechanism of the mode development is not well understood. Exploiting a recently deployed permanent airgun source in the Hutubi basin, Xinjiang, northwest China, we conducted a field experiment to investigate the development of multimode surface waves. We observed surface waves at the frequency of 0.3–5.0 Hz with apparent group velocities of 200–900 m/s, and identified five modes of surface waves (three Rayleigh-wave modes and two Love-wave modes) through time–frequency and particle-motion analyses. We then measured 125 group velocity dispersion curves of the fundamental- and higher-mode surface waves, and further inverted the 1D S-wave velocity structure of the Hutubi basin. The S-wave velocity increases abruptly from 238 m/s at the surface to 643 m/s at 300 m depth. Synthetic seismograms with the inverted velocity structure capture the main features of the surface waves of the different modes. Synthetic tests suggest that the low velocity, high velocity gradient, and shallow source depth are likely the dominant contributing factors in the development of higher-mode surface waves.

Zeroth radial modes of azimuthal surface waves in dense plasma-loaded, coaxial helix traveling-wave-tube-like waveguides

An analytical model of coaxial traveling-wave-tube-like waveguides with plasma filling has been justified and utilized to analyze the eigenmodes. Very often, introducing plasma into vacuum electronic devices leads to essential advantages as compared with evacuated tubes. The cylindrical structure under the present consideration consists of a central dielectric rod, placed inside a plasma coaxial layer with a metallic helix sheath on its outer interface, and a metal screen separated from the plasma by another dielectric layer. The dispersion properties of electromagnetic waves propagating across the external axial static magnetic field in such traveling-wave-tube-like waveguides are studied and summarized. The presence of a dense plasma coaxial layer makes the media nontransparent for waves in the electron cyclotron frequency range. However, surface type electromagnetic waves can propagate in this case. These waves are called azimuthal surface waves (ASWs). The helix sheath causes coupling of ordinarily and extraordinarily polarized ASWs. The zeroth radial ASW modes have been found to be most dangerous for parasitic wave excitation in dense plasma-loaded, coaxial traveling-wave-tube-like waveguides.

Long-Range Spoof Surface Plasmons(LRSSP) on the Asymmetric Double Metal Gratings

Spoof surface plasmons (SSP) on the corrugated metal surfaces have been widely studied over the past decade in both microwave and Terahertz (THz) band. Previous studies show that SSP mode on the metal grating suffers from high dissipative losses in high THz band especially near asymptotic frequency which may limit its real applications. The issue can be addressed by utilizing long-range SSP mode (LRSSP). LRSSP is a special low-loss symmetric propagating surface wave mode along double-layer corrugated metallic waveguides. In this paper, the asymmetric double metal gratings are proposed to support LRSSP which can significantly reduce the damping losses of the other short-range SSP mode (SRSSP) on the conventional doubly-corrugated metallic surfaces, thus enabling new possibilities to utilizing this SRSSP mode within long-range manner. According to our dispersion theory and the numerical calculations, the propagation loss of LRSSP is still lower than that of SRSSP within asymmetric regime, which demonstrates good tolerance to the asymmetry of the double-layer corrugated structure. However, its long-range propagation superiority of LRSSP vanishes gradually as the degree of asymmetry is enlarged. This work provides an alternative approach to increase the propagation length of SRSSP mode on the doubly-corrugated metallic surfaces and can open up new avenues to develop some novel LRSSP-based plasmonic devices such as waveguides, filters, sensors and active powerful radiation sources induced by energy beam below optical spectrum.

Customized broadband pentamode metamaterials by topology optimization

Pentamode metamaterials (PMs), a kind of metafluids composed of complex solid medium, have shown enormous potential for both elastic wave and underwater acoustic wave manipulation. However, due to the lack of thorough understanding of the formation mechanism, most reported artificial and empirical PMs share very similar topological features, thus depriving the possibility of obtaining rigorous combination of wave parameters that are required to deliver desirable and prescribed properties and functionalities. To tackle this challenge, with the assumption of C2v, C4v and C6v symmetries in both square and triangle lattices, we propose a unified inverse strategy to systematically design and explore a series of novel isotropic or anisotropic PM microstructures through bottom-up topology optimization. Optimized PM microstructures are designed to provide customized effective mass density, elastic modulus, anisotropy degree and pentamode features on demand. We demonstrate that most optimized microstructures possess broadband single-mode range of exclusive longitudinal waves; some even feature record-breaking relative single-mode bandwidths exceeding 150%. Upon shielding lights on the beneficial topological features of the broadband PMs, we extract the main topological features to form simplified PM configurations, i.e., multiple symmetric solid blocks with slender rods, which can induce the multiform multiple-order rotational vibrations or the integration of the low-order rotational vibrations and anisotropic local resonances for the broadband single-mode nature. At a higher design level, we establish a dedicated inverse-design strategy, under the function-macrostructure-microstructure paradigm, to conceive a novel broadband subwavelength underwater pentamode shielding device, which enables the conversion of propagating acoustic wave to the evanescent surface wave mode within the frequency range [1000 Hz, 4000 Hz]. Our study offers new possibilities for the practical realization of broadband PMs and underwater pentamode devices with rigorously tailored effective parameters, thus bring the PM-based technology within reach for practical applications.

Hybrid-mode driven dual-band absorber in long-wave infrared with a phase-gradient metasurface

Long-wave infrared perfect absorbers have many potential applications such as thermal imaging and materials identifications. In contrast with previously reported absorbers which result from either electric or magnetic resonances, we propose a dual-band absorber through exciting the hybrid mode supported by the reflective phase-gradient metasurface. Surface wave mode and dipole-like resonance are respectively investigated to demonstrate the origins of two absorption peaks near 8.1 µm and 14.1 µm. Eigen-mode calculations agree well with the full-wave simulation results. To clarify the role of phase gradient metasurface in enhancing the absorbance, comparisons with single unit-cell metasurfaces are illustrated. The absorptions for incidence with different polarization states also confirm phase gradient design. Our findings may find applications in the long-wave infrared filters, minerals identifications and optoelectronic detectors.

Thermoelastic damping in a thin circular transversely isotropic Kirchhoff–Love plate due to GN theory of type III

This research deals with the study of thermoelastic damping in transversely isotropic thin circular Kirchhoff–Love plate. Mathematical model is formed for time-harmonic displacement and temperature fields due to the GN theory of thermoelasticity of type III. The model is solved to obtain the expressions for thermoelastic damping, displacement, and temperature fields for circumferential surface wave modes for simply supported and clamped plate resonators. The numerical results for both the simply supported and clamped boundary conditions for an axisymmetric circular plate are illustrated. It is observed that the damping of vibrations is considerably influenced by surface wave modes. The thickness of the plate also has major effects on the vibrations of resonators. The computer-simulated results to illustrate the effect of circumferential surface wave modes on thermoelastic damping for the GN III theory of thermoelasticity have been depicted graphically.

Comparative Analysis on Multimode Sensitivity Kernels of Rayleigh Wave Based on Adjoint Method

Different modes of surface waves possess different phase velocities for each wavelength, which reflects the layer information of different depths. Penetrating depth of surface wave data is significant to determine stratigraphic models and invert their velocity structures. Instead of ray theory, we use the sensitivity kernels to investigate the relationship between multimode wavelengths and penetrating depth for a layered model based on the adjoint wave equation. We use linear Radon transform to perform Rayleigh-wave multimode separation and reconstruction. The results confirm that longer wavelength components are sensitive to deeper layers. Different modes of surface waves are sensitive to different depths. The kernels in HVL (high-velocity-layer model) and LVL (low-velocity-layer model) suggest that the velocity anomaly layer has a shielding effect on sensitivity penetrating. Rayleigh waves are insensitive to the layers beneath a velocity anomaly layer and the HVL itself.

Electromagnetic Energy Surface Modes in Metamaterial-Filled Bi-layer Graphene Structures

This paper presents a theoretical study on the propagation of electromagnetic surface waves supported by the metamaterial-filled bi-layered graphene structure. The effective surface conductivity approach based upon the Kubo’s formalism is used to model the atomically thick graphene layer, while the analytical modeling of the metamaterials used the framework of causality principle-based Kramers-Kroing relations. With respect to the index of refraction, the two configurations of metamaterials have been considered—i.e., double positive (DPS) and double negative (DNG). The impedance boundary conditions (IBCs) have been employed at the interface for the computation of characteristics equations of odd and even surface modes under DPS and DNG configurations. The numerical results regarding the dispersion relations, effective mode index, and phase speed for the odd and even modes of electromagnetic surface waves supported by each configuration of structure have been presented. Further, the influence of chemical potential and thickness of metamaterial filling in parallel graphene layers on the wave propagation characteristics has been analyzed. To check the accuracy of the numerical results, special conditions were employed, which converge to the published results. The proposed work may have potential applications in plasmonic based logic designs, renewable energy devices, THz surface wave guides, and near-field communication devices.

Exceptional points and enhanced sensitivity in PT-symmetric continuous elastic media

We investigate non-Hermitian degeneracies, also known as exceptional points, in continuous elastic media, and their potential application to the detection of mass and stiffness perturbations. Degenerate states are induced by enforcing parity-time symmetry through tailored balanced gain and loss, introduced in the form of complex stiffnesses and may be implemented through piezoelectric transducers. The introduction of external perturbations leads to a splitting of the eigenvalues, which is explored as a sensitive approach to the detection of such perturbations. Numerical simulations on one-dimensional waveguides illustrate the presence of several exceptional points in their vibrational spectrum, and conceptually demonstrate their sensitivity to point mass inclusions. Second order exceptional points are shown to exhibit a frequency shift in the spectrum with a square root dependence on the perturbed mass, which is confirmed by a perturbation approach and by frequency response analyses. Elastic domains supporting guided waves are then investigated, where exceptional points are formed by the hybridization of Lamb wave modes. After illustrating a similar sensitivity to point mass inclusions, we also show how these concepts can be applied to surface wave modes for sensing crack-type defects. The presented results describe fundamental vibrational properties of PT-symmetric elastic media supporting exceptional points, whose sensitivity to perturbations goes beyond the linear dependency commonly encountered in Hermitian systems. The findings are thus promising for applications involving sensing of perturbations such as added masses, stiffness discontinuities and surface cracks.

Surface Wave Attenuation in Multilayer Structures With Lossy Media and Impedance Surfaces

A methodology for analyzing the attenuation constant of surface wave propagating in general multilayer structures is proposed. The multilayer structure may include any number of layers, that can be made up of lossy dielectric, magnetic-material, and impedance surfaces. The non-linear characteristic equation (transverse resonance equation - TRE) of the multilayer structure is defined by utilizing transmission line (TL) theory. Consequently, the root(s) of the TRE is/are computed which indicates the complex propagation constant of that characteristic equation. The obtained results are validated over the completely shielded waveguide structures where the full wave simulation is possible. The proposed approach is employed to analyze and discuss the propagation and attenuation constant of surface wave modes in several representative examples. The analysis is carried out in the frequency range from 1 to 12 GHz.

A Low-Profile Dielectric Resonator Antenna With Compact-Size and Wide Bandwidth by Using Metasurface

A dielectric resonator antenna (DRA) with the loading of metasurface (MS) is proposed for low-profile, wide-bandwidth and compact-size. Firstly, an MS structure consisting of $6\times6$ periodic metallic patch cells is loaded above the DRA. It aims to excite an additional TM surface wave above the fundamental TE111 mode of the rectangular DRA. Then, the shorting walls are printed on two sides of the dielectric, thus moving down the operating frequency with respect to its TM surface wave mode. As such, the bandwidth of the antenna is significantly widened with compact-size under the operation of TE111 and TM surface wave modes. Finally, the proposed DRA with enhanced performance is fabricated and tested. The results show that an impedance bandwidth of the antenna is dramatically increased to about 17.2%, covering the frequency range from 1.75 to 2.08 GHz, which is about 9.6 times wider than the traditional DRA at the same thickness (1.8%). Besides, it still maintains the broadside radiation pattern with stable gain of around 6.6 dBi and fairly low cross polarizations of below −26 dB. Particularly, the overall size of the radiator still maintains as small as about $0.32\lambda _{0} \times 0.32\lambda _{0} \times 0.044\lambda _{0}$ . It should be noted that the analysis of the antenna is carried out by using Ansys HFSS software version 14.0 and ADS 2011.

Study of transmission characteristics of disk transducer in the radially propagated Rayleigh wave excitation mode

A mathematical model of a capacitive ultrasonic transducer is designed allowing to emit ultrasonic vibrations into an electrically conductive product. The influence of a polarizing electrostatic field on the Coulomb forces formation in the surface layer of a metal sample is determined. A closed solution to the electrostatics problem is obtained for a piecewise homogeneous medium in which a half-space is filled with metal having finite values of electrical conductivity and magnetic permeability. An expression is obtained for calculating the surface density of a static electric charge on the metal sample surface. As part of the mathematical model of a capacitive sensor in the mode of converting electric energy to high-frequency mechanical (ultrasonic) energy in metals, closed solutions for electrostatics and electrodynamics problems are constructed in relation to a piecewise-homogeneous medium in which a half-space is filled with metal having finite values of electrical conductivity and magnetic permeability. It is determined that a capacitive disk transducer excites forces acting normally to the surface of electrically conductive products. A quantitative assessment of the surface density of the Coulomb forces is made. The main factors determining the sensitivity of a capacitive disk transducer are specified. As an example of using the simulation results, the amplitude factor of radially propagating Rayleigh waves is calculated. The concept of the wave characteristics of the transducer in the excitation mode of ultrasonic surface waves is introduced.

Local coupling and conversion of surface waves due to Earth’s rotation. Part 1: theory

SUMMARYEarth’s rotation affects wave propagation to first order in the rotation through the Coriolis force. The imprint of rotation on wave motion has been accounted for in normal mode theory. By extending the theory to propagating surface waves we account for the imprint of rotation as a function of propagation distance. We describe the change in phase velocity and polarization, and the mode conversion of surface waves by Earth’s rotation by extending the formalism of Kennett for surface wave mode conversion due to lateral heterogeneity to include the Coriolis force. The wavenumber of Rayleigh waves is changed by Earth’s rotation and Rayleigh waves acquire a transverse component. The wavenumber of Love waves in not affected by Earth’s rotation, but Love waves acquire a small additional Rayleigh wave polarization. In contrast to different Rayleigh wave modes, different Love wave modes are not coupled by Earth’s rotation. We show that the backscattering of surface waves by Earth’s rotation is weak. The coupling between Rayleigh waves and Love waves is strong when the phase velocities of these modes are close. In that regime of resonant coupling, Earth’s rotation causes the difference between the Rayleigh wave and Love wave phase velocities that are coupled to increase through the process of level-repulsion.

Regional Crustal Imaging by Inversion of Multimode Rayleigh Wave Dispersion Curves Measured From Seismic Noise: Application to the Basque‐Cantabrian Zone (N Spain)

AbstractSeismic‐noise tomography is routinely applied for imaging geological structures at different spatial scales. The frequently used time‐domain approach presents two limitations. First, extracting surface‐wave group velocities from time‐domain cross‐correlations requires interstation distances of at least three wavelengths, which may be problematic when working at local or regional scales. Second, the presence of higher modes of surface waves in the cross‐correlation functions is often disregarded, which may cause loss of valuable information about the shear‐wave velocity structure. In this work, we present a complete inversion scheme that avoids these limitations and use it to obtain a 3D shear‐wave velocity model of the Basque‐Cantabrian Zone (N Spain), a structurally complex area affected by multiple tectonic events. The resulting model agrees with the existing geological and geophysical knowledge and significantly extends the area for which high‐resolution information is available.

Plasmonic Metasurfaces Enabled Ultra‐Compact Broadband Waveguide TM‐Pass Polarizer

AbstractSilicon waveguide polarizers offer a simple yet robust approach to address the polarization‐dependent issue of silicon‐based optical components, and hence have found numerous applications in silicon photonics. However, the available silicon waveguide polarizers suffer from the issue of large device footprint, high insertion loss (IL), and/or fabrication complexities. Here, a silicon waveguide transverse magnetic (TM)‐pass polarizer is constructed by coating a silicon waveguide with an ultra‐thin plasmonic metasurface structure that is capable of guiding slow surface wave (SW) mode. The transverse electric (TE) waveguide mode can be converted into SW mode with the involvement of metasurfaces, and hence is intrinsically absorbed and forbidden to pass, while the TM waveguide mode can be well guided due to little influence. A typical metasurface polarizer with an ultra‐short length of 2.4 µm enables the IL of 28.16 dB for the TE mode, and that of 0.53 dB for the TM mode at 1550 nm. Multiple‐band TM‐pass polarizers can be obtained by cascading two or more different metasurface‐coated silicon waveguides along the propagation direction, and a dual‐band TM‐pass polarizer is demonstrated with the IL being of 19.21 and 29.09 dB for the TE mode at 1310 and 1550 nm, respectively.

Analytic modelling of a planar Goubau line with circular conductor

Planar Goubau lines show promise as high frequency, low-loss waveguides on a substrate. However, to date only numerical simulations and experimental measurements have been performed. This paper analytically investigates the surface wave mode propagating along a planar Goubau line consisting of a perfectly conducting circular wire on top of a dielectric substrate of finite thickness but infinite width. An approximate equation for the propagation constant is derived and solved through numerical integration. The dependence of the propagation constant on various system parameters is calculated and the results agree well with full numerical simulations. In addition, the spatial distribution of the longitudinal electric field is reported and excellent agreement with a numerical simulation and previous studies is found. Moreover, validation against experimental phase velocity measurements is also reported. Finally, insights gained from the model are considered for a Goubau line with a rectangular conductor. The analytic model reveals that the propagating mode of a planar Goubau line is hybrid in contrast to the transverse magnetic mode of a classic Goubau line.

Ambient noise wavefield decomposition and shear-wave velocity retrieval in the south of Tehran, Iran and in the Colfiorito basin, Italy

Knowledge about ambient noise wavefield, through decomposition into different participant waves and determination of precise singularities in ellipticity curves, could be very beneficial to improve the obtained subsurface velocity structures. In this paper, two array processing methods; WaveDec and high-resolution Rayleigh three-component beamforming (RTBF) and four single-station methods; Horizontal-to-Vertical Spectral Ratio (HVSR) or H/V, HVTFA (H/V using time frequency analysis), RayDec (Random Decrement Technique) and DOP-E (Degree Of Polarization) are applied to decompose ambient noise wavefield and to extract dispersion and ellipticity curves of surface waves. Two sites with different geological and geophysical conditions are chosen to examine the results of the measurements. The first selected site is in the south of Tehran, Iran, as a site with a low impedance contrast structure. The second one is in the Colfiorito basin, Italy, as a major impedance contrast structure site. Wavefield decomposition resulted in Rayleigh and Love wave separation and also mode distinction. The decomposed modes of surface waves and ellipticity curves of Rayleigh waves are used in a joint inversion process. The retrieved shear-wave velocity profiles are in close agreement with previous studies in the mentioned sites.

Two-dimensional resonant triad interactions in a two-layer system

Abstract

Spurious signals attenuation using SVD-based Wiener filter for near-surface ambient noise surface wave imaging

In recent years, high-frequency passive surface wave methods based on seismic interferometry have been applied to estimate near-surface shear wave velocity structure in urban geophysical investigations. One of key steps of using surface-wave methods is to image the dispersion energy and identify different modes of surface waves. In the dispersion image generated by multichannel analysis of passive surface waves method, however, a type of “crossed” artifacts usually overlaps and smears the true dispersion energy in a high frequency range. The “crossed” artifacts are spatial aliasing of a reverse-directional propagating wave with a directional velocity scan. In urban areas, the coherent noise signals could be repetitively induced by traffic in a short time segment, which will produce repetitive signals in the cross-correlation function, leading to spurious reverse-directional propagating waves in the causal or acausal part. We propose to use the Wiener filter based on singular value decomposition (SVD) to attenuate the spurious signals in the cross-correlation functions so as to reduce “crossed” artifacts in the dispersion image. A synthetic example demonstrates that the “crossed” artifacts related to spurious signals in the dispersion image can be well attenuated by applying the SVD-based Wiener filter (SVDWF) to cross-correlation functions. Two field examples suggest that high-mode dispersion energy in the dispersion images generated from the SVDWF denoised cross-correlation functions becomes more continuous and clearer in high frequency bands, which benefits from the advantages of both SVD and Wiener filters.

A Low-Profile Planar Surface-Wave Antenna With Metasurface for Endfire Radiation

A low-profile planar surface-wave antenna with metasurface is proposed for endfire radiation. The antenna has the advantages of low profile, high gain, and wide bandwidth of endfire radiation. The surface-wave structure is based on a substrate integrated waveguide (SIW) structure, which can be considered as a laterally-bounded conductor-backed coplanar waveguide (CPW) with a metasurface that is made of periodic staggered patches. The propagation properties are analyzed with a magnetic-field integral equation method. With the analysis, it is found that the structure supports an improper leaky mode and a proper mode that behaves as a surface-wave mode in lower frequency range. With the surface-wave mode, an endfire surface-wave antenna is designed. A prototype of the antenna is fabricated and measured. The measurement results show that the antenna provides a 3 dB gain bandwidth of 32%, with the gain varying from 12.3 to 15.3 dBi in the operation band from 9.6 o 13.6 GHz at a fixed direction close to endfire.