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Recently, man-made dielectric materials composed of finite-sized dielectric constituents have emerged as a promising platform for quasi-bound states in the continuum (QBICs). These states allow for an extraordinary confinement of light within regions smaller than the wavelength scale. Known for their exceptional quality factors, they have become crucial assets across a diverse array of applications. Given the circumstances, there is a compelling drive to find meta-designs that can possess multiple QBICs. Here, we demonstrate the existence of two different types of QBICs in silicon-based metasurfaces: accidental QBIC and symmetry-protected QBIC. The accidental QBIC evinces notable resilience to variations in geometrical parameters and symmetry, underscoring its capacity to adeptly navigate manufacturing tolerances while consistently upholding a distinguished quality factor of $10^5$. Conversely, the symmetry-protected QBIC inherently correlates with the disruption of unit cell symmetry. As a result, a phase delay yields an efficient channel for substantial energy transference to the continuum, endowing this variant with an exceedingly high quality factor, approaching $10^8$. Moreover, the manifestation of these QBICs stems from the intricate interplay among out-of-plane electric and magnetic dipoles, alongside in-plane quadrupoles exhibiting odd parities.

The confinement of waves in open systems represents a fundamental phenomenon extensively explored across various branches of wave physics. Recently, significant attention has been directed towards bound states in the continuum (BIC), a class of modes that are trapped but do not decay in an otherwise unbounded continuum. Here, we theoretically investigate and experimentally demonstrate the existence of quasi-BIC (QBIC) for ultrasonic waves by leveraging an elastic Fabry-P\'erot metasurface resonator. We unveil several intriguing properties of the ultrasound QBIC that are robust to parameter scanning, and we present experimental evidence of a remarkable Q-factor of 350 at around 1 MHz frequency, far exceeding the state-of-the-art using a fully acoustic underwater system. Our findings contribute novel insights into the understanding of BIC for acoustic waves, offering a new paradigm for the design of efficient, ultra-high Q-factor ultrasound devices., Comment: 9 pages, 5 figures

Metamaterials have gained popularity in recent years as a promising avenue for producing innovative materials with distinctive properties that offer unprecedented features. In this study, we address the thermal and acoustic challenges of building materials. We numerically and experimentally investigate a clay metaBrick, which is an innovative metamaterial design based on the existing hollow brick that has shown strong sound and thermal performances. We evaluate the acoustic and thermal characteristics of the clay metaBrick, including sound transmission and heat resistance, using the finite element method. Furthermore, we validate the results experimentally by investigating the behaviors of the wall built on metaBricks in two tests: sound and thermal. We contrast the findings of the metaBrick based wall with performances of a standard hollow brick wall. The metaBrick offers enhanced acoustic and thermal insulation properties compared to the standard brick, with a compressive strength above standards required in the building materials., Comment: 16 pages, 10 figures

Over the last few decades, both heat and broadband sound reduction have become increasingly significant as a result of concerns about the environment and noise pollution. In order to address this challenge, we provide a finite element analysis study of an acoustic metamaterial panel consisting of a unit cell made of two Helmholtz Resonators with a guide in between. These panels can attenuate and control both sound propagation and heat flux. For noise pollution in a building, we first determine the geometric dimension that corresponds to the operative frequency range. Furthermore, we investigate the sound transmission loss of the proposed panel as a function of the periodicity of an array of unit cells. Additionally, we investigate the thermal flux induced by the panel, especially within a 24-hour period. The simulation results show that the proposed panel provides a level of sound attenuation within the frequency range of 400 Hz to 2.5 kHz, as well as interesting heat protection. The structure is compared to panels made up of a homogeneous medium and without Helmholtz resonators., Comment: 7 pages, 10 figures

Maxwell's fisheye is a paradigm for an absolute optical instrument with a refractive index deduced from the stereographic projection of a sphere on a plane. We investigate experimentally the dynamics of flexural waves in a thin plate with a thickness varying according to the Maxwell fisheye index profile and a clamped boundary. We demonstrate subwavelength focusing and temporal pulse compression at the image point. This is achieved by introducing a sink emitting a cancelling signal optimally shaped using a time-reversal procedure. Perfect absorption and outward going wave cancellation at the focus point are demonstrated. The time evolution of the kinetic energy stored inside the cavity reveals that the sink absorbs energy out of the plate ten times faster than the natural decay rate.

The recent emergence of chirality in mechanical metamaterials has revolutionized the field, enabling achievements in wave propagation and polarization control. Despite being an intrinsic feature of some molecules and ubiquitous in our surroundings, the incorporation of chirality into mechanical systems has only gained widespread recognition in the last few years. The extra degrees of freedom induced by chirality has propelled the study of systems to new heights, leading to a better understanding of the physical laws governing these systems. In this study, we present a structural design of a butterfly meta-structure that exploits the chiral effect to create a 3D chiral butterfly capable of inducing a rotation of 90{\deg} in the plane of polarization, enabling a switch between various polarization states within a solid material. Furthermore, our numerical investigation using Finite Element Analysis (FEA) has revealed an unexpected conversion of compressional movement to transverse movement within these structures, further highlighting the transformative potential of chirality in mechanical metamaterials. Thus, revealing an additional degree of freedom that can be manipulated, namely the polarization state., Comment: 7 Pages, 11 figures

Despite the steady advancements in nanofabrication made over the past decade that had prompted a plethora of intriguing applications across various fields, achieving compatibility between miniaturized photonic devices and electronic dimensions remains unachievable due to the inherent diffraction limit of photonic devices. Several approaches have emerged to overcome the diffraction restriction and leverage the spatial information carried by the evanescent waves. Negative dielectric permittivity materials can be utilized to build photonic crystals (PhCs) based on surface plasmon-polaritons. This approach, however, is known to be exceedingly dissipative, leading to significant optical losses for photonic components. Herein, we report an approach based on the anisotropic scaling of the shapes of PhCs to impede the diffraction barrier and enable a tunable diffraction limit. This approach opens up avenues for high-frequency wave guiding in cermet configuration, which was previously unachievable. Furthermore, asymmetric and symmetric dimer network-type PhCs were explored, with the asymmetric case demonstrating a quasi-bound state in the continuum with a quality factor of up to 41000.

In the current work, through a finite element analysis, we demonstrate that a configuration of chiral cells having syndiotactic symmetry provides dual Fano resonances at low frequency. From the phononic dispersion and transmission response, we compare the signature provided by a composite made of chiral cells to the ones of homogeneous medium, isotactic nonchiral, and isotactic chiral beams. The study results in an innovative design of a mechanical metamaterial that induces the Fano resonance at low frequency with a relatively high quality factor. This might be a significant step forward for mechanical wave filtering and detection. Performances have been evaluated using a sensor that will be implemented as a thermometer., Comment: 7 pages, 5 figures

Advances in material architectures have enabled endowing materials with exotic attributes not commonly available in the conventional realm of mechanical engineering. Twisting, a mechanism whereby metamaterials are used to transform static axial load into twist motion, is of particular interest to this study. Herein, computations based on the finite element method, corroborated by an analytical approach derived from applying Lagrange's equations to a monoatomic spring-mass system, are employed to explore the longitudinal-twist (L-T) conversion exhibited by a chiral tetragonal-beam metamaterial. Firstly, we perform an eigenvalue analysis taking into account the polarization states to highlight the potential contribution of the longitudinal mode in the L-T conversion. We contrast the twisting behavior of the chiral cell with that of other homogeneous medium, octagonal-tube, and non-chiral cells. Moreover, we demonstrate the influence of the cell's chirality on the L-T conversion using both time-domain and frequency-domain studies. The findings indicate that at least a portion of the longitudinally propagating wave is transformed into twist throughout a broad frequency range and even quasi-totally converted at distinct frequencies., Comment: 7 pages, 5 figures

Recent developments in the engineering of metamaterials have brought forth a myriad of mesmerizing mechanical properties that do not exist in ordinary solids. Among these, twisting metamaterials, acoustical chirality, or Willis coupling are sample-size dependent. The purpose of this work is, first, to examine the mechanical performance of a new twisting cubic metamaterial. Then, we perform a comparative investigation of its twisting behavior using the finite element method on microstructure elements computation, an analytical model, and we compare them to Eringen micropolar continuum. Notably, the results of the three models are in good qualitative and quantitative agreements. Finally, a systematic comparison of dispersion relations was made for the continuum and for the microstructures with different sizes in unit cells as final proof of perfect mapping., Comment: 9 pages, 5 figures

We propose a design of cylindrical elastic cloak for coupled in-plane shear waves consisting of concentric layers of sub-wavelength resonant stress-free inclusions shaped as swiss-rolls. The scaling factor between inclusions' sizes is according to Pendry's transform. Unlike the hitherto known situations, the present geometric transform starts from a Willis medium and further assumes that displacement fields ${\bf u}$ in original medium and ${\bf u}'$ in transformed medium remain unaffected (${\bf u}'={\bf u}$), and this breaks the minor-symmetries of the rank-4 and rank-3 tensors in the Willis equation that describes the transformed effective medium. We achieve some cloaking for a shear polarized source at specific, resonant sub-wavelength, frequencies, when it is located near a clamped obstacle surrounded by the structured cloak. Such an effective medium allows for strong Willis coupling [Quan et al., Physical Review Letters {\bf 120}(25), 254301 (2018)], notwithstanding potential chiral elastic effects [Frenzel et al., Science {\bf 358}(6366), 1072 (2017)], and thus mitigates roles of Willis and Cosserat media in the achieved elastodynamic cloaking., Comment: 7 pages, 3 figures

Metre size inertial resonators located in the ground have been theoretically shown to interact with a seismic wave (attenuation, band gaps) to enable protection of surface structures such as buildings. The challenge for Civil Engineering is to both reduce the size of these resonators and to increase their efficiency. Here we explore steel spheres, connected to a concrete bulk medium, either by a coating of rubber, or rubber and steel ligaments, or air and steel ligaments. We show that for a cubic lattice periodicity of 1 metre, we achieve stop bands in the frequency range 14 to 20 Hz; by splitting spheres in 2 and 8 pieces, we tune down the stop bands frequencies and further increase their bandwidth. We thus demonstrate we are able to provide a variety of inertial resonators with stop bands below 10 Hz i.e., in the frequency range of interest for earthquake engineering.

We outline some recent research advances on the control of elastic waves in thin and thick plates, that have occurred since the large scale experiment [Phys. Rev. Lett. 112, 133901, 2014] that demonstrated significant interaction of surface seismic waves with holes structuring sedimentary soils at the meter scale. We further investigate the seismic wave trajectories in soils structured with buildings. A significant substitution of soils by inclusions, acting as foundations, raises the question of the effective dynamic properties of these structured soils. Buildings, in the case of perfect elastic conditions for both soil and buildings, are shown to interact and strongly influence elastic surface waves; such site-city seismic interactions were pointed out in [Bulletin of Seismological Society of America 92, 794-811, 2002], and we investigate a variety of scenarios to illustrate the variety of behaviours possible., Comment: 15 pages, 9 figures

In [AIP Advances 6, 121707 (2016)], a soil structured with concrete columns distributed within two specially designed seismic cloaks thanks to a combination of transformational elastodynamics and effective medium theory was shown to detour Rayleigh waves of frequencies lower than 10 Hz around a cylindrical region. The aforementioned studies motivate our exploration of interactions of surface elastic waves propagating in a thick plate (with soil parameters) structured with concrete pillars above it. Pillars are 40 m in height and the plate is 100 m in thickness, so that typical frequencies under study are below 1 Hz, a frequency range of particular interest in earthquake engineering. We demonstrate that three seismic cloaks allow for an unprecedented flow of elastodynamic energy. These designs are achieved by first computing ideal cloaks' parameters deduced from a geometric transform in the Navier equations that leads to almost isotropic and symmetric elasticity (4th order) and density (2nd order) tensors. To do this we extend the theory of Non-Euclidean cloaking for light as proposed by the theoretical physicists Leonhardt and Tyc. In a second step, ideal heterogeneous nearly isotropic cloak's parameters are approximated by averaging elastic properties of sets of pillars placed at the nodes of a bipolar coordinate grid, which is an essential ingredient in our Non-Euclidean cloaking theory for elastodynamic waves. Cloaking effects are studied for a clamped obstacle (reduction of the disturbance of the wave wavefront and its amplitude behind a clamped obstacle). Protection is achieved through reduction of the wave amplitude within the center of the cloak.These results represent a first step towards designs of Non-Euclidean seismic cloaks for surface (Rayleigh and Love) waves propagating in semi-infinite elastic media structured with pillars., Comment: Latex, 10pages, 4 figures. Pacs: 41.20.Jb,42.25.Bs,42.70.Qs,43.20.Bi,43.25.Gf

It is well known in metamaterials that local resonance and hybridization phenomena dramatically influence the shape of dispersion curves; the metasurface created by a cluster of resonators, subwavelength rods, atop an elastic surface being an exemplar with these features. On this metasurface, band-gaps, slow or fast waves, negative refraction and dynamic anisotropy can all be observed by exploring frequencies and wavenumbers from the Floquet-Bloch problem and by using the Brillouin zone. These extreme characteristics, when appropriately engineered, can be used to design and control the propagation of elastic waves along the metasurface. For the exemplar we consider, two parameters are easily tuned: rod height and cluster periodicity. The height is directly related to the band-gap frequency, and hence to the slow and fast waves, while the periodicity is related to the appearance of dynamic anisotropy. Playing with these two parameters generates a gallery of metasurface designs to control the propagation of both flexural waves in plates and surface Rayleigh waves for half-spaces. Scalability with respect to the frequency and wavelength of the governing physical laws allows the application of these concepts in very different fields and over a wide range of lengthscales., Comment: Paper currently submitted to Frontiers in Mechanics of Materials

Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones and saddle points; identifying these, and the nature of the associated modes, from a direct reading of the dispersion surfaces is not straightforward, especially in three-dimensions or at high frequencies when several dispersion surfaces fold back in the Brillouin zone. A recently proposed asymptotic high frequency homogenisation theory is applied to a challenging time-domain experiment with elastic waves in a pinned metallic plate. The prediction of a narrow high-frequency spectral region where the effective medium tensor dramatically switches from positive definite to indefinite is confirmed experimentally; a small frequency shift of the pulse carrier results in two distinct types of highly anisotropic modes. The underlying effective equation mirrors this behaviour with a change in form from elliptic to hyperbolic exemplifying the high degree of wave control available and the importance of a simple and effective predictive model., Comment: 5 pages, 4 figures

We explore interactions of elastic waves propagating in plates (with soil parameters) structured with concrete pillars buried in the soil. Pillars are 2 m in diameter, 30 m in depth and the plate is 50 m in thickness. We study the frequency range 5 to 10 Hz, for which Rayleigh wave wavelengths are smaller than the plate thickness. This frequency range is compatible with frequency ranges of particular interest in earthquake engineering. It is demonstrated in this paper that two seismic cloaks' configurations allow for an unprecedented flow of elastodynamic energy associated with Rayleigh surface waves. The first cloak design is inspired by some approximation of ideal cloaks' parameters within the framework of thin plate theory. The second, more accomplished but more involved, cloak design is deduced from a geometric transform in the full Navier equations that preserves the symmetry of the elasticity tensor but leads to Willis' equations, well approximated by a homogenization procedure, as corroborated by numerical simulations. The two cloaks's designs are strikingly different, and the superior efficiency of the second type of cloak emphasizes the necessity for rigor in transposition of existing cloaks's designs in thin plates to the geophysics setting. Importantly, we focus our attention on geometric transforms applied to thick plates, which is an intermediate case between thin plates and semi-infinite media, not studied previously. Cloaking efficiency (reduction of the disturbance of the wave wavefront and its amplitude behind an obstacle) and protection (reduction of the wave amplitude within the center of the cloak) are studied for ideal and approximated cloaks' parameters. These results represent a preliminary step towards designs of seismic cloaks for surface Rayleigh waves propagating in sedimentary soils structured with concrete pillars., Comment: V2: Major changes. Quantitative study carried out. New figures. Investigation of elastic trapped modes and resonances. Latex, 13 pages, 8 pages. Pacs: 41.20.Jb,42.25.Bs,42.70.Qs,43.20.Bi,43.25.Gf. The last version will appear at AIP Advances

We investigate the elastic stop band properties of a theoretical cubic array of iron spheres connected to a bulk of concrete via iron or rubber ligaments. Each sphere can move freely within a surrounding air cavity, but ligaments couple it to the bulk and further facilitate bending and rotational motions. Associated low frequency local resonances are well predicted by an asymptotic formula. We find complete stop bands (for all wave-polarizations) in the frequency range $[16,21]$ Hertz (resp. $[6,11]$ Hertz) for $7.4$-meter (resp. $0.74$-meter) diameter iron spheres with a $10$-meter (resp. $1$-meter) center-to-center spacing, when they are connected to concrete via steel (resp. rubber) ligaments. The scattering problem shows that only bending modes are responsible for damping and that rotational modes are totally overwritten by bending modes. Regarding seismic applications, we further consider soil as a bulk medium, in which case the relative bandwidth of the low frequency stop band can be enlarged through ligaments of different sizes that allow for well separated bending and rotational modes. We finally achieve some damping of elastodynamic waves from $8$ to $49$ Hertz (relative stop band of $143$ percent) for iron spheres $0.74$-meter in diameter that are connected to soil with six rubber ligaments of optimized shapes. These results represent a preliminary step in the design of seismic shields placed around, or underneath, the foundations of large civil infrastructures.

We propose that wave propagation through a class of mechanical metamaterials opens unprecedented avenues in seismic wave protection based on spectral properties of auxetic-like metamaterials. The elastic parameters of these metamaterials like the bulk and shear moduli, the mass density, and even the Poisson ratio, can exhibit negative values in elastic stop bands. We show here that the propagation of seismic waves with frequencies ranging from 1Hz to 40Hz can be influenced by a decameter scale version of auxetic-like metamaterials buried in the soil, with the combined effects of impedance mismatch, local resonances and Bragg stop bands. More precisely, we numerically examine and illustrate the markedly different behaviors between the propagation of seismic waves through a homogeneous isotropic elastic medium (concrete) and an auxetic-like metamaterial plate consisting of 64 cells (40mx40mx40m), utilized here as a foundation of a building one would like to protect from seismic site effects. This novel class of seismic metamaterials opens band gaps at frequencies compatible with seismic waves when they are designed appropriately, what makes them interesting candidates for seismic isolation structures.

Numerical simulations shed light on control of shear elastic wave propagation in plates structured with inertial resonators. The structural element is composed of a heavy core connected to the main freestanding plate through tiny ligaments. It is shown that such a configuration exhibits a complete band gap in the low frequency regime. As a byproduct, we further describe the asymmetric twisting vibration of a single scatterer via modal analysis, dispersion and transmission loss. This might pave the way to new functionalities such as focusing and self-collimation in elastic plates.

We experimentally demonstrate that a Duraluminium thin plate with a thickness profile varying radially in a piecewise constant fashion as h(r)=h(0)(1+(r/Rmax)), with h(0)=0.5 mm, h(Rmax)=2 mm and Rmax=10 cm behaves in many ways as Maxwell's fish-eye lens in optics, since its imaging properties for a Gaussian pulse with central frequencies 30~kHz and 60~kHz are very similar to those predicted by ray trajectories (great circles) on a virtual sphere (rays emanating from the North pole meet at the South pole). However, refocusing time depends on the carrier frequency as a direct consequence of the dispersive nature of flexural waves in thin plates. Importantly, experimental results are in good agreement with Finite-Difference-Time-Domain simulations., Comment: 5 pages, 5 figures, Supplementary materials 2 pages, 1 figure, 1 video