Elastic Metasurface Research Articles

Moiré-Driven Topological Transitions and Extreme Anisotropy in Elastic Metasurfaces.

The twist angle between a pair of stacked 2D materials has been recently shown to control remarkable phenomena, including the emergence of flat‐band superconductivity in twisted graphene bilayers, of higher‐order topological phases in twisted moiré superlattices, and of topological polaritons in twisted hyperbolic metasurfaces. These discoveries, at the foundations of the emergent field of twistronics, have so far been mostly limited to explorations in atomically thin condensed matter and photonic systems, with limitations on the degree of control over geometry and twist angle, and inherent challenges in the fabrication of carefully engineered stacked multilayers. Here, this work extends twistronics to widely reconfigurable macroscopic elastic metasurfaces consisting of LEGO pillar resonators. This work demonstrates highly tailored anisotropy over a single‐layer metasurface driven by variations in the twist angle between a pair of interleaved spatially modulated pillar lattices. The resulting quasi‐periodic moiré patterns support topological transitions in the isofrequency contours, leading to strong tunability of highly directional waves. The findings illustrate how the rich phenomena enabled by twistronics and moiré physics can be translated over a single‐layer metasurface platform, introducing a practical route toward the observation of extreme phenomena in a variety of wave systems, potentially applicable to both quantum and classical settings without multilayered fabrication requirements.

Sparse binary metasurfaces for steering the flexural waves

As an analogue of the binary acoustic metasurfaces (BAMs), the sparse binary elastic metasurfaces (SBEMs) which consist of two different coding units with sparse arrangement is designed. A systematic design method based on topology optimization (TO) is developed to search the coding units. With the remarkable ability in regulating flexural waves, splitting and focusing of the flexural waves are achieved by using SBEMs. Furthermore, a piezoelectric disc is attached to the focus spot as a simple energy harvester. The output voltages are measured and the performance of the SBEM energy harvester is evaluated. Compared to a bare plate, the average power output on the SBEM is amplified significantly. The numerical simulation and experimental measurement are in good agreements. The good results prove the effectiveness of the SBEMs, and the design strategy provides a new routine for tailoring flexural waves.

A helical elastic wave metasurface based on GSL

Based on the Generalized Snell’s Law (GSL), combined with the elastic wave propagation theory in the thin plate and beam structure, a new type of elastic wave metasurface is constructed. The metasurface structure realizes the design of equal gradient of transmitted wave phase according to the difference of the length of different helical curved beams. Through this structure, the transmission wavefront of the Lamb wave in the thin plate is controlled, and acoustic phenomena such as negative refraction and asymmetric transmission are realized, which proves the accuracy of the GSL theory and the feasibility of the structure. And on this basis, the use of the design of symmetrical attachment to the metasurface solves the problem of destroying the plate structure in the traditional elastic wave metasurface, and provides an effective new idea for the elastic wave metasurface.

Extreme transmission of elastic metasurface for deep subwavelength focusing

Extreme transmission of elastic metasurface for deep subwavelength focusing

Anomalous wave control by an adaptive elastic metasurface shunted with negative capacitance circuit

A metasurface is an artificially engineered structure that has received extensive research attention recently because of its ability to modulate wavefronts arbitrarily. A metasurface can be designed to either passively or actively manipulate wave propagation. Among the types of metasurfaces, an adaptive metasurface is more advantageous because of its tunability for various functionalities in a wide frequency range without structural modification. In this paper, an adaptive elastic metasurface composed of piezoelectric stacks shunted with negative capacitance circuit is proposed to actively control the propagation of elastic longitudinal wave. Through tuning of the negative capacitance via an external electrical circuit, an effective and tuned Young's modulus of the proposed metasurface is obtained. This tuning allows adaptive phase velocity manipulation of the propagating wave, resulting in full 2π phase span coverage. Additionally, analytical modeling and numerical analysis are used to study the transmission and phase shift of the proposed metasurface unit cell connected to a negative capacitance shunt. Both analytical and numerical results show excellent agreement. Based on numerical findings, the proposed elastic metasurface proficiently demonstrates multiple functionalities at broadband frequencies by distributing the required phase response tuned by the corresponding negative capacitance.

Refraction of Flexural Waves by Ultra-Broadband Achromatic Meta-Slab With Wavelength-Dependent Phase Shifts

Abstract Great progress has been made in modulating flexural waves by elastic metasurfaces. Most of the proposed elastic metasurfaces suffer from chromatic aberration, limited in a narrow bandwidth around the designed frequency. In this paper, overcoming the chromatic aberration, an ultra-broadband achromatic meta-slab (UAM) with subunits of gradient thickness is proposed to realize the refraction angle unchanged with the incident frequency. Based on the phase compensation principle, wavelength-dependent phase shifts for the UAM that realize achromaticity are obtained. In order to verify the effectiveness of the theoretical design, the transmitted wavefields are solved according to the phased array theory, and the results correspond with those obtained by the finite element (FE) simulations and experiments, which show that the refraction angle is unchanged for incident frequencies from 2 kHz to 8 kHz. Besides, the UAM is extended into a periodic meta-slab, and multifrequency achromaticity is realized. Our designed meta-slabs overcome the chromatic aberration by simple configurations, which have significance in the applications of vibration control, vibrational energy harvesting, and health monitoring.

On the broadband vibration isolation performance of nonlocal total-internal-reflection metasurfaces

The concept of a nonlocal elastic metasurface has been recently proposed and experimentally demonstrated in Zhu et al. (2020). When implemented in the form of a total-internal-reflection (TIR) interface, the metasurface can act as an elastic wave barrier that is impenetrable to deep subwavelength waves over an exceptionally wide frequency band. The underlying physical mechanism capable of delivering this broadband subwavelength performance relies on an intentionally nonlocal design that leverages long-range connections between the units forming the fundamental supercell. This paper explores the design and application of a nonlocal TIR metasurface to achieve broadband passive vibration isolation in a structural assembly made of multiple dissimilar elastic waveguides. The specific structural system comprises shell, plate, and beam waveguides, and can be seen as a prototypical structure emulating mechanical assemblies of practical interest for many engineering applications. The study also reports the results of an experimental investigation that confirms the significant vibration isolation capabilities afforded by the embedded nonlocal TIR metasurface. These results are particularly remarkable because they show that the performance of the nonlocal metasurface is preserved when applied to a complex structural assembly and under non-ideal incidence conditions of the incoming wave, hence significantly extending the validity of the results presented in Zhu et al. (2020). Results also confirm that, under proper conditions, the original concept of a planar metasurface can be morphed into a curved interface while still preserving full wave control capabilities.

Full-wave Tailoring Between Different Elastic Media: A Double-Unit Elastic Metasurface

We present a study of full-wave tailoring with an elastic metasurface between two different media. Unlike previous research on elastic metasurface, the current study has a crucial difference that the metasurface is placed between two different media. Interestingly, we find that previous studies have a theoretical limitation that negates the simultaneous achievement of various phase shifts and full transmission between inhomogeneous media. To overcome this, we propose a double-unit elastic metasurface composed of two units, phase modulator and impedance matcher, to avoid the constraint restricting various phase shifts with full transmission. Numerical and experimental investigations are performed to validate the operation of the double-unit elastic metasurface. The proposed metasurface is expected to be applied in various ultrasonic applications.

Advances in the study of elastic metasurfaces

<p indent=0mm>The development of elastic metasurfaces, which are ultra-thin metamaterials, has opened new possibilities for realizing extraordinary wave manipulation, particularly for elastic waves at low frequencies. First, according to different types of elastic wave modes, we introduce the basic concept, working principle, and latest research indications of elastic metasurfaces. In addition, we discuss the existing problems in the current research of elastic metasurfaces. Then, we focus on engineering applications of these metasurfaces, including mode separation, energy transmission, and vibration isolation at low frequencies. Finally, suggestions are put forward for future research work.

Reflective elastic metasurface for flexural wave based on surface impedance model

Inspired by the recent advance of acoustic metasurface in achieving wave manipulation, a surface impedance matched method rather than Generalized Snell's Law for designing a reflective elastic metasurface is presented to redirect the flexural waves without much loss in thin plates. The designed elastic metasurface that is simply fabricated by regularly arranged structural beams allows nearly arbitrary control of reflected waves, including extraordinary reflection, normal incidence and negative reflection. Obtained results show that the designed metasurface has a high accuracy of redirecting reflected waves into desired way and simultaneously the scattering waves in other directions are efficiently suppressed. We also demonstrate the elastic metasurfaces with free and fixed boundary conditions which all show electromagnetic and acoustic analogies of anomalous reflection response. Based on the surface impedance matched method, the theoretical prediction of redirecting reflection waves has an agreement with numerical simulation and experiments, and we think that the minimum characteristic scale of a non-resonant reflective elastic metasurface is confined to the first period of input impedance. This work provides an effective strategy for designing an elastic metasurface, and it is potentially useful for the functionalities of flexural wave manipulation.

Stiffness tuning of a functional-switchable active coding elastic metasurface

Recently, a new type of metasurface namely coding metasurface has emerged as a new technology in manipulating waves. Based on its R-bit, a coding metasurface utilizes 2R of coding units to achieve real-time wave controls which makes the operation of a metasurface easier. Although coding metasurfaces have simpler configurations than conventional metasurfaces, it is yet unavoidable to have structural reconfiguration of metasurface in order to perform different functionalities in single or different frequencies. To overcome this drawback, a functionally switchable 3-bit active coding elastic metasurface comprised of stacked piezoelectric patches shunted with negative capacitance circuit is proposed to manipulate elastic longitudinal waves. By tuning the negative capacitance in the circuitry element, arbitrary tuning of stiffness can be attained which leads to the coverage of full 2π phase range without modifying the structure of metasurface. In addition, analytical model and numerical simulations are developed to verify capability of the proposed coding metasurface for covering full 2π phase shift besides having high transmission at the same time. By utilizing the 8 fundamental coding units with different phase response, the proposed metasurface is designed and simulated based on a finite element approach to illustrate switchable functionalities such as arbitrary refraction and wave focusing, which can be realized through proper tuning of the negative capacitance, in broadband frequencies.

Coupling the first and second attenuation zones in seismic metasurface

Semi-infinite elastic metamaterials and metasurfaces on homogeneous elastic half-spaces have attracted significant attention in the past two decades as efficient artificial structures to control and mitigate surface waves. In this research, the first two attenuation zones of an elastic metasurface composed of different arrangements of pillars on a substrate are investigated. First, the lowest frequency attenuation zone (LFAZ) is numerically investigated. Then, the rainbow trapping effect of the second attenuation zone (SAZ) is demonstrated by numerical simulations and experiments. The different characteristics of these two attenuation zones are brought together to connect the lower bound of the SAZ and the upper bound of the LFAZ, allowing to design a seismic metasurface that only uses one kind of artificial structure on a half-space to attenuate Rayleigh waves in the frequency range extending from 5 to 22 Hz.

Localization and amplification of Rayleigh waves by topological elastic metasurfaces

Recently, the concept of metasurface becomes a hot research topic due to its outstanding advantages compared with its bulk counterpart metamaterial, such as low propagation loss, cheap fabrication cost, compact geometrical structure, high integration level, and specifically excellent performance in wavefront manipulation. Instead of designing elastic metasurfaces for wavefront manipulation based on generalized Snell’s law that have been widely studied, in this paper we focus on the topological performance of one dimensional elastic metasurface for manipulation of Rayleigh waves. We present two methods to design the topological metasurface, and several kinds of metasurfaces will be studied. We will show the existence of topologically protected interface modes in these topological metasurfaces that can realize energy localization around interfaces in the topological metasurface, and the displacement at the interface can be amplified more than two times than the input Rayleigh waves. This research may have important applications in sensitive Rayleigh wave detection, nondestructive testing, energy harvesting of surface waves and other Rayleigh wave related techniques.

Experimental realization of a pillared metasurface for flexural wave focusing

A metasurface is an array of subwavelength units with modulated wave responses that show great potential for the control of refractive/reflective properties in compact functional devices. In this work, we propose an elastic metasurface consisting of a line of pillars with gradient heights, erected on a homogeneous plate. The change in the resonant frequencies associated with the height gradient allows us to achieve transmitted phase response covering a range of 2π, while the amplitude response remains at a relatively high level. We employ the pillared units to design a focusing metasurface and compare the properties of the focal spots through simulation and experiment. The subwavelength transverse and lateral full width at half maximum of the focusing intensity profiles are observed in both simulation and experiment, with the underlying mechanism being the interference and diffraction of the scattered waves from the resonant pillars as well as the boundaries (especially for experiment). The good correspondence between the experimental and simulated relative focal lengths shows the robustness of the focusing pillared metasurfaces with respect to fabrication imperfections. This proposed compact, simple, and robust metasurface with unaffected mechanical properties provides a new platform for elastic wave manipulation for energy harvesting, wave communication, sensing, and non-destructive testing among others.

Excitation and manipulation of guided shear-horizontal plane wave using elastic metasurfaces

The lowest order shear horizontal wave (SH0 wave) is of great importance in structural health monitoring (SHM) and nondestructive testing (NDT), since it is the only non-dispersive guided wave mode in elastic plates. However, SH0 wave is less used than Lamb waves in the past decades, which is mainly attributed to the fact that controllable excitation of pure mode SH0 wave and manipulation of its propagation are more difficult than Lamb waves. In this work, inspired by the unique feature of SH0 wave that it can propagate around curved surfaces with negligible reflection, metasurfaces based on multiple arch-shaped strips are proposed for generating plane SH0 wave from a cylindrical wave source and realizing anomalous refraction of SH0 wave. Firstly, after analyzing the wave modes in finite-width arch-shaped strips, the strips’ capability of covering full 2π phase shift with high transmittances is demonstrated. Then three types of metasurfaces, i.e. the device for converting cylindrical SH0 wave to plane wave, the metasurface for directional refraction and the one for delivering the wave energy along a circular path are designed and validated by simulations. After that, experiments are conducted to investigate the designed metasurfaces’ performances and the obtained results are in good agreement with the design expectations. The proposed metasurfaces provide a cheap way to generate plane SH0 wave and manipulate its propagation, which will have great potential applications in NDT and SHM.

Modular elastic metasurfaces with mass oscillators for transmitted flexural wave manipulation

In the present study, a modular mass oscillator elastic metasurface (MMEM) is proposed to manipulate the wavefield of flexural waves by assembling and replacing mass-oscillator-like functional units. Based on the bandgap analysis of phononic crystals, the MMEMs were found to achieve a full range of phase shift with relatively high transmission using functional unit arrangements of varying sizes (masses). According to the generalized Snell’s law, the modulation of abnormal refraction, lens focusing, and beam self-acceleration can be realized. To broaden the operating frequency domain, we present the idea of a multiple mass oscillator array design, which can control flexural waves at broadband frequencies of 13–41 kHz by adding/removing mass oscillators within a functional unit. This study presents a method to realize tunable metasurfaces and provides an innovative concept for broadening the operating frequency of elastic metasurfaces.

Elastic Metasurfaces for Full Wavefront Control and Low-Frequency Energy Harvesting

Abstract Controlling and manipulating elastic/acoustic waves via artificially structured metamaterials, phononic crystals, and metasurfaces have gained an increasing research interest in the last decades. Unlike others, a metasurface is a single layer in the host medium with an array of subwavelength-scaled patterns introducing an abrupt phase shift in the wave propagation path. In this study, an elastic metasurface composed of an array of slender beam resonators is proposed to control the elastic wavefront of low-frequency flexural waves. The phase gradient based on Snell’s law is achieved by tailoring the thickness of thin beam resonators connecting two elastic host media. Through analytical and numerical models, the phase-modulated metasurfaces are designed and verified to accomplish three dynamic wave functions, namely, deflection, non-paraxial propagation, and focusing. An oblique incident wave is also demonstrated to show the versatility of the proposed design for focusing of wave energy incident from multiple directions. Experimentally measured focusing metasurface has nearly three times wave amplification at the designed focal point which validates the design and theoretical models. Furthermore, the focusing metasurface is exploited for low-frequency energy harvesting and the piezoelectric harvester is improved by almost nine times in terms of the harvested power output as compared to the baseline harvester on the pure plate without metasurface.

Steering Flexural Waves by Amplitude-Shift Elastic Metasurfaces

Abstract As 2D materials with subwavelength thicknesses, elastic metasurfaces show remarkable abilities to manipulate elastic waves at will through artificial boundary conditions. However, current elastic metasurfaces are still far away from arbitrary wave manipulations since they just play a role of phase compensator. Herein, we present the next generation of elastic metasurfaces by incorporating amplitude discontinuities as an additional degree of freedom. A general theory predicting target wave fields steered by metasurfaces is proposed by modifying the Huygens–Fresnel principle. As examples, two amplitude-shift metasurfaces concerning flexural waves in thin plates are carried out: one is to transform a cylindrical wave into a Gaussian beam by elaborating both amplitude and phase shifts, and the other one is to focus incident waves by metasurfaces of amplitude modulations only. These examples coincide well over theoretical calculations, numerical simulations, and experimental tests. This work may underlie the design of metasurfaces with complete control over guided elastic waves and may extend to more sophisticated applications, such as analog signal processing and holographic imaging.

Elastic Metasurfaces for Deep and Robust Subwavelength Focusing and Imaging

Metasurfaces are planar metamaterials with a flat surface and a subwavelength thickness that are able to shape arbitrary wave fronts such as focusing or imaging. There is a broad interest in the literature about subwavelength focusing and imaging based on bulk metamaterials while the utilization of metasurfaces for elastic waves has rarely been reported. Here, we present a type of elastic metasurface consisting of a line of gradient resonant pillars for robust deep subwavelength focusing and imaging of elastic waves in a plate. Numerical approaches supported by analytic Huygens-Fresnel demonstrations show that the subwavelength full width at half maximum (FWHM) behaves linearly as a function of the ratio F/D where F is the measured focal length and D the metasurface length. We discuss the range of F/D where FWHM remains smaller than half a wavelength in the near field. The focal length F and the FWHM exhibit stable performances when submitted to disorder perturbations in the geometrical parameters and to frequency fluctuations. We show that the enhanced focusing resolution with smaller FWHM can be very beneficial for energy harvesting since the output electric power can be increased by more than one order of magnitude. The proposed elastic metasurfaces bring a way for high resolution focusing and imaging which is useful for applications in various domains such as energy harvesting, wave sensing, communication, nondestructive evaluation.

Tunable multifunctional fish-bone elastic metasurface for the wavefront manipulation of the transmitted in-plane waves

In this work, a tunable fish-bone elastic metasurface is used to manipulate in-plane waves, which are more complex than flexural or out-of-plane waves because of the coupling of P- and SV-waves. First, refracted generalized Snell's law (GSL) for a mixed in-plane wave is deduced, which is also testified by the numerical results. Then, according to the GSL, elastic metasurfaces are designed to realize multifunctions such as directional refraction and wave focusing for different working frequencies. Critical refraction is discussed for the directional refraction, and the behavior of the SV-wave is predicted when the P-wave is designed to focus at any point by the metasurface.