We report an experimental study of surface acoustic wave (SAW) localization and propagation in random metasurfaces composed of Al scatters using pump–probe spectroscopy. Thanks to this technique, wideband high frequency acoustic modes are generated, and their dynamical propagation directly from inside of the media with a high (micrometric) spatial resolution is enabled. During SAW propagation, part of the acoustic wavefront energy is trapped within free areas between the scatterers, acting as cavities. The spectral content of the localized modes of a few GHz is found to depend on the shape and size of the cavities but also on the landscape seen by the wave during its propagation before arriving inside them. The experimental results are supported by numerical simulations using the finite element method. This study is the phononic part of a more global research on the co-localization of elastic and optical waves on random metasurfaces, with the main objective of enhancing the photon–phonon interaction. Applications could range from the design of acousto-optic modulators to ultrasensitive sensors.

This broad review summarizes recent advances and “hot” research topics in nanophononics and elastic, acoustic, and mechanical metamaterials based on results presented by the authors at the EUROMECH 610 Colloquium held on April 25–27, 2022 in Benicássim, Spain. The key goal of the colloquium was to highlight important developments in these areas, particularly new results that emerged during the last two years. This work thus presents a “snapshot” of the state-of-the-art of different nanophononics- and metamaterial-related topics rather than a historical view on these subjects, in contrast to a conventional review article. The introduction of basic definitions for each topic is followed by an outline of design strategies for the media under consideration, recently developed analysis and implementation techniques, and discussions of current challenges and promising applications. This review, while not comprehensive, will be helpful especially for early-career researchers, among others, as it offers a broad view of the current state-of-the-art and highlights some unique and flourishing research in the mentioned fields, providing insight into multiple exciting research directions.

We propose the design of a phononic crystal to sense the acoustic properties of a liquid that is constituted by an array of silicon ridges on a membrane. In contrast to other concepts, the ridges are immersed in the liquid. The introduction of a suitable cavity in the periodic array gives rise to a confined defect mode with high localization in the cavity region and strong solid–liquid interaction, which make it sensitive to the acoustic properties of the liquid. By using a finite element method simulation, we theoretically study the transmission and cavity excitation of an incident flexural wave of the membrane. The observation of the vibrations of this mode can be achieved either outside the area of the phononic crystal or just above the cavity. We discuss the existence of the resonant modes, as well as its quality factor and sensitivity to liquid properties as a function of the geometrical parameters. The performance of the proposed sensor has then been tested to detect the variation in NaI concentration in a NaI–water mixture.

The Fano resonance, as a phenomenon of wave scattering, is based on the interaction between a “bright mode” and a “dark mode” giving rise to an asymmetric and ultrasharp spectral peak. However, the Fano resonant frequency is sensitive to structural imperfections such as defects or disorders, which will shift the resonant peak, or even damage the Fano line shape. Here, we harness the coupling between the first-order and the higher-order topological insulators to overcome this shortcoming. We construct a first-order topological edge state to serve as a bright mode, and a second-order topological corner state to be the dark mode using the same base configuration. As a result, a topological Fano resonance is expected to occur around the resonant frequency of the dark mode. The robustness of the Fano resonance is verified by deliberately introducing various types of imperfections into the system. Our findings may further enhance confidence in using the resonance such as acoustic switching, refractive index sensing, high quality factor filters, and accurate interferometers.

We present a numerical investigation of an acoustic sensor based on a cylindrical resonator to monitor the acoustic properties of liquids flowing in a tube. The sensor design consists of a hollow cylindrical washer surrounding the tube, which carries the liquid, and which can be filled during the sensing process. Due to the impedance mismatch between the liquid and the solid washer, we demonstrate the presence of high-quality factor resonances associated with the acoustic properties of the liquid (such as velocity, density, or viscosity) appearing as sharp spectral features in the transmission and detection measurements. An appropriate choice of geometrical parameters allows either to obtain two distinct resonances associated with the liquid and the surrounding washer or to overlap the narrow resonance of the liquid with the broad resonance of the washer and achieve a Fano-type resonance from their interaction. The sensitivity of the resonances to the acoustic properties of the liquid are investigated as a function of the geometrical parameters. We show that for highly viscous fluids, the vanishing of very narrow peaks can be avoided by increasing the thickness of the washer and, therefore, decreasing the quality factors. The calculations are performed in the framework of a finite element method. Our design provides a promising platform for sensing several acoustic characteristics of liquids flowing in tubes.

The introduction of engineered resonance phenomena on surfaces has opened a new frontier in surface science and technology. Pillared phononic crystals, metamaterials, and metasurfaces are an emerging class of artificial structured media, featuring surfaces that consist of pillars—or branching substructures—standing on a plate or a substrate. A pillared phononic crystal exhibits Bragg band gaps, while a pillared metamaterial may feature both Bragg band gaps and local resonance hybridization band gaps. These two band-gap phenomena, along with other unique wave dispersion characteristics, have been exploited for a variety of applications spanning a range of length scales and covering multiple disciplines in applied physics and engineering, particularly in elastodynamics and acoustics. The intrinsic placement of pillars on a semi-infinite surface—yielding a metasurface—has similarly provided new avenues for the control and manipulation of wave propagation. Classical waves are admitted in pillared media, including Lamb waves in plates and Rayleigh and Love waves along the surfaces of substrates, ranging in frequency from hertz to several gigahertz. With the presence of the pillars, these waves couple with surface resonances richly creating new phenomena and properties in the subwavelength regime and in some applications at higher frequencies as well. At the nanoscale, it was shown that atomic-scale resonances—stemming from nanopillars—alter the fundamental nature of conductive thermal transport by reducing the group velocities and generating mode localizations across the entire spectrum of the constituent material well into the terahertz regime. In this article, we first overview the history and development of pillared materials, then provide a detailed synopsis of a selection of key research topics that involve the utilization of pillars or similar branching substructures in different contexts. Finally, we conclude by providing a short summary and some perspectives on the state of the field and its promise for further future development.

We propose the design of a tubular phononic crystal (TPC) for the purpose of sensing the physical properties of a liquid filling the hollow part of the tube. The TPC is constituted by a periodic repetition of washers along a hollow pipe with the advantage of avoiding any perturbation of a flowing fluid by any element inside the tube. Using finite element simulations, we demonstrate the existence of complete as well as polarization dependent bandgaps inside which one can design localized modes associated with defects. The most sensitive cavity to the liquid sound velocity is found to be constituted by a Fabry–Pérot (F–P) cavity. The signature of the cavity modes can be detected as peaks or dips in the transmission spectrum as well as at the external surface of the cavity. We study the dramatic effect of the liquid viscosity, more particularly shear viscosity, on these features and discuss the conditions for their practical observation. A TPC test sample made of a polymer is fabricated by means of 3D printing and characterized without the liquid by transmission measurements. The comparison with the simulations showed the necessity of considering the damping of the polymer whose effect on the transmission features is discussed. Our sensor design can find many applications at different scales in several systems transporting a fluid as microfluidic channels in micro- and nanotechnologies, syringes in medicine, or pipelines in civil engineering.

We theoretically investigate, with the help of the finite element method, the interaction between aluminum pillars erected on top of a semi-infinite substrate of silicon in the low frequency range. Our interest is to control and manipulate the propagation of the surface acoustic waves through a linear chain of pillars for frequencies in the [0, 2] GHz range. We show that two pillars can interact together in near field through the excitation of their resonant compressional eigen mode. We will then investigate the resonant modes of a finite linear chain of N pillars, in order to analyze the possibility of propagation along the chain. To reach this objective and to relax the numerical stresses, we have considered a periodicity in the direction perpendicular to the propagation where the lattice parameter is significantly higher to avoid any interaction between two adjacent lines of pillars.

We demonstrate experimentally and theoretically the broadband sub-diffraction and ultra-high energy density focusing of elastic wave inside planar gradient-index (GRIN) plate lenses based on thickness variation. The full width at half maximum is -0.40 times the minimum wavelength inside the lens ?0 or -1/11 times the incident wavelength in the background plate ?B. We analytically elucidate the underlying physical mechanism as the rapid oscillations in the propagator function at the focal distance. Our design displays several advantages including the broadband sub-diffraction behavior, three-order of magnitudes higher energy intensity at the focal point, and focusing capacity with a narrow transverse width of the lens, over the usual metastructure and/or phononic crystal based GRIN lenses. The broadband sub-diffraction and ultra-high energy density focusing can be used for energy harvesting and signal sensing.

In this work we propose a topological valley phononic crystal plate and we extensively investigate the refraction of valley modes into the surrounding homogeneous medium. This phononic crystal includes two sublattices of resonators (A and B) modeled by mass-spring systems. We show that two edge states confined at the AB/BA and BA/AB type domain walls exhibit different symmetries in physical space and energy peaks in the Fourier space. As a result, distinct refraction behaviors, especially through an armchair cut edge, are observed. On the other hand, the decay depth of these localized topological modes, which is found to be solely determined by the relative resonant strength between the scatterers, significantly affects the refraction patterns. More interestingly, the outgoing traveling wave through a zigzag interface becomes evanescent when operating at deep subwavelength scale. This is realized by tuning the average resonant strength. We show that the evanescent modes only exist along a particular type of outlet edge and that they can couple with both topological interface states. We also present a near-ideal monopole and a dipole emitter based on our phononic structure.

We present a theoretical investigation of the dispersion and transmission properties of a tubular phononic crystal for sensing application. We show the existence of modes confined in a cavity with displacement field spreading over both the solid and fluid parts. Therefore, the frequency of the transmission peak associated to this mode should be sensitive to the sound velocity of the fluid filling the tube.

We report on a new mechanism involving the torsional resonance of stubs to achieve the negative effective shear modulus of an elastic metamaterial plate. Combined with a mechanism to create a negative mass density, we develop a general method to set up and enlarge a shear-horizontal-polarized double-negative branch in the elastic metamaterial plate with stubs on both sides. We explore the capabilities of this structure for polarization filtering, mode conversion and abnormal refraction. It is shown that, this metamaterial plate behaves divergently against the polarization of incident waves propagating along ΓX direction in a square lattice crystal: it behaves as a double-negative system for zero-order shear horizontal (SH0) wave but as a single-negative one for zero-order antisymmetric (A0) or symmetric (S0) Lamb waves. Mode conversion is achieved when the propagation deviates from ΓX direction. Moreover, we observe abnormal refracted patterns with both positive and negative refraction occurring at the interface between a prism-shaped supercell and the surrounding plate. Furthermore, we propose a chiral pillar to efficiently couple the torsional resonance with an incident A0 Lamb wave.

We describe the so-called "Transient Grating Method" which is a non-invasive experimental technique well suited to measure the dispersion properties of ordered or disordered nanostructures and thin films, at frequencies up to a few GHz. This pump-and-probe technique involves the interference pattern produced by two incoming IR optical pulses to set a standing elastic wave on the surface of the sample through photoelastic processes. The wave vector of this elastic wave can be easily tuned by adjusting the angle between the two incident beams. Two continuous visible laser beams in a heterodyne detection scheme are used to detect the vibrations on the surface and in turn the dispersion of the related elastic modes. The achievements of the technique are illustrated by the measurement of the dispersion of surface acoustic waves in piezogenerators consisting of GaN nanowires embedded into a dielectric matrix (HSQ). We then report on the analysis of the experimental data that allowed extracting the elastic parameters of this composite medium.

We have numerically investigated the transmission of an antisymmetric Lamb wave through a line of silicon pillars erected onto a homogeneous silicon plate when the frequency is tuned to a resonant frequency of the pillars. For either a bending mode or a compressional mode, the resonators emit in the plate a wave 180° out-of-phase with the exciting Lamb wave, resulting in dips in the transmission spectrum. We show that transmission at resonance can be actively controlled by applying an external force, either tangential (bending eigenmode) or axial (compressional eigenmode), on top of the pillars. The transmission coefficient can be precisely controlled by finely tuning either the phase or the amplitude of the external force. For specific dimensions of the structure, both resonant modes arise at the same frequency. This geometry has the advantage of offering an additional degree of freedom for the direction of the external force but is less favorable from an energy point of view.

The advances in topological condensed matter physics enable the manipulation of classic waves in different ways, such as unidirectional propagation featuring the suppression of backscattering and the robustness against impurities and disorder, making it possible to endow classical phenomena with topological properties. Fano resonance, a widely spread and basic kind of resonance, features an asymmetric line shape with an ultrahigh quality factor Q that usually requires delicate designs and precise fabrication. In this work, we achieve a robust Fano mechanical resonance with topological protection by engineering band inversion of two different vibrating symmetries of a pillared beam that gives rise to dark and bright edge modes. The Fano resonance results from the constructive and destructive interferences between topological dark and bright modes. It is further demonstrated that the Fano asymmetric shape of the transmission peak and its frequency are robust against random perturbations in the pillars' position as long as the symmetry is conserved. If random perturbations break the symmetry and only band inversion is involved, the asymmetric line shape of the Fano resonance weakens until disappearing before the closure of the bulk band gap, since the excitation will couple all fundamental modes of the beam. The analysis of the robustness of Fano resonance originating from band inversion and symmetry protection reveals the nature of topological protection which can be applied to design topological high-Q resonance in sensing application.

We present a design of a pillared phononic crystal based structure for Love wave manipulation to achieve high mass sensitivity. The structure is made of phononic micro-pillars constructed by stacking tungsten and SiO2 layers, distributed on a substrate designed for Love wave propagation. The multilayered pillar allows the creation of bandgaps, which leads to the existence of resonant modes where the elastic energy is confined within the SiO2 free surface layer of the pillar. We study particularly a resonant mode where this layer exhibits torsional mechanical motion which can only be excited by shear horizontal surface waves. We show that Love wave interaction with the torsional mode gives rise to a sharp attenuation in the surface wave transmission spectrum with a high quality factor. We also study the variation of the mass sensitivity of the system by evaluating the resonant mode's frequency shift induced by a mass perturbation using two theoretical approaches: a perturbation theory based approximation and a numerical method. The system presents very promising mass sensitivity which provides an interesting approach to increase the detection performance of Love wave based bio-sensors.