Ultrasonic metamaterials with negative modulus

Exploiting the leaky-wave properties of transmission-line metamaterials for single-microphone direction finding

A transmission-line acoustic metamaterial is an engineered, periodic arrangement of relatively small unit-cells, the acoustic properties of which can be manipulated to achieve anomalous physical behaviours. These exotic properties open the door to practical applications, such as an acoustic leaky-wave antenna, through the implementation of radiating channels along the metamaterial. In the transmitting mode, such a leaky-wave antenna is capable of steering sound waves in frequency-dependent directions. Used in reverse, the antenna presents a well defined direction-frequency behaviour. In this paper, an acoustic leaky-wave structure is presented in the receiving mode. It is shown that it behaves as a sound source direction-finding device using only one sensor. After a general introduction of the acoustic leaky-wave antenna concept, its radiation pattern and radiation efficiency are expressed in closed form. Then, numerical simulations and experimental assessments of the proposed transmission-line based structure, implementing only one sensor at one termination, are presented. It is shown that such a structure is capable of finding the direction of an incoming sound wave, from backward to forward, based on received sound power spectra. This introduces the concept of sound source localization without resorting to beam-steering techniques based on multiple sensors.

Membrane- and plate-type acoustic metamaterials

Over the past decade there has been a great amount of research effort devoted to the topic of acoustic metamaterials (AMMs). The recent development of AMMs has enlightened the way of manipulating sound waves. Several potential applications such as low-frequency noise reduction, cloaking, angular filtering, subwavelength imaging, and energy tunneling have been proposed and implemented by the so-called membrane- or plate-type AMMs. This paper aims to offer a thorough overview on the recent development of membrane- or plate-type AMMs. The underlying mechanism of these types of AMMs for tuning the effective density will be examined first. Four different groups of membrane- or plate-type AMMs (membranes with masses attached, plates with masses attached, membranes or plates without masses attached, and active AMMs) will be reviewed. The opportunities, limitations, and challenges of membrane- or plate-type AMMs will be also discussed.

Implementation of dispersion-free slow acoustic wave propagation and phase engineering with helical-structured metamaterials

The ability to slow down wave propagation in materials has attracted significant research interest. A successful solution will give rise to manageable enhanced wave–matter interaction, freewheeling phase engineering and spatial compression of wave signals. The existing methods are typically associated with constructing dispersive materials or structures with local resonators, thus resulting in unavoidable distortion of waveforms. Here we show that, with helical-structured acoustic metamaterials, it is now possible to implement dispersion-free sound deceleration. The helical-structured metamaterials present a non-dispersive high effective refractive index that is tunable through adjusting the helicity of structures, while the wavefront revolution plays a dominant role in reducing the group velocity. Finally, we numerically and experimentally demonstrate that the helical-structured metamaterials with designed inhomogeneous unit cells can turn a normally incident plane wave into a self-accelerating beam on the prescribed parabolic trajectory. The helical-structured metamaterials will have profound impact to applications in explorations of slow wave physics.

There is great interest in slow wave propagation for a variety of applications. Here, Zhu et al. present a dispersion-free helical-structured metamaterial that implements acoustic wave deceleration at broad bandwidth and demonstrates specially designed phase modulation to incident sound through helicity tuning.

Gradient Index Devices for the Full Control of Elastic Waves in Plates

In this work, we present a method for the design of gradient index devices for elastic waves in plates. The method allows the design of devices to control the three fundamental modes, despite the fact that their dispersion relation is managed by different elastic constants. It is shown that by means of complex graded phononic crystals and thickness variations it is possible to independently design the three refractive indexes of these waves, allowing therefore their simultaneous control. The effective medium theory required for this purpose is presented, and the method is applied to the design of the Luneburg and Maxwell lenses as well as to the design of a flat gradient index lens. Finally, numerical simulations are used to demonstrate the performance of the method in a broadband frequency region.

Use of slow sound to design perfect and broadband passive sound absorbing materials

Perfect (100%) absorption by thin structures consisting of a periodic arrangement of rectangular quarter-wavelength channels with side detuned quarter-wavelength resonators is demonstrated. The thickness of these structures is 13-17 times thinner than the acoustic wavelength. This low frequency absorption is due to a slow sound wave propagating in the main rectangular channel. A theoretical model is proposed to predict the complex wavenumber in this channel. It is shown that the speed of sound in the channel is much lower than in the air, almost independent of the frequency in the low frequency range, and it is dispersive inside the induced transparency band which is observed. The perfect absorption condition is found to be caused by a critical coupling between the rectangular channel (sub-wavelength resonators) and the incoming wave. It is shown that the width of a large absorption peak in the frequency spectrum can be broadened if several rectangular channels in the unit cell are detuned. The detuning is achieved by varying the length of the side resonators for each channel. The predicted absorption coefficients are validated experimentally. Two resonant cells were produced with stereolithography which enabled the authors to incorporate curved side resonators.

Elastic metamaterials for independent realization of negativity in density and stiffness

In this paper, we present the first realization of an elastic metamaterial allowing independent tuning of negative density and stiffness for elastic waves propagating along a designated direction. In electromagnetic (or acoustic) metamaterials, it is now possible to tune permittivity (bulk modulus) and permeability (density) independently. Apparently, the tuning methods seem to be directly applicable for elastic case, but no realization has yet been made due to the unique tensorial physics of elasticity that makes wave motions coupled in a peculiar way. To realize independent tunability, we developed a single-phased elastic metamaterial supported by theoretical analysis and numerical/experimental validations.

Harnessing Deformation to Switch On and Off the Propagation of Sound

A new class of architected materials is designed to control the propagation of sound. The proposed system comprises an array of elastomeric helices in background air and is characterized by frequency ranges of strong wave attenuation (bandgaps) in the undeformed configuration. Upon axially stretching the helices, such bandgaps are suppressed, enabling the design of a new class of acoustic switch.

Controlled Unusual Stiffness of Mechanical Metamaterials

Mechanical metamaterials that are engineered with sub-unit structures present unusual mechanical properties depending on the loading direction. Although they show promise, their practical utility has so far been somewhat limited because, to the best of our knowledge, no study about the potential of mechanical metamaterials made from sophisticatedly tailored sub-unit structures has been made. Here, we present a mechanical metamaterial whose mechanical properties can be systematically designed without changing its chemical composition or weight. We study the mechanical properties of triply periodic bicontinuous structures whose detailed sub-unit structure can be precisely fabricated using various sub-micron fabrication methods. Simulation results show that the effective wave velocity of the structures along with different directions can be designed to introduce the anisotropy of stiffness by changing a volume fraction and aspect ratio. The ratio of Young's modulus to shear modulus can be increased by up to at least 100, which is a 3500% increase over that of isotropic material (2.8, acrylonitrile butadiene styrene). Furthermore, Poisson's ratio of the constituent material changes the ratio while Young's modulus does not influence it. This study presents the promising potential of mechanical metamaterials for versatile industrial and biomedical applications.

Acoustic metamaterials: From local resonances to broad horizons

Within a time span of 15 years, acoustic metamaterials have emerged from academic curiosity to become an active field driven by scientific discoveries and diverse application potentials. This review traces the development of acoustic metamaterials from the initial findings of mass density and bulk modulus frequency dispersions in locally resonant structures to the diverse functionalities afforded by the perspective of negative constitutive parameter values, and their implications for acoustic wave behaviors. We survey the more recent developments, which include compact phase manipulation structures, superabsorption, and actively controllable metamaterials as well as the new directions on acoustic wave transport in moving fluid, elastic, and mechanical metamaterials, graphene-inspired metamaterials, and structures whose characteristics are best delineated by non-Hermitian Hamiltonians. Many of the novel acoustic metamaterial structures have transcended the original definition of metamaterials as arising from the collective manifestations of constituent resonating units, but they continue to extend wave manipulation functionalities beyond those found in nature.

Extreme stiffness tunability through the excitation of nonlinear defect modes

The incremental stiffness characterizes the variation of a material's force response to a small deformation change. In lattices with noninteracting vibrational modes, the excitation of localized states does not have any effect on material properties, such as the incremental stiffness. We report that, in nonlinear lattices, driving a defect mode introduces changes in the static force-displacement relation of the material. By varying the defect excitation frequency and amplitude, the incremental stiffness can be tuned continuously to arbitrarily large positive or negative values. Furthermore, the defect excitation parameters also determine the displacement region at which the force-displacement relation is being tuned. We demonstrate this phenomenon experimentally in a compressed array of spheres tuning its incremental stiffness from a finite positive value to zero and continuously down to negative infinity.

Acoustic dispersive prism

The optical dispersive prism is a well-studied element, which allows separating white light into its constituent spectral colors, and stands in nature as water droplets. In analogy to this definition, the acoustic dispersive prism should be an acoustic device with capability of splitting a broadband acoustic wave into its constituent Fourier components. However, due to the acoustical nature of materials as well as the design and fabrication difficulties, there is neither any natural acoustic counterpart of the optical prism, nor any artificial design reported so far exhibiting an equivalent acoustic behaviour. Here, based on exotic properties of the acoustic transmission-line metamaterials and exploiting unique physical behaviour of acoustic leaky-wave radiation, we report the first acoustic dispersive prism, effective within the audible frequency range 800 Hz–1300 Hz. The dispersive nature, and consequently the frequency-dependent refractive index of the metamaterial are exploited to split the sound waves towards different and frequency-dependent directions. Meanwhile, the leaky-wave nature of the structure facilitates the sound wave radiation into the ambient medium.

Shear-mediated contributions to the effective properties of soft acoustic metamaterials including negative index

Here we show that, for sub-wavelength particles in a fluid, viscous losses due to shear waves and their influence on neighbouring particles significantly modify the effective acoustic properties, and thereby the conditions at which negative acoustic refraction occurs. Building upon earlier single particle scattering work, we adopt a multiple scattering approach to derive the effective properties (density, bulk modulus, wavenumber). We show,through theoretical prediction, the implications for the design of “soft” (ultrasonic) metamaterials based on locally-resonant sub-wavelength porous rubber particles, through selection of particle size and concentration, and demonstrate tunability of the negative speed zones by modifying the viscosity of the suspending medium. For these lossy materials with complex effective properties, we confirm the use of phase angles to define the backward propagation condition in preference to “single-” and “double-negative” designations.

Time-Domain Filtering of Metasurfaces

In general electromagnetic response of each material to a continuous wave does not vary in time domain if the frequency component remains the same. Recently, it turned out that integrating several circuit elements including schottky diodes with periodically metallised surfaces, or the so-called metasurfaces, leads to selectively absorbing specific types of waveforms or pulse widths even at the same frequency. These waveform-selective metasurfaces effectively showed different absorbing performances for different widths of pulsed sine waves by gradually varying their electromagnetic responses in time domain. Here we study time-filtering effects of such circuit-based metasurfaces illuminated by continuous sine waves. Moreover, we introduce extra circuit elements to these structures to enhance the time-domain control capability. These time-varying properties are expected to give us another degree of freedom to control electromagnetic waves and thus contribute to developing new kinds of electromagnetic applications and technologies, e.g. time-windowing wireless communications and waveform conversion.

Metamaterials and imaging

Resolution of the conventional lens is limited to half the wavelength of the light source by diffraction. In the conventional optical system, evanescent waves, which carry sub-diffraction spatial information, has exponentially decaying amplitude and therefore cannot reach to the image plane. New optical materials called metamaterials have provided new ways to overcome diffraction limit in imaging by controlling the evanescent waves. Such extraordinary electromagnetic properties can be achieved and controlled through arranging nanoscale building blocks appropriately. Here, we review metamaterial-based lenses which offer the new types of imaging components and functions. Perfect lens, superlenses, hyperlenses, metalenses, flat lenses based on metasurfaces, and non-optical lenses including acoustic hyperlens are described. Not all of them offer sub-diffraction imaging, but they provide new imaging mechanisms by controlling and manipulating the path of light. The underlying physics, design principles, recent advances, major limitations and challenges for the practical applications are discussed in this review.

Soft resonator of omnidirectional resonance for acoustic metamaterials with a negative bulk modulus

Monopolar resonance is of fundamental importance in the acoustic field. Here, we present the realization of a monopolar resonance that goes beyond the concept of Helmholtz resonators. The balloon-like soft resonator (SR) oscillates omnidirectionally and radiates from all parts of its spherical surface, eliminating the need for a hard wall for the cavity and baffle effects. For airborne sound, such a low-modulus resonator can be made extremely lightweight. Deep subwavelength resonance is achieved when the SR is tuned by adjusting the shell thickness, benefiting from the large density contrast between the shell material and the encapsulated gas. The SR resonates with near-perfect monopole symmetry, as demonstrated by the theoretical and experimental results, which are in excellent agreement. For a lattice of SRs, a band gap occurs and blocks near-total transmission, and the effective bulk modulus exhibits a prominent negative band, while the effective mass density remains unchanged. Our study shows that the SR is suitable for building 3D acoustic metamaterials and provides a basis for constructing left-handed materials as a new means of creating a negative bulk modulus.

Topologically protected elastic waves in phononic metamaterials

Surface waves in topological states of quantum matter exhibit unique protection from backscattering induced by disorders, making them ideal carriers for both classical and quantum information. Topological matters for electrons and photons are largely limited by the range of bulk properties, and the associated performance trade-offs. In contrast, phononic metamaterials provide access to a much wider range of material properties. Here we demonstrate numerically a phononic topological metamaterial in an elastic-wave analogue of the quantum spin Hall effect. A dual-scale phononic crystal slab is used to support two effective spins for phonons over a broad bandwidth, and strong spin–orbit coupling is realized by breaking spatial mirror symmetry. By preserving the spin polarization with an external load or spatial symmetry, phononic edge states are shown to be robust against scattering from discrete defects as well as disorders in the continuum, demonstrating topological protection for phonons in both static and time-dependent regimes.

Metamaterials are engineered media with properties that mimic those of natural materials, but offer a much wider range of possibilities. Here, the authors numerically demonstrate an elastic-wave analogue of the quantum spin Hall effect in a phononic topological metamaterial.

Elastic Waves Scattering without Conversion in Metamaterials with Simultaneous Zero Indices for Longitudinal and Transverse Waves

We theoretically investigate elastic waves propagating in metamaterials with simultaneous zero indices for both the longitudinal and transverse waves. With scattering objects (here cylinders) present in the metamaterial slabs, while the elastic waves can mostly transmit through the metamaterial slabs perfectly, exhibiting the well-known cloaking effect of zero-index metamaterials, they nevertheless become totally blocked at resonances, indicating strong elastic wave scattering by the objects in the cases. However, despite the occurrence of the elastic wave scattering, there is, counterintuitively, no mode conversion between the longitudinal and transverse waves in the process, completely in contrast to that in conventional elastic media. A design of a two-dimensional phononic crystal with these peculiar properties is presented.

Ultra-sparse metasurface for high reflection of low-frequency sound based on artificial Mie resonances

Acoustic metamaterials offer great flexibility for manipulating sound waves and promise unprecedented functionality, ranging from transformation acoustics, super-resolution imaging to acoustic cloaking. However, the design of acoustic metamaterials with exciting functionality remains challenging with traditional approaches using classic acoustic elements such as Helmholtz resonators and membranes. Here we demonstrate an ultraslow-fluid-like particle with intense artificial Mie resonances for low-frequency airborne sound. Eigenstate analysis and effective parameter retrieval show two individual negative bands in the single-size unit cell, one of which exhibits a negative bulk modulus supported by the monopolar Mie resonance, whereas the other exhibits a negative mass density induced by the dipolar Mie resonance. The unique single-negative nature is used to develop an ultra-sparse subwavelength metasurface with high reflectance for low-frequency sound. We demonstrate a 0.15λ-thick, 15%-filling ratio metasurface with an insertion loss over 93.4%. The designed Mie resonators provide diverse routes to construct novel acoustic devices with versatile applications.

Topological Phononic Crystals with One-Way Elastic Edge Waves

We report a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication, and acoustic imaging.

Symmetry issues in the hybridization of multi-mode waves with resonators: an example with Lamb waves metamaterial

Locally resonant metamaterials derive their effective properties from hybridization between their resonant unit cells and the incoming wave. This phenomenon is well understood in the case of plane waves that propagate in media where the unit cell respects the symmetry of the incident field. However, in many systems, several modes with orthogonal symmetries can coexist at a given frequency, while the resonant unit cells themselves can have asymmetric scattering cross-sections. In this paper we are interested in the influence of symmetry breaking on the hybridization of a wave field that includes multiple propagative modes. The A₀ and S₀ Lamb waves that propagate in a thin plate are good candidates for this study, as they are either anti-symmetric or symmetric. First we designed an experimental setup with an asymmetric metamaterial made of long rods glued to one side of a metallic plate. We show that the flexural resonances of the rods induce a break of the orthogonality between the A₀/S₀ modes of the free-plate. Finally, based on numerical simulations we show that the orthogonality is preserved in the case of a symmetric metamaterial leading to the presence of two independent polariton curves in the dispersion relation.

Acoustic metamaterial for subwavelength edge detection

Metamaterials have demonstrated the possibility to produce super-resolved images by restoring propagative and evanescent waves. However, for efficient information transfer, for example, in compressed sensing, it is often desirable to visualize only the fast spatial variations of the wave field (carried by evanescent waves), as the one created by edges or small details. Image processing edge detection algorithms perform such operation, but they add time and complexity to the imaging process. Here we present an acoustic metamaterial that transmits only components of the acoustic field that are approximately equal to or smaller than the operating wavelength. The metamaterial converts evanescent waves into propagative waves exciting trapped resonances, and it uses periodicity to attenuate the propagative components. This approach achieves resolutions ∼5 times smaller than the operating wavelength and makes it possible to visualize independently edges aligned along different directions.

Super-resolution imaging is based on the restoration of evanescent and propagative waves. Here, the authors present an acoustic metamaterial that transmits only components of the acoustic field equal to or smaller than the operating wavelength, which can be used to provide sharp images of the edge of an object.

Single-sensor multispeaker listening with acoustic metamaterials

Designing a "cocktail party listener" that functionally mimics the selective perception of a human auditory system has been pursued over the past decades. By exploiting acoustic metamaterials and compressive sensing, we present here a single-sensor listening device that separates simultaneous overlapping sounds from different sources. The device with a compact array of resonant metamaterials is demonstrated to distinguish three overlapping and independent sources with 96.67% correct audio recognition. Segregation of the audio signals is achieved using physical layer encoding without relying on source characteristics. This hardware approach to multichannel source separation can be applied to robust speech recognition and hearing aids and may be extended to other acoustic imaging and sensing applications.

Acoustic transmission enhancement through a soft interlayer with a reactance boundary

Research has shown that acoustic transmission enhancement (ATE) can occur in stiff materials with high acoustic impedance that include a soft interlayer with low acoustic impedance inserted between them without any opening (i.e., without any links between the two stiff materials). Previously, ATE was induced either by coupling acoustic surface waves or Love waves with the Fabry-Perot resonant modes inside the apertures or by the locally resonant modes of the structure. However, in this article ATE is achieved using wave-vector redistribution induced by a reactance boundary. An optimal boundary was designed to adjust the wave vector in the propagation direction, decreasing reflection caused by impedance differences. The role of boundary conditions on ATE was also clarified.

Bulk and surface acoustic waves in solid-fluid Fibonacci layered materials

We study theoretically the propagation and localization of acoustic waves in quasi-periodic structures made of solid and fluid layers arranged according to a Fibonacci sequence. We consider two types of structures: either a given Fibonacci sequence or a periodic repetition of a given sequence called Fibonacci superlattice. Various properties of these systems such as: the scaling law and the self-similarity of the transmission spectra or the power law behavior of the measure of the energy spectrum have been highlighted for waves of sagittal polarization in normal and oblique incidence. In addition to the allowed modes which propagate along the system, we study surface modes induced by the surface of the Fibonacci superlattice. In comparison with solid-solid layered structures, the solid-fluid systems exhibit transmission zeros which can break the self-similarity behavior in the transmission spectra for a given sequence or induce additional gaps other than Bragg gaps in a periodic structure.

Theoretical requirements for broadband perfect absorption of acoustic waves by ultra-thin elastic meta-films

We derive and numerically demonstrate that perfect absorption of elastic waves can be achieved in two types of ultra-thin elastic meta-films: one requires a large value of almost pure imaginary effective mass density and a free space boundary, while the other requires a small value of almost pure imaginary effective modulus and a hard wall boundary. When the pure imaginary density or modulus exhibits certain frequency dispersions, the perfect absorption effect becomes broadband, even in the low frequency regime. Through a model analysis, we find that such almost pure imaginary effective mass density with required dispersion for perfect absorption can be achieved by elastic metamaterials with large damping. Our work provides a feasible approach to realize broadband perfect absorption of elastic waves in ultra-thin films.

Note: Vibration energy harvesting based on a round acoustic fence

An energy harvester based on a round acoustic fence (RAF) has been proposed and studied. The RAF is composed of cylindrical stubs stuck in a circular array on a thin metal plate, which can confine the acoustic energy efficiently. By removing one stub and thus opening a small gap in the RAF, acoustic leakage with larger intensity can be produced at the gap opening. With the vibration source surrounded by the RAF, the energy harvesting at the gap opening has a wide bandwidth and is insensitive to the position of the vibration source. The results may have potential applications in harvesting the energy of various vibration sources in solid structure.

Molding acoustic, electromagnetic and water waves with a single cloak

We describe two experiments demonstrating that a cylindrical cloak formerly introduced for linear surface liquid waves works equally well for sound and electromagnetic waves. This structured cloak behaves like an acoustic cloak with an effective anisotropic density and an electromagnetic cloak with an effective anisotropic permittivity, respectively. Measured forward scattering for pressure and magnetic fields are in good agreement and provide first evidence of broadband cloaking. Microwave experiments and 3D electromagnetic wave simulations further confirm reduced forward and backscattering when a rectangular metallic obstacle is surrounded by the structured cloak for cloaking frequencies between 2.6 and 7.0 GHz. This suggests, as supported by 2D finite element simulations, sound waves are cloaked between 3 and 8 KHz and linear surface liquid waves between 5 and 16 Hz. Moreover, microwave experiments show the field is reduced by 10 to 30 dB inside the invisibility region, which suggests the multi-wave cloak could be used as a protection against water, sonic or microwaves.

Focusing on Plates: Controlling Guided Waves using Negative Refraction

Elastic waves are guided along finite structures such as cylinders, plates, or rods through reflection, refraction, and mode conversion at the interfaces. Such wave propagation is ubiquitous in the world around us, and studies of elastic waveguides first emerged in the later part of the 19^th century. Early work on elastic waveguides revealed the presence of backward propagating waves, in which the phase velocity and group velocity are anti-parallel. While backward wave propagation exists naturally in very simple finite elastic media, there has been remarkably little attention paid to this phenomenon. Here we report the development of a tunable acoustic lens in an isotropic elastic plate showing negative refraction over a finite acoustic frequency bandwidth. As compared to engineered acoustic materials such as phononic crystals and metamaterials, the design of the acoustic lens is very simple, with negative refraction obtained through thickness changes rather than internal periodicity or sub-wavelength resonant structures. A new class of acoustic devices, including resonators, filters, lenses, and cloaks, may be possible through topography optimization of elastic waveguide structures to exploit the unique properties of backward waves.

Spectroscopic evidence for negative electronic compressibility in a quasi-three-dimensional spin-orbit correlated metal

Negative compressibility is a sign of thermodynamic instability of open or non-equilibrium systems. In quantum materials consisting of multiple mutually coupled subsystems, the compressibility of one subsystem can be negative if it is countered by positive compressibility of the others. Manifestations of this effect have so far been limited to low-dimensional dilute electron systems. Here, we present evidence from angle-resolved photoemission spectroscopy (ARPES) for negative electronic compressibility (NEC) in the quasi-three-dimensional (3D) spin-orbit correlated metal (Sr1-xLax)3Ir2O7. Increased electron filling accompanies an anomalous decrease of the chemical potential, as indicated by the overall movement of the deep valence bands. Such anomaly, suggestive of NEC, is shown to be primarily driven by the lowering in energy of the conduction band as the correlated bandgap reduces. Our finding points to a distinct pathway towards an uncharted territory of NEC featuring bulk correlated metals with unique potential for applications in low-power nanoelectronics and novel metamaterials.

Transfer matrix modeling and experimental validation of cellular porous material with resonant inclusions

Porous materials are widely used for improving sound absorption and sound transmission loss of vibrating structures. However, their efficiency is limited to medium and high frequencies of sound. A solution for improving their low frequency behavior while keeping an acceptable thickness is to embed resonant structures such as Helmholtz resonators (HRs). This work investigates the absorption and transmission acoustic performances of a cellular porous material with a two-dimensional periodic arrangement of HR inclusions. A low frequency model of a resonant periodic unit cell based on the parallel transfer matrix method is presented. The model is validated by comparison with impedance tube measurements and simulations based on both the finite element method and a homogenization based model. At the HR resonance frequency (i) the transmission loss is greatly improved and (ii) the sound absorption of the foam can be either decreased or improved depending on the HR tuning frequency and on the thickness and properties of the host foam. Finally, the diffuse field sound absorption and diffuse field sound transmission loss performance of a 2.6 m(2) resonant cellular material are measured. It is shown that the improvements observed at the Helmholtz resonant frequency on a single cell are confirmed at a larger scale.

Waveform selectivity at the same frequency

Electromagnetic properties depend on the composition of materials, i.e. either angstrom scales of molecules or, for metamaterials, subwavelength periodic structures. Each material behaves differently in accordance with the frequency of an incoming electromagnetic wave due to the frequency dispersion or the resonance of the periodic structures. This indicates that if the frequency is fixed, the material always responds in the same manner unless it has nonlinearity. However, such nonlinearity is controlled by the magnitude of the incoming wave or other bias. Therefore, it is difficult to distinguish different incoming waves at the same frequency. Here we present a new concept of circuit-based metasurfaces to selectively absorb or transmit specific types of waveforms even at the same frequency. The metasurfaces, integrated with schottky diodes as well as either capacitors or inductors, selectively absorb short or long pulses, respectively. The two types of circuit elements are then combined to absorb or transmit specific waveforms in between. This waveform selectivity gives us another degree of freedom to control electromagnetic waves in various fields including wireless communications, as our simulation reveals that the metasurfaces are capable of varying bit error rates in response to different waveforms.

Soft 3D acoustic metamaterial with negative index

Many efforts have been devoted to the design and achievement of negative-refractive-index metamaterials since the 2000s. One of the challenges at present is to extend that field beyond electromagnetism by realizing three-dimensional (3D) media with negative acoustic indices. We report a new class of locally resonant ultrasonic metafluids consisting of a concentrated suspension of macroporous microbeads engineered using soft-matter techniques. The propagation of Gaussian pulses within these random distributions of 'ultra-slow' Mie resonators is investigated through in situ ultrasonic experiments. The real part of the acoustic index is shown to be negative (up to almost - 1) over broad frequency bandwidths, depending on the volume fraction of the microbeads as predicted by multiple-scattering calculations. These soft 3D acoustic metamaterials open the way for key applications such as sub-wavelength imaging and transformation acoustics, which require the production of acoustic devices with negative or zero-valued indices.

Wave propagation in granular chains with local resonances

We study wave propagation in a chain of spherical particles containing a local resonator. The resonant particles are made of an aluminum outer spherical shell and a steel inner mass connected by a polymeric plastic structure acting as a spring. We characterize the dynamic response of individual particles and the transmitted linear spectra of a chain of particles in contact. A wide band gap is observed both in theoretical and experimental results. We show the ability to tune the acoustic transmission by varying the contact interaction between particles. Higher driving amplitude leads to the generation of nonlinearities both in the response of a single particle and that of the whole chain. For a single resonant particle, we observe experimentally a resonant frequency downshift, which follows a complex nonlinear behavior. In the chain of particles, nonlinearity leads to the generation of nonlinear harmonics and the presence of localized modes inside the band gap.

Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach

We report experimental results and study theoretically soliton formation and propagation in an air-filled acoustic waveguide side loaded with Helmholtz resonators. We propose a theoretical modeling of the system, which relies on a transmission-line approach, leading to a nonlinear dynamical lattice model. The latter allows for an analytical description of the various soliton solutions for the pressure, which are found by means of dynamical systems and multiscale expansion techniques. These solutions include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons that are observed in the experiment, as well as nonlinear Schrödinger envelope solitons, that are predicted theoretically. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.

Metamaterials and imaging

Resolution of the conventional lens is limited to half the wavelength of the light source by diffraction. In the conventional optical system, evanescent waves, which carry sub-diffraction spatial information, has exponentially decaying amplitude and therefore cannot reach to the image plane. New optical materials called metamaterials have provided new ways to overcome diffraction limit in imaging by controlling the evanescent waves. Such extraordinary electromagnetic properties can be achieved and controlled through arranging nanoscale building blocks appropriately. Here, we review metamaterial-based lenses which offer the new types of imaging components and functions. Perfect lens, superlenses, hyperlenses, metalenses, flat lenses based on metasurfaces, and non-optical lenses including acoustic hyperlens are described. Not all of them offer sub-diffraction imaging, but they provide new imaging mechanisms by controlling and manipulating the path of light. The underlying physics, design principles, recent advances, major limitations and challenges for the practical applications are discussed in this review.

Sound pressure level gain in an acoustic metamaterial cavity

The inherent attenuation of a homogeneous viscous medium limits radiation propagation, thereby restricting the use of many high-frequency acoustic devices to only short-range applications. Here, we design and experimentally demonstrate an acoustic metamaterial localization cavity which is used for sound pressure level (SPL) gain using double coiled up space like structures thereby increasing the range of detection. This unique behavior occurs within a subwavelength cavity that is 1/10^th of the wavelength of the incident acoustic wave, which provides up to a 13 dB SPL gain. We show that the amplification results from the Fabry-Perot resonance of the cavity, which has a simultaneously high effective refractive index and effective impedance. We also experimentally verify the SPL amplification in an underwater environment at higher frequencies using a sample with an identical unit cell size. The versatile scalability of the design shows promising applications in many areas, especially in acoustic imaging and underwater communication.

Acoustic rainbow trapping by coiling up space

We numerically realize the acoustic rainbow trapping effect by tapping an air waveguide with space-coiling metamaterials. Due to the high refractive-index of the space-coiling metamaterials, our device is more compact compared to the reported trapped-rainbow devices. A numerical model utilizing effective parameters is also calculated, whose results are consistent well with the direct numerical simulation of space-coiling structure. Moreover, such device with the capability of dropping different frequency components of a broadband incident temporal acoustic signal into different channels can function as an acoustic wavelength division de-multiplexer. These results may have potential applications in acoustic device design such as an acoustic filter and an artificial cochlea.

Three-dimensional ultrathin planar lenses by acoustic metamaterials

Acoustic lenses find applications in various areas ranging from ultrasound imaging to nondestructive testing. A compact-size and high-efficient planar acoustic lens is crucial to achieving miniaturization and integration, and should have deep implication for the acoustic field. However its realization remains challenging due to the trade-off between high refractive-index and impedance-mismatch. Here we have designed and experimentally realized the first ultrathin planar acoustic lens capable of steering the convergence of acoustic waves in three-dimensional space. A theoretical approach is developed to analytically describe the proposed metamaterial with hybrid labyrinthine units, which reveals the mechanism of coexistence of high refractive index and well-matched impedance. A hyperbolic gradient-index lens design is fabricated and characterized, which can enhance the acoustic energy by 15 dB at the focal point with very high transmission efficiency. Remarkably, the thickness of the lens is only approximately 1/6 of the operating wavelength. The lens can work within a certain frequency band for which the ratio between the bandwidth and the center frequency reaches 0.74. By tailoring the structure of the metamaterials, one can further reduce the thickness of the lens or even realize other acoustic functionalities, opening new opportunity for manipulation of low-frequency sounds with versatile potential.

Enhanced acoustic sensing through wave compression and pressure amplification in anisotropic metamaterials

Acoustic sensors play an important role in many areas, such as homeland security, navigation, communication, health care and industry. However, the fundamental pressure detection limit hinders the performance of current acoustic sensing technologies. Here, through analytical, numerical and experimental studies, we show that anisotropic acoustic metamaterials can be designed to have strong wave compression effect that renders direct amplification of pressure fields in metamaterials. This enables a sensing mechanism that can help overcome the detection limit of conventional acoustic sensing systems. We further demonstrate a metamaterial-enhanced acoustic sensing system that achieves more than 20 dB signal-to-noise enhancement (over an order of magnitude enhancement in detection limit). With this system, weak acoustic pulse signals overwhelmed by the noise are successfully recovered. This work opens up new vistas for the development of metamaterial-based acoustic sensors with improved performance and functionalities that are highly desirable for many applications.

Dynamics of periodic mechanical structures containing bistable elastic elements: from elastic to solitary wave propagation

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

Harnessing buckling to design tunable locally resonant acoustic metamaterials

We report a new class of tunable and switchable acoustic metamaterials comprising resonating units dispersed into an elastic matrix. Each resonator consists of a metallic core connected to the elastomeric matrix through elastic beams, whose buckling is intentionally exploited as a novel and effective approach to control the propagation of elastic waves. We first use numerical analysis to show the evolution of the locally resonant band gap, fully accounting for the effect of nonlinear pre-deformation. Then, we experimentally measure the transmission of vibrations as a function of the applied loading in a finite-size sample and find excellent agreement with our numerical predictions. The proposed concept expands the ability of existing acoustic metamaterials by enabling tunability over a wide range of frequencies. Furthermore, we demonstrate that in our system the deformation can be exploited to turn on or off the band gap, opening avenues for the design of adaptive switches.

Generation of acoustic self-bending and bottle beams by phase engineering

Directing acoustic waves along curved paths is critical for applications such as ultrasound imaging, surgery and acoustic cloaking. Metamaterials can direct waves by spatially varying the material properties through which the wave propagates. However, this approach is not always feasible, particularly for acoustic applications. Here we demonstrate the generation of acoustic bottle beams in homogeneous space without using metamaterials. Instead, the sound energy flows through a three-dimensional curved shell in air leaving a close-to-zero pressure region in the middle, exhibiting the capability of circumventing obstacles. By designing the initial phase, we develop a general recipe for creating self-bending wave packets, which can set acoustic beams propagating along arbitrary prescribed convex trajectories. The measured acoustic pulling force experienced by a rigid ball placed inside such a beam confirms the pressure field of the bottle. The demonstrated acoustic bottle and self-bending beams have potential applications in medical ultrasound imaging, therapeutic ultrasound, as well as acoustic levitations and isolations.

Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces

The introduction of metasurfaces has renewed the Snell's law and opened up new degrees of freedom to tailor the optical wavefront at will. Here, we theoretically demonstrate that the generalized Snell's law can be achieved for reflected acoustic waves based on ultrathin planar acoustic metasurfaces. The metasurfaces are constructed with eight units of a solid structure to provide discrete phase shifts covering the full 2π span with steps of π/4 by coiling up the space. By careful selection of the phase profiles in the transverse direction of the metasurfaces, some fascinating wavefront engineering phenomena are demonstrated, such as anomalous reflections, conversion of propagating waves into surface waves, planar aberration-free lens and nondiffracting Bessel beam generated by planar acoustic axicon. Our results could open up a new avenue for acoustic wavefront engineering and manipulations.

Experimental demonstration of ordered and disordered multiresonant metamaterials for lamb waves

We demonstrate the experimental realization of a multiresonant metamaterial for Lamb waves, i.e., elastic waves propagating in plates. The metamaterial effect comes from the resonances of long aluminum rods that are attached to an aluminum plate. Using time-dependent measurements, we experimentally prove that this metamaterial exhibits wide band gaps as well as sub- and suprawavelength modes for both a periodic and a random arrangement of the resonators. The dispersion curve inside the metamaterial is predicted through hybridizations between flexural and compressional resonances in the rods and slow and fast Lamb modes in the plate. We finally underline how the various degrees of freedom of such system paves the way to the design of metamaterials for the control of Lamb waves in unprecedented ways.

Spatiotemporal path discontinuities of wavepackets propagating across a meta-atom

The realization of phase discontinuities across metasurfaces has led to a new class of reflection and refraction. Here we present theory and experiment on the discontinuous propagation of wavepackets across subwavelength-thickness meta-atoms. Using acoustic waves, we observe the process of wavepackets traversing a meta-atom with abrupt displacements, which appear as path discontinuities on a space-time diagram. We construct a tunable meta-atom from two coupled resonators at ~500 Hz, map the spatiotemporal trajectories of individual sonic pulses, and reveal discontinuities at the meta-atom where the pulses exit at a time ~50 ms ahead or behind their arrivals. Applications include thin acoustic metasurface lenses.

Resonant acoustic propagation and negative density in liquid foams

We measured the dispersion relation for acoustic longitudinal waves in liquid foams, over a broad frequency range (60-600 kHz). Strong dispersion was found, with two nondispersive behaviors, separated by a negative density regime. A new model, based on the coupled displacements of films, liquid channels, and gas in the foam, rationalizes all the experimental findings.

Experiments on seismic metamaterials: molding surface waves

Materials engineered at the micro- and nanometer scales have had a tremendous and lasting impact in photonics and phononics. At much larger scales, natural soils civil engineered at decimeter to meter scales may interact with seismic waves when the global properties of the medium are modified, or alternatively thanks to a seismic metamaterial constituted of a mesh of vertical empty inclusions bored in the initial soil. Here, we show the experimental results of a seismic test carried out using seismic waves generated by a monochromatic vibrocompaction probe. Measurements of the particles' velocities show a modification of the seismic energy distribution in the presence of the metamaterial in agreement with numerical simulations using an approximate plate model. For complex natural materials such as soils, this large-scale experiment was needed to show the practical feasibility of seismic metamaterials and to stress their importance for applications in civil engineering. We anticipate this experiment to be a starting point for smart devices for anthropic and natural vibrations.

Experimental study on acoustic subwavelength imaging of holey-structured metamaterials by resonant tunneling

A holey-structured metamaterial is proposed for near-field acoustic imaging beyond the diffraction limit. The structured lens consists of a rigid slab perforated with an array of cylindrical holes with periodically modulated diameters. Based on the effective medium approach, the structured lens is characterized by multilayered metamaterials with anisotropic dynamic mass, and an analytic model is proposed to evaluate the transmission properties of incident evanescent waves. The condition is derived for the resonant tunneling, by which evanescent waves can completely transmit through the structured lens without decaying. As an advantage of the proposed lens, the imaging frequency can be modified by the diameter modulation of internal holes without the change of the lens thickness in contrast to the lens due to the Fabry-Pérot resonant mechanism. In this experiment, the lens is assembled by aluminum plates drilled with cylindrical holes. The imaging experiment demonstrates that the designed lens can clearly distinguish two sources separated in the distance below the diffraction limit at the tunneling frequency.