Locally resonant sonic materials

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.

Extraordinary absorption of sound in porous lamella-crystals

We present the design of a structured material supporting complete absorption of sound with a broadband response and functional for any direction of incident radiation. The structure which is fabricated out of porous lamellas is arranged into a low-density crystal and backed by a reflecting support. Experimental measurements show that strong all-angle sound absorption with almost zero reflectance takes place for a frequency range exceeding two octaves. We demonstrate that lowering the crystal filling fraction increases the wave interaction time and is responsible for the enhancement of intrinsic material dissipation, making the system more absorptive with less material.

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.

Closed-cell crystalline foams: self-assembling, resonant metamaterials

Internal degrees of freedom and periodic structure are critical requirements in the design of acoustic/elastic metamaterials since they can give rise to extraordinary properties like negative effective mass and stiffness. However, they are challenging to realize in three dimensions. Closed-cell, crystalline foams are a particularly advantageous basis to develop metamaterials as they intrinsically have a complex microstructure, exhibiting internal resonances. Recently self-assembly techniques have been implemented to produce such foams: a Kelvin (body centered cubic) foam, a face centered cubic foam, and a Weaire-Phelan structure. Numerical models are employed to demonstrate that such foams are superanisotropic, selectively behaving as a fluid or a solid, pentamode solids as a result of fluid-structure interaction, in addition to having regimes characterized by film resonances and high density of states. Microstructural deformations obtained from numerical models allow the derivation of equivalent mechanical models.

Effective medium theory of thin-plate acoustic metamaterials

Effective dynamic properties of acoustic metamaterials made of multilayered flexible thin-plates with periodically attached mass-spring resonators are studied. By using the transfer matrix method, the thin-plate acoustic metamaterial under the plane wave incidence is characterized by a homogeneous effective medium with anisotropic mass density. An approximate analytic expression of effective mass density is derived for a single-layer metamaterial in the normally incident case, and it is shown that the effective mass density can follow either Lorentz or Drude medium models. For the obliquely incident case, it is found that effective mass density is dependent on the lateral wave number of incident waves. Such spatial dispersion comes from the coincidence effect between the incident acoustic wave and flexural wave in the thin plate, and it occurs at much lower frequencies than that for a uniform plate without resonators. Based on the observed spatial dispersion, an acoustic device made of thin-plate metamaterials is designed for frequency-controlled acoustic directive radiation in the low-frequency regime.

Bloch-wave expansion technique for predicting wave reflection and transmission in two-dimensional phononic crystals

In this paper acoustic wave reflection and transmission are studied at the interface between a phononic crystal (PC) and a homogeneous medium using a Bloch wave expansion technique. A finite element analysis of the PC yields the requisite dispersion relationships and a complete set of Bloch waves, which in turn are employed to expand the transmitted pressure field. A solution for the reflected and transmitted wave fields is then obtained using continuity conditions at the half-space interface. The method introduces a group velocity criterion for Bloch wave selection, which when not enforced, is shown to yield non-physical results. Following development, the approach is applied to example PCs and results are compared to detailed numerical solutions, yielding very good agreement. The approach is also employed to uncover bands of incidence angles whereby perfect acoustic reflection from the PC occurs, even for frequencies outside of stop bands.

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.

Acoustically trapped colloidal crystals that are reconfigurable in real time

Photonic and phononic crystals are metamaterials with repeating unit cells that result in internal resonances leading to a range of wave guiding and filtering properties and are opening up new applications such as hyperlenses and superabsorbers. Here we show the first, to our knowledge, 3D colloidal phononic crystal that is reconfigurable in real time and demonstrate its ability to rapidly alter its frequency filtering characteristics. Our reconfigurable material is assembled from microspheres in aqueous solution, trapped with acoustic radiation forces. The acoustic radiation force is governed by an energy landscape, determined by an applied high-amplitude acoustic standing wave field, in which particles move swiftly to energy minima. This creates a colloidal crystal of several milliliters in volume with spheres arranged in an orthorhombic lattice in which the acoustic wavelength is used to control the lattice spacing. Transmission acoustic spectroscopy shows that the new colloidal crystal behaves as a phononic metamaterial and exhibits clear band-pass and band-stop frequencies which are adjusted in real time.

Phononic crystal with adaptive connectivity

The band structure of a phononic crystal can be controlled by tuning the mechanical stiffness of the links connecting its constituting elements. The first implementation of a phononic crystal with adaptive connectivity is obtained by using piezoelectric resonators as variable stiffness elements, and its wave-propagation properties are experimentally characterized.

Emission enhancement of sound emitters using an acoustic metamaterial cavity

The emission enhancement of sound without electronic components has wide applications in a variety of remote systems, especially when highly miniaturized (smaller than wavelength) structures can be used. The recent advent of acoustic metamaterials has made it possible to realize this. In this study, we propose, design, and demonstrate a new class of acoustic cavity using a double-walled metamaterial structure operating at an extremely low frequency. Periodic zigzag elements which exhibit Fabry-Perot resonant behavior below the phononic band-gap are used to yield strong sound localization within the subwavelength gap, thus providing highly effective emission enhancement. We show, both theoretically and experimentally, 10 dB sound emission enhancement near 1060 Hz that corresponds to a wavelength approximately 30 times that of the periodicity. We also provide a general guideline for the independent tuning of the quality factor and effective volume of acoustic metamaterials. This approach shows the flexibility of our design in the efficient control of the enhancement rate.

Non-reciprocal and highly nonlinear active acoustic metamaterials

Unidirectional devices that pass acoustic energy in only one direction have numerous applications and, consequently, have recently received significant attention. However, for most practical applications that require unidirectionality at audio and low frequencies, subwavelength implementations capable of the necessary time-reversal symmetry breaking remain elusive. Here we describe a design approach based on metamaterial techniques that provides highly subwavelength and strongly non-reciprocal devices. We demonstrate this approach by designing and experimentally characterizing a non-reciprocal active acoustic metamaterial unit cell composed of a single piezoelectric membrane augmented by a nonlinear electronic circuit, and sandwiched between Helmholtz cavities tuned to different frequencies. The design is thinner than a tenth of a wavelength, yet it has an isolation factor of >10 dB. The design method generates relatively broadband unidirectional devices and is a good candidate for numerous acoustic applications.

Nanophononic metamaterial: thermal conductivity reduction by local resonance

We present the concept of a locally resonant nanophononic metamaterial for thermoelectric energy conversion. Our configuration, which is based on a silicon thin film with a periodic array of pillars erected on one or two of the free surfaces, qualitatively alters the base thin-film phonon spectrum due to a hybridization mechanism between the pillar local resonances and the underlying atomic lattice dispersion. Using an experimentally fitted lattice-dynamics-based model, we conservatively predict the metamaterial thermal conductivity to be as low as 50% of the corresponding uniform thin-film value despite the fact that the pillars add more phonon modes to the spectrum.

Shear Bloch waves and coupled phonon-polariton in periodic piezoelectric waveguides

Coupled electro-elastic SH waves propagating in a periodic piezoelectric finite-width waveguide are considered in the framework of the full system of Maxwell's electrodynamic equations. We investigate Bloch-Floquet waves under homogeneous or alternating boundary conditions for the elastic and electromagnetic fields along the guide walls. Zero frequency stop bands, trapped modes as well as some anomalous features due to piezoelectricity are identified. For mixed boundary conditions, by modulating the ratio of the length of the unit cell to the width of the waveguide, the minimum widths of the stop bands can be moved to the middle of the Brillouin zone. The dispersion equation has been investigated also for phonon-polariton band gaps. It is shown that for waveguides at acoustic frequencies, acousto-optic coupling gives rise to polariton behavior at wavelengths much larger than the length of the unit cell but at optical frequencies polariton resonance occurs at wavelengths comparable with the period of the waveguide.

25th anniversary article: ordered polymer structures for the engineering of photons and phonons

The engineering of optical and acoustic material functionalities via construction of ordered local and global architectures on various length scales commensurate with and well below the characteristic length scales of photons and phonons in the material is an indispensable and powerful means to develop novel materials. In the current mature status of photonics, polymers hold a pivotal role in various application areas such as light-emission, sensing, energy, and displays, with exclusive advantages despite their relatively low dielectric constants. Moreover, in the nascent field of phononics, polymers are expected to be a superior material platform due to the ability for readily fabricated complex polymer structures possessing a wide range of mechanical behaviors, complete phononic bandgaps, and resonant architectures. In this review, polymer-centric photonic and phononic crystals and metamaterials are highlighted, and basic concepts, fabrication techniques, selected functional polymers, applications, and emerging ideas are introduced.

Tuning Mie scattering resonances in soft materials with magnetic fields

An original approach is proposed here to reversibly tune Mie scattering resonances occurring in random media by means of external low induction magnetic fields. This approach is valid for both electromagnetic and acoustic waves. The experimental demonstration is supported by ultrasound experiments performed on emulsions made of fluorinated ferrofluid spherical droplets dispersed in a Bingham fluid. We show that the electromagnet-induced change of droplet shape into prolate spheroids, with a moderate aspect ratio of 2.5, drastically affects the effective properties of the disordered medium. Its effective acoustic attenuation coefficient is shown to vary by a factor of 5, by controlling both the flux density and orientation of the applied magnetic field.

Metamaterials beyond electromagnetism

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.

Acoustics of porous media with inner resonators

This paper deals with the acoustics of rigid porous media with inner resonators both saturated by the same gas. The aim is to define porous media microstructures in which inner resonance phenomena may occur, and to provide the modeling of acoustic waves in this situation. The first part, focuses on the design of a periodic medium consisting in damped Helmholtz resonators embedded in a porous matrix. In the second part, the macroscopic description of this system is established through the homogenization method. In the third part, the features of acoustic wave propagation are determined, and the occurrence of a broad band gap along with strongly dispersed waves is discussed according to the characteristics of the porous matrix and of the damped resonators.

Sound and heat revolutions in phononics

The phonon is the physical particle representing mechanical vibration and is responsible for the transmission of everyday sound and heat. Understanding and controlling the phononic properties of materials provides opportunities to thermally insulate buildings, reduce environmental noise, transform waste heat into electricity and develop earthquake protection. Here I review recent progress and the development of new ideas and devices that make use of phononic properties to control both sound and heat. Advances in sonic and thermal diodes, optomechanical crystals, acoustic and thermal cloaking, hypersonic phononic crystals, thermoelectrics, and thermocrystals herald the next technological revolution in phononics.

Composite media mixing Bragg and local resonances for highly attenuating and broad bandgaps

In this article, we investigate composite media which present both a local resonance and a periodic structure. We numerically and experimentally consider the case of a very academic and simplified system that is a quasi-one dimensional split ring resonator medium. We modify its periodicity to shift the position of the Bragg bandgap relative to the local resonance one. We observe that for a well-chosen lattice constant, the local resonance frequency matches the Bragg frequency thus opening a single bandgap which is at the same time very wide and strongly attenuating. We explain this interesting phenomenon by the dispersive nature of the unit cell of the medium, using an analogy with the concept of white light cavities. Our results provide new ways to design wide and efficient bandgap materials.

Comparisons of two effective medium approaches for predicting sound scattering by periodic arrays of elastic shells

Two effective medium models are presented and used to predict complex reflection and transmission coefficients of finite periodic arrays of resonant elastic shells as well as their effective density and bulk modulus at low frequencies. Comparisons with full multiple scattering theory and measurements show that the self-consistent model fails to correctly predict the shape of the transmission/reflection curves when scatterer resonances are close to the first Bragg bandgap. The low frequency grating model, which neglects the evanescent modes and considers scattered wave propagation only in the same direction as the incident one, gives a much better agreement with both measurements and the full multiple scattering theory. Moreover, because it does not require the wavelength to strongly exceed the size of scatterers, the model gives reliable predictions even at frequencies around the first periodicity related bandgap. In contrast to the self-consistent model, the low frequency grating model is applicable when the resonant scatterers have more than two low frequency resonances.

Defect-controlled hypersound propagation in hybrid superlattices

We employ spontaneous Brillouin light scattering spectroscopy and detailed theoretical calculations to reveal and identify elastic excitations inside the band gap of hypersonic hybrid superlattices. Surface and cavity modes, their strength and anticrossing are unambiguously documented and fully controlled by layer thickness, elasticity, and sequence design. This new soft matter based superlattice platform allows facile engineering of the density of states and opens new pathways to tunable phoxonic crystals.

Local resonance bandgaps in periodic media: theory and experiment

Periodic composites such as acoustic metamaterials use local resonance phenomenon in designing low frequency sub-Bragg bandgaps. These bandgaps emerge from a resonant scattering interaction between a propagating wave and periodically arranged resonators. This paper develops a receptance coupling technique to combine the dynamics of the resonator with the unit cell dynamics of the background medium to analyze flexural wave transmission in a periodic structure, involving a single degree of freedom coupling between the medium and the resonator. Receptance techniques allow for a straightforward extension to higher dimensional systems with multiple degrees of freedom coupling and for easier experimental measurements. Closed-form expressions for the location and width of sub-Bragg bandgaps are obtained. Rigid body modes of the unit cell of the background medium are shown to set the bounding frequencies for local resonance bandgaps. Results from the receptance analysis compare well with Bloch wave analysis and experiments performed on a finite structural beam with periodic masses and resonators. Stronger coupling and inertia of the resonator increase the local resonance bandgap width. Two-fold periodicity widens the Bragg bandgap, narrowed by local resonators, thus expanding the design space and highlighting the advantages of hierarchical periodicity.

On the coupling of resonance and Bragg scattering effects in three-dimensional locally resonant sonic materials

Three-dimensional (3D) locally resonant sonic materials (LRSMs) are studied theoretically for purpose of optimising their sub-wavelength performance by coupling resonance and Bragg scattering effects together. Through the study of effective sound speeds of LRSMs, we find that the starting frequency of Bragg scattering can be shifted to sub-wavelength region by softening coats of resonators when the matrix is a low shear-velocity medium. A similar result can be achieved by compressing the lattice constant. By using a layer-multiple-scattering method, we investigate the complex band structure and the transmission spectrum of an LRSM whose Bragg gap is already close to the resonance gap in frequency. The wave fields of the composite simulated by COMSOL are further analysed at several typical frequencies. The result shows that the approaching of two kinds of gaps not only broadens the bandwidth of the resonance gap, but also increases the depth of the Bragg gap since the interaction between resonant modes and scattering waves are enhanced. By varying the shear velocity of coats, we obtain a coupled gap, which exhibits a broad transmission gap in the sub-wavelength region. When the loss of coats is considered, the coupled gap can not only maintain a good sound blocking performance, but also perform an efficient absorption in the low frequency region.

Increasing the modal density in plates for mono-element focusing in air

Acoustic focusing experiments usually require large arrays of transducers. It has been shown by Etaix et al. [J. Acoust. Soc. Am. 131, 395-399 (2012)] that the use of a cavity allows reducing this number of transducers. This paper presents experiments with Duralumin plates (the cavities) containing scatterers to improve the contrast of focusing. The use of a scatterer array in the plate allows increasing the modal density at given frequencies. The scatterers used are membranes and buttons that are manufactured in Duralumin plates. Their resonances are studied both experimentally and numerically. Such scatterers present the advantage of having a tunable frequency resonance, which allows controlling the frequencies at which the modal density increases. The dispersion relations of plates with scatterer array show high modal density at given frequencies. Finally acoustic focusing experiments in air, using these plates, are compared to the ones of simple duralumin plates demonstrating the improvement of contrast. Acoustic source localization is also realized using these plates.

Interaction of a contact resonance of microspheres with surface acoustic waves

We study the interaction of surface acoustic waves (SAWs) with a contact-based vibrational resonance of 1 μm silica microspheres forming a two-dimensional granular crystal adhered to a substrate. The laser-induced transient grating technique is used to excite SAWs and measure their dispersion. The measured dispersion curves exhibit "avoided crossing" behavior due to the hybridization of the SAWs with the microsphere resonance. We compare the measured dispersion curves with those predicted by our analytical model and find excellent agreement. The approach presented can be used to study the contact mechanics and adhesion of micro- and nanoparticles as well as the dynamics of microscale granular crystals.

Double negative elastic metamaterial design through electrical-mechanical circuit analogies

Previous studies into solid elastic metamaterials which have a simultaneously negative effective bulk modulus and density have proposed designs for materials with relatively narrow bandwidths, because of the reliance on resonators to provide the dispersive material properties. Some of the proposed novel applications for metamaterials, such as invisibility cloaks and sub-wavelength lenses, generally require materials with inherently larger bandwidths for practical exploitation. In this paper, a well-known electromagnetic metamaterial design is used together with the electrical-mechanical circuit analogies to propose a simultaneously double negative elastic metamaterial design which does not suffer from the narrow bandwidth constraints of previous designs. An interesting consequence of the proposed design is that it has an effective wavelength which asymptotically goes to infinity with frequency.

Fabrication of novel silicone capsules with tunable mechanical properties by microfluidic techniques

A novel approach for the synthesis of silicone capsules using double W/O/W emulsions as templates is introduced. The low viscosity of the silicone precursors enables the use of microfluidic techniques to accurately control the size and morphology of the double emulsion droplets, which after cross-linking result in the desired monodisperse silicone capsules. Their shell thickness can be finely tuned, which in turn allows control over their permeability and mechanical properties; the latter are particularly important in a variety of practical applications where the capsules are subjected to large external forces. The potential of these capsules for controlled release is also demonstrated using a model hydrophilic substance.

Experimental observation of negative effective gravity in water waves

The gravity of Earth is responsible for the formation of water waves and usually difficult to change. Although negative effective gravity was recently predicted theoretically in water waves, it has not yet been observed in experiments and remains a mathematical curiosity which is difficult to understand. Here we experimentally demonstrate that close to the resonant frequency of purposely-designed resonating units, negative effective gravity can occur for water waves passing through an array of resonators composing of bottom-mounted split tubes, resulting in the prohibition of water wave propagation. It is found that when negative gravity occurs, the averaged displacement of water surface in a unit cell of the array has a phase difference of π to that along the boundary of the unit cell, consistent with theoretical predictions. Our results provide a mechanism to block water waves and may find applications in wave energy conversion and coastal protection.

Phonons in two-dimensional colloidal crystals with bond-strength disorder

We study phonon modes in two-dimensional colloidal crystals composed of soft microgel particles with hard polystyrene particle dopants distributed randomly on the triangular lattice. This experimental approach produces close-packed lattices of spheres with random bond strength disorder, i.e., the effective springs coupling nearest neighbors are very stiff, very soft, or of intermediate stiffness. Particle tracking video microscopy and covariance matrix techniques are then employed to derive the phonon modes of the corresponding "shadow" crystals with bond strength disorder as a function of increasing dopant concentration. At low frequencies, hard and soft particles participate equally in the phonon modes, and the samples exhibit Debye-like density of states behavior characteristic of crystals. For mid- and high-frequency phonons, the relative participation of hard versus soft particles in each mode is found to vary systematically with dopant concentration. Additionally, a few localized modes, primarily associated with hard particle motions, are found at the highest frequencies.

Acoustic rainbow trapping

Spatial modulation of sound velocity below the wavelength scale can introduce strong frequency-dependent acoustic responses in tailored composite materials, regardless the fact that most natural bulk materials have negligible acoustic dispersions. Here, for the first time, we experimentally demonstrate a metamaterial that traps broadband acoustic waves and spatially separates different frequency components, as the result of dispersion and wave velocity control by designed gradient subwavelength structures. The trapping positions can be predicted by the microscopic picture of balanced interplay between the acoustic resonance inside individual apertures and the mutual coupling among them. With the enhanced wave-structure interactions and the tailored frequency responses, such metamaterial allows precise spatial-spectral control of acoustic waves and opens new venue for high performance acoustic wave sensing, filtering, and nondestructive metrology.

Coupled membranes with doubly negative mass density and bulk modulus

We present a structurally and conceptually simple acoustic double negative metamaterial comprising two coupled membranes. Owing to its symmetry, the system can generate both monopolar and dipolar resonances that are separately tunable, thereby making broadband double negativity possible. A homogenization scheme is implemented that enables the exact characterization of our metamaterial by the effective mass density and bulk modulus even beyond the usual long-wavelength regime, with the measured displacement fields on the sample's surfaces as inputs. Double negativity is achieved in the frequency range of 520-830 Hz. Transmission and reflection predictions using effective parameters are shown to agree remarkably well with the experiment.

Coherent phonon-grain boundary scattering in silicon inverse opals

We report measurements and modeling of thermal conductivity in periodic three-dimensional dielectric nanostructures, silicon inverse opals. Such structures represent a three-dimensional "phononic crystal" but affect heat flow instead of acoustics. Employing the Stober method, we fabricate high quality silica opal templates that on filling with amorphous silicon, etching and recrystallizing produce silicon inverse opals. The periodicities and shell thicknesses are in the range 420-900 and 18-38 nm, respectively. The thermal conductivity of inverse opal films are relatively low, ~0.6-1.4 W/mK at 300 K and arise due to macroscopic bending of heat flow lines in the structure. The corresponding material thermal conductivity is in the range 5-12 W/mK and has an anomalous ~T(1.8) dependence at low temperatures, distinct from the typical ~T(3) behavior of bulk polycrystalline silicon. Using phonon scattering theory, we show such dependence arising from coherent phonon reflections in the intergrain region. This is consistent with an unconfirmed theory proposed in 1955. The low thermal conductivity is significant for applications in photonics where they imply significant temperature rise at relatively low absorption and in thermoelectrics, where they suggest the possibility of enhancement in the figure of merit for polysilicon with optimal doping.

Analytical approximations for low frequency band gaps in periodic arrays of elastic shells

This paper presents and compares three analytical methods for calculating low frequency band gap boundaries in doubly periodic arrays of resonating thin elastic shells. It is shown that both Foldy-type equations (derived with lattice sum expansions in the vicinity of its poles) and a self-consistent scheme could be used to predict boundaries of low-frequency (below the first Bragg band gap) band gaps due to axisymmetric (n=0) and dipolar (n=1) shell resonances. The accuracy of the former method is limited to low filling fraction arrays, however, as the filling fraction increases the application of the matched asymptotic expansions could significantly improve approximations of the upper boundary of band gap related to axisymmetric resonance. The self-consistent scheme is shown to be very robust and gives reliable results even for dense arrays with filling fractions around 70%. The estimates of band gap boundaries can be used in analyzing the performance of periodic arrays (in terms of the band gap width) without using full semi-analytical and numerical models. The results are used to predict the dependence of the position and width of the low frequency band gap on the properties of shells and their periodic arrays.

Space-coiling metamaterials with double negativity and conical dispersion

Metamaterials are effectively homogeneous materials that display extraordinary dispersion. Negative index metamaterials, zero index metamaterials and extremely anisotropic metamaterials are just a few examples. Instead of using locally resonating elements that may cause undesirable absorption, there are huge efforts to seek alternative routes to obtain these unusual properties. Here, we demonstrate an alternative approach for constructing metamaterials with extreme dispersion by simply coiling up space with curled channels. Such a geometric approach also has an advantage that the ratio between the wavelength and the lattice constant in achieving a negative or zero index can be changed in principle. It allows us to construct for the first time an acoustic metamaterial with conical dispersion, leading to a clear demonstration of negative refraction from an acoustic metamaterial with airborne sound. We also design and realize a double-negative metamaterial for microwaves under the same principle.

Sustainable sonic crystal made of resonating bamboo rods

The acoustic transmission coefficient of a resonant sonic crystal made of hollow bamboo rods is studied experimentally and theoretically. The plane wave expansion and multiple scattering theory (MST) are used to predict the bandgap in transmission coefficient of a non-resonant sonic crystal composed of rods without holes. The predicted results are validated against experimental data for the acoustic transmission coefficient. It is shown that a sonic crystal made from a natural material with some irregularities can exhibit a clear transmission bandgap. Then, the hollow bamboo rods are drilled between each node to create an array of Helmholtz resonators. It is shown that the presence of Helmholtz resonators leads to an additional bandgap in the low-frequency part of the transmission coefficient. The MST is modified in order to account for the resonance effect of the holes in the drilled bamboo rods. This resonant multiple scattering theory is validated experimentally and could be further used for the description and optimization of more complex resonant sonic crystals.

A Refined Finite Element Formulation for the Microstructure-Dependent Analysis of Two-Dimensional (2D) Lattice Materials

A finite element approximation is proposed for the dynamic analysis of two-dimensional (2D) lattice materials. The unit cell is modeled by means of a defined number of shear deformable micro-beams. The main innovative feature concerns the presence of a microstructure-dependent scale length, which allows the consideration of the so called size-effect that can be highly relevant, due to the characteristics of the lattice at the local scale. Some numerical results show the influence of the microstructure parameter on the dynamic behavior of two-dimensional lattice materials.

Localization-delocalization transition for disordered cubic harmonic lattices

We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams exhibit regions of stable and unstable waves, the universality of the transitions is the same for mass and spring constant disorder throughout all the phase boundaries. The combined value for the critical exponent of the localization lengths of ν = 1.550(-0.017)(+0.020) confirms the agreement with the universality class of the standard electronic Anderson model of localization. We further support our investigation with studies of the density of states, the participation numbers and wave function statistics.

Determination of effective mass density and modulus for resonant metamaterials

This work presents a method to determine the effective dynamic properties of resonant metamaterials. The longitudinal vibration of a rod with periodically attached oscillators was predicted using wave propagation analysis. The effective mass density and modulus were determined from the transfer function of vibration responses. Predictions of these effective properties compared favorably with laboratory measurements. While the effective mass density showed significant frequency dependent variation near the natural frequency of the oscillators, the elastic modulus was largely unchanged for the setup considered in this study. The effective mass density became complex-numbered when the spring element of the oscillator was viscoelastic. As the real part of the effective mass density became negative, the propagating wavenumber components disappeared, and vibration transmission through the metamaterial was prohibited. The proposed method provides a consistent approach for evaluating the effective parameters of resonant metamaterials using a small number of vibration measurements.

Super-resolution imaging by resonant tunneling in anisotropic acoustic metamaterials

The resonant tunneling effects that could result in complete transmission of evanescent waves are examined in acoustic metamaterials of anisotropic effective mass. The tunneling conditions are first derived for the metamaterials composed of classical mass-in-mass structures. It is found that the tunneling transmission occurs when the total length of metamaterials is an integral number of half-wavelengths of the periodic Bloch wave. Due to the local resonance of building units of metamaterials, the Bloch waves are spatially modulated within the periodic structures, leading to the resonant tunneling occurring in the low-frequency region. The metamaterial slab lens with anisotropic effective mass is designed by which the physics of resonant tunneling and the features for evanescent field manipulations are examined. The designed lens interacts with evanescent waves in the way of the propagating wavenumber weakly dependent on the spatial frequency of evanescent waves. Full-wave simulations validate the imaging performance of the proposed lens with the spatial resolution beyond the diffraction limit.

Effects of the local resonance on the wave propagation in periodic frame structures: generalized Newtonian mechanics

This work is devoted to the study of the wave propagation in infinite two-dimensional structures made up of the periodic repetition of frames. Such materials are highly anisotropic and, because of lack of bracing, can present a large contrast between the shear and compression deformabilities. Moreover, when the thickness to length ratio of the frame elements is small, these elements can resonate in bending at low frequencies when compressional waves propagate in the structure. The frame size being small compared to the wavelength of the compressional waves, the homogenization method of periodic discrete media is extended to situations with local resonance, and it is applied to identify the macroscopic behavior at the leading order. In particular, the local resonance in bending leads to an effective mass different from the real mass and to the generalization of the Newtonian mechanics at the macroscopic scale. Consequently, compressional waves become dispersive and frequency bandgaps occur. The physical origin of these phenomena at the microscopic scale is also presented. Finally, a method is proposed for the design of such materials.

Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young's modulus

A mechanical model representing an acoustic metamaterial that exhibits simultaneously negative mass density and negative Young's modulus was proposed. Wave propagation was studied in the frequency range of double negativity. In view of positive energy flow, it was found that the phase velocity in this range is negative. This phenomenon was also observed using transient wave propagation finite-element analyses of a transient sinusoidal wave and a transient wave packet. In contrast to wave propagation in the region of positive mass and modulus, the peculiar backward wave motion in the region of double negativity was clearly displayed.

Scaling of membrane-type locally resonant acoustic metamaterial arrays

Metamaterials have emerged as promising solutions for manipulation of sound waves in a variety of applications. Locally resonant acoustic materials (LRAM) decrease sound transmission by 500% over acoustic mass law predictions at peak transmission loss (TL) frequencies with minimal added mass, making them appealing for weight-critical applications such as aerospace structures. In this study, potential issues associated with scale-up of the structure are addressed. TL of single-celled and multi-celled LRAM was measured using an impedance tube setup with systematic variation in geometric parameters to understand the effects of each parameter on acoustic response. Finite element analysis was performed to predict TL as a function of frequency for structures with varying complexity, including stacked structures and multi-celled arrays. Dynamic response of the array structures under discrete frequency excitation was investigated using laser vibrometry to verify negative dynamic mass behavior.

Micro-/nanostructured mechanical metamaterials

Mechanical properties of materials have long been one of the most fundamental and studied areas of materials science for a myriad of applications. Recently, mechanical metamaterials have been shown to possess extraordinary effective properties, such as negative dynamic modulus and/or density, phononic bandgaps, superior thermoelectric properties, and high specific energy absorption. To obtain such materials on appropriate length scales to enable novel mechanical devices, it is often necessary to effectively design and fabricate micro-/nano- structured materials. In this Review, various aspects of the micro-/nano-structured materials as mechanical metamaterials, potential tools for their multidimensional fabrication, and selected methods for their structural and performance characterization are described, as well as some prospects for the future developments in this exciting and emerging field.