Digitally virtualized atoms for acoustic metamaterials

Nonreciprocal interlayer coupling is difficult to practically implement in bilayer non-Hermitian topological photonic systems. In this work, we identify a similarity transformation between the Hamiltonians of systems with nonreciprocal interlayer coupling and on-site gain/loss. The similarity transformation is widely applicable, and we show its application in one- and two-dimensional bilayer topological systems as examples. The bilayer non-Hermitian system with nonreciprocal interlayer coupling, whose topological number can be defined using the gauge-smoothed Wilson loop, is topologically equivalent to the bilayer system with on-site gain/loss. We also show that the topological number of bilayer non-Hermitian C6v-typed domain-induced topological interface states can be defined in the same way as in the case of the bilayer non-Hermitian Su–Schrieffer–Heeger model. Our results show the relations between two microscopic provenances of the non-Hermiticity and provide a universal and convenient scheme for constructing and studying nonreciprocal interlayer coupling in bilayer non-Hermitian topological systems. This scheme is useful for observation of non-Hermitian skin effect in three-dimensional systems.Graphical

Parity-time ($\mathcal{PT}$) symmetry plays an important role both in non-Hermitian and topological systems. In non-Hermitian systems $\mathcal{PT}$ symmetry can lead to an entirely real energy spectrum, while in topological systems $\mathcal{PT}$ symmetry gives rise to stable and protected Dirac points. Here, we study a $\mathcal{PT}$-symmetric system which is both non-Hermitian and topological, namely a $\mathcal{PT}$-symmetric Dirac semimetal with non-Hermitian perturbations in three dimensions. We find that, in general, there are only two types of symmetry allowed non-Hermitian perturbations, namely non-Hermitian kinetic potentials, and non-Hermitian anti-commuting potentials. For both of these non-Hermitian potentials we investigate the band topology for open and periodic boundary conditions, determine the exceptional points, and compute the surface states. We find that with periodic boundary conditions, the non-Hermitian kinetic potential leads to exceptional rings, while the non-Hermitian anti-commuting potential generates exceptional spheres, which separate regions with broken $\mathcal{PT}$ symmetry from regions with unbroken $\mathcal{PT}$ symmetry. With open boundary conditions, the non-Hermitian kinetic potential induces a non-Hermitian skin effect which is localized on both sides of the sample due to symmetry, while the non-Hermitian anticommuting potential leads to Fermi ribbon surface states.

Acoustic metamaterials with negative constitutive parameters (modulus and/or mass density) have shown great potential in diverse applications ranging from sonic cloaking, abnormal refraction and superlensing, to noise canceling. In conventional acoustic metamaterials, the negative constitutive parameters are engineered via tailored structures with fixed geometries; therefore, the relationships between constitutive parameters and acoustic frequencies are typically fixed to form a 2D phase space once the structures are fabricated. Here, by means of a model system of magnetoactive lattice structures, stimuli-responsive acoustic metamaterials are demonstrated to be able to extend the 2D phase space to 3D through rapidly and repeatedly switching signs of constitutive parameters with remote magnetic fields. It is shown for the first time that effective modulus can be reversibly switched between positive and negative within controlled frequency regimes through lattice buckling modulated by theoretically predicted magnetic fields. The magnetically triggered negative-modulus and cavity-induced negative density are integrated to achieve flexible switching between single-negative and double-negative. This strategy opens promising avenues for remote, rapid, and reversible modulation of acoustic transportation, refraction, imaging, and focusing in subwavelength regimes.

Aiming at the isolation of low-frequency noise, an acoustic metamaterial is designed based on Helmholtz cavity and thin film structure. It consists of a Helmholtz cavity with film bottom and the mass block attached to the cavity. By the finite element method, the transmission losses and resonance frequencies of metamaterials in a frequency range of 20－1200 Hz are calculated and also verified experimentally. The results show that the metamaterial has great sound insulation performance in the frequency range. There are six sound insulation peaks, of which the two sound insulation peaks below 100 Hz have the transmission losses of 44.29 dB and 67.43 dB, respectively. The maximum transmission loss in the whole frequency range is 90.18 dB. Comparing with the normal Helmholtz cavity or thin film acoustic metamaterial or traditional material, the sound insulation performance of the metamaterial is improved greatly. By analyzing the resonance and vibration mode diagram at the sound insulation peaks comprehensively, the sound insulation mechanism of the metamaterial is further explored. The results show that many resonance modes have no effect on transmission loss only when the resonance mode can be coupled with the incident wave and is not an antisymmetric mode which can affect the transmission loss. The transmission and reflection coefficient of the metamaterial are calculated by the finite element method, and through the method for retrieving effective properties, the effective mass density and effective modulus are obtained. It is found that there is a negative effective mass density at the sound insulation peak, meanwhile the effective modulus is close to zero. The generation mechanism of abnormal equivalent parameters is analyzed from the energy view point. The acoustic impedance of the metamaterial is obtained by an equivalent circuit method, through which the first resonance frequency is calculated relatively accurately. According to the results of the previous study on sound insulation mechanism, the effect of the eccentric mass unit on the sound insulation performance of metamaterial is studied. It is found that the eccentric mass can greatly reduce the antisymmetric resonance mode and increase the sound insulation peak of the structure, which is also verified experimentally. The results provide a reference for designing the 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.

In this paper, we proposed a type of locally resonator which works by introducing more than one vibration modes, and thus can provide a new approach to formulate acoustic or elastic metamaterial. Such new concept of resonator is fundamentally different from traditional translational and rotational resonators. The potential application and design of acoustic metamaterial based on this kind of structures are also studied both analytically and numerically. The acoustic metamaterial filter we developed has proved to have unique property that only allow the waves with specific frequency to pass while other waves will be attenuated. We also proposed a kind of plane wave lens which can transfer plane wave with uniformly distributed amplitude profiles into pure plane wave. With this novel resonator, the research and application regarding it are highly anticipated in the near future.

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.

Novel plenum window with sonic crystals for indoor noise control

An acoustic metamaterial consisting of a homogeneous damped plate with parallel attached resonators is presented. Theoretical analysis shows that the metamaterial plate can generate multiple resonant-type band gaps and the lower-bound frequency of each band gap coincides with the resonance frequencies of the resonators. The parallel arrangement of resonators, compared with the metamaterial plate with resonators attached in series reported by Peng et al. (2015), results in a wider second band gap with a lower edge, while the first band gap is almost the same, creating therefore an easier combination of the multiple band gaps into a wider one. It is noted that damping has a significant influence on the band gaps and the effective mass density (especially for the damping of resonators). Specifically, it can be concluded that damping cannot be neglected in practical engineering applications, damping in the material of the host plate can smooth and lower the responses in the whole frequency range, especially in the higher frequency range, and a high level of damping of resonators deactivates the effect of band gaps. Such weak/damped resonators actualise the metamaterial damping poorly, and rather tend only to contribute to the overall damping such as the damping of the host plate.

Sonic crystals are media with a periodic modulation of the acoustic parameters, such as the density and the bulk modulus. They have recently attracted a great interest, because of their potential applications in the control of sound propagation, used as reflectors, focusers, or waveguides. All these properties are related with the dispersion introduced by the crystal anisotropy. We report on the nondiffractive propagation of sound in two-dimensional sonic crystals. It is shown that, for given frequencies and directions of incidence, a narrow sonic beam can propagate without diffractive broadening. Such nondiffractive sonic beams exist in crystals with perfect symmetry and do not require the presence of defects, differently from other waveguiding phenomena reported previously. The cancellation of diffraction has been predicted using the plane-wave expansion method to evaluate the dispersion surfaces of the crystal and the spatial dispersion (isofrequency) curves. It occurs for frequencies and wave vectors for which dispersion curves have zero curvature, denoting a transition between focusing and defocusing regimes. By means of perturbative techniques, a simple analytical expression for the nondiffractive conditions has been obtained. The phenomenon is also demonstrated by numerical integration of the acoustic equations using FDTD techniques. [Support from Spanish MEC, Project FIS2005-07931-C03-01/03, is acknowledged.]

A two-dimensional (2D) lattice model with anisotropic resonant microstructures is found to provide an anisotropic band gap structure. A 2D continuum with anisotropic effective mass density is introduced to represent this lattice system. Two methods are proposed to derive the equivalent continuum. In the first method, the effective mass density of the equivalent continuum is obtained by matching the dispersion relations for harmonic waves propagating in the principal directions. The second approach employs an approximate estimation of the effective mass density by volume-averaging an effective mass that represents the resonant microstructure. For both equivalent continuum models, the effective mass density is frequency-dependent and may become negative in certain frequency ranges. Subsequently, the effective mass density of the equivalent continuum assumes the form of a second-order tensor. Thus, it suffices to determine the effective mass density tensor with respect to the principle directions. It is shown numerically that the local-resonance effect is accurately described by the equivalent continuum model. In addition, the effect of anisotropic mass density on wave propagation is numerically illustrated and discussed.

Design of low-frequency and broadband acoustic metamaterials with I-shaped antichiral units

Acoustic metamaterials are artificially engineered composites composed of mesoscopic subwavelength units, which have recently become an active field with an enormous range of potential applications. These media, which derive their properties from their structure rather than from the chemical properties of their constitutive materials, can be tailored in such a fashion to exhibit arbitrary effective constitutive parameters, ranging from very large positive to negative values. Initially proposed to achieve super absorption, acoustic metamaterials are today investigated to obtain numerous extraordinary effects, which include compact wavefront modulation, cloaking, asymmetric transmission, sub-diffraction focusing, etc. In this article, we review some of the most relevant works in this field and analyse the basic phenomena governing the behaviour of different kinds of acoustic metamaterials. We conclude with an outlook on active acoustic metamaterials, in which inclusions can provide energy to the impinging wave to obtain effective material properties that are not possible in passive structures.KeywordsSDG9Acoustic metamaterialsMetasurfacesLow-frequency sound absorptionActive acoustic metamaterials

Acoustic metamaterials, capable of both sound insulation and energy harvesting, composed of Helmholtz resonators and built-in decorated membranes are proposed. It is theoretically and experimentally proved that the proposed metamaterial can obtain two sound insulation bands where the sound energy is also efficiently harvested at the same frequency simultaneously. The peak of the output power can reach up to 244 nW when the incident sound pressure is 1 Pa, which is about 14 times larger than structures composed of single membrane reported before with the same input. Moreover, considerable energy harvesting with average output power of about 20 nW can be achieved within wider frequency ranges (with bandwidth up to 90 Hz) by choosing proper parameters. Additionally, the hybrid resonance mechanism of the proposed metamaterials is explained well with an equivalent theoretical model. These novel properties of the proposed metamaterial can be applied in many potential applications in noise control and energy harvesting.

Sound transmission loss of a novel acoustic metamaterial sandwich panel: Theory and experiment