Acoustic metamaterial

Acoustic metamaterials trace their origins to the broader field of metamaterials. The concept of artificial media with unusual effective properties was first proposed by Victor Veselago in 1967 and later advanced by John Pendry in the late 1990s, leading to the first realization of negative-index electromagnetic materials in 2000. Building on these developments, the acoustic counterpart emerged the same year, when Liu and colleagues demonstrated locally resonant sonic materials composed of heavy inclusions in a soft matrix, showing band gaps at subwavelength scales. ==Basic principles==

Properties of acoustic metamaterials usually arise from structure rather than composition, with techniques such as the controlled fabrication of small inhomogeneities to enact effective macroscopic behavior. Bulk modulus and mass density The bulk modulus β is a measure of a substance's resistance to uniform compression. It is defined as the ratio of pressure increase needed to cause a given relative decrease in volume. The mass density (or just density) of a material is defined as mass per unit volume and is expressed in grams per cubic centimeter (g/cm3). In all three classic states of matter—gas, liquid, or solid—the density varies with a change in temperature or pressure, with gases being the most susceptible to those changes. The spectrum of densities is wide-ranging: from 1015 g/cm3 for neutron stars, 1.00 g/cm3 for water, to 1.2×10−3 g/cm3 for air. In combination with a well-defined polarization during wave propagation; k = |n|ω, is an equation for refractive index as sound waves interact with acoustic metamaterials (below):{{cite book|last =Krowne| first = Clifford M.|author2= Yong Zhang :n^2=\frac{\rho}{\beta} The inherent parameters of the medium are the mass density ρ, bulk modulus β, and chirality k. Chirality, or handedness, determines the polarity of wave propagation (wave vector). Hence within the last equation, Veselago-type solutions (n2 = u*ε) are possible for wave propagation as the negative or positive state of ρ and β determine the forward or backward wave propagation. In electromagnetic metamaterials negative permittivity can be found in natural materials. However, negative permeability has to be intentionally created in the artificial transmission medium. For acoustic materials neither negative ρ nor negative β are found in naturally occurring materials; they are derived from the resonant frequencies of an artificially fabricated transmission medium, and such negative values are an anomalous response. Negative ρ or β means that at certain frequencies the medium expands when experiencing compression (negative modulus), and accelerates to the left when being pushed to the right (negative density). Electromagnetic field vs acoustic field The electromagnetic spectrum extends from low frequencies used for modern radio to gamma radiation at the short-wavelength end, covering wavelengths from thousands of kilometers down to a fraction of the size of an atom. In comparison, infrasonic frequencies range from 20 Hz down to 0.001 Hz, audible frequencies are 20 Hz to 20 kHz and the ultrasonic range is above 20 kHz. While electromagnetic waves can travel in vacuum, acoustic wave propagation requires a medium. Mechanics of lattice waves In a rigid lattice structure, atoms exert force on each other, maintaining equilibrium. Most of these atomic forces, such as covalent or ionic bonds, are of electric nature. The magnetic force, and the force of gravity are negligible.{{cite book| last =Lavis| first =David Anthony There is a minimum possible wavelength, given by the equilibrium separation a between atoms. Any wavelength shorter than this can be mapped onto a long wavelength, due to effects similar to aliasing. ==Research and applications==

Applications of acoustic metamaterial research include seismic wave reflection and vibration control technologies related to earthquakes, as well as precision sensing. Phononic crystals can be engineered to exhibit band gaps for phonons, similar to the existence of band gaps for electrons in solids and to the existence of electron orbitals in atoms. However, unlike atoms and natural materials, the properties of metamaterials can be fine-tuned (for example through microfabrication). For that reason, they constitute a potential testbed for fundamental physics and quantum technologies. They also have a variety of engineering applications, for example they are widely used as a mechanical component in optomechanical systems. Sonic crystals In 2000, the research of Liu et al. paved the way to acoustic metamaterials through sonic crystals, which exhibit spectral gaps two orders of magnitude smaller than the wavelength of sound. The spectral gaps prevent the transmission of waves at prescribed frequencies. The frequency can be tuned to desired parameters by varying the size and geometry. The amplitudes of the sound waves entering the surface were compared with the sound waves at the center of the structure. The oscillations of the coated spheres absorbed sonic energy, which created the frequency gap; the sound energy was absorbed exponentially as the thickness of the material increased. The key result was the negative elastic constant created from resonant frequencies of the material. Projected applications of sonic crystals are seismic wave reflection and ultrasonics. In 2004 split-ring resonators (SRR) became the object of acoustic metamaterial research. An analysis of the frequency band gap characteristics, derived from the inherent limiting properties of artificially created SRRs, paralleled an analysis of sonic crystals. The band gap properties of SRRs were related to sonic crystal band gap properties. Inherent in this inquiry is a description of mechanical properties and problems of continuum mechanics for sonic crystals, as a macroscopically homogeneous substance. In order to speed up the calculation of the frequency band structure, the Reduced Bloch Mode Expansion (RBME) method can be used. Phononic crystals effectively reduce low-frequency noise, since their locally resonant systems act as spatial frequency filters. However, they have narrow band gaps, impose additional weight on the primary system, and work only at the adjusted frequency range. For widening band gaps, the unit cells must be large in size or contain dense materials. As a solution to the disadvantages mentioned above of phononic crystals, proposes a novel three-dimensional lightweight re-entrant meta-structure composed of a cross-shaped beam scatterer embedded in a host plate with holes based on the square lattice metamaterial. By combining the re-entry networks mechanism and the Floquet–Bloch theory, on the basis of cross-shaped beam theory and perforation mechanism, it was demonstrated that such a lightweight phononic structure can filter elastic waves across a broad frequency range (not just a specific narrow region) while simultaneously reducing structure weight to a significant degree. Double-negative acoustic metamaterial of a plane wave moving from top to bottom. Right: the same wave after a central section underwent a phase shift, for example, by passing through metamaterial inhomogeneities of different thickness than the other parts. (The illustration on the right ignores the effect of diffraction whose effect increases over large distances). Electromagnetic (isotropic) metamaterials have built-in resonant structures that exhibit effective negative permittivity and negative permeability for some frequency ranges. In contrast, it is difficult to build composite acoustic materials with built-in resonances such that the two effective response functions are negative within the capability or range of the transmission medium. The mass density ρ and bulk modulus β are position dependent. Using the formulation of a plane wave the wave vector is: Even for composite materials, the effective bulk modulus and density should be normally bounded by the values of the constituents, i.e., the derivation of lower and upper bounds for the elastic moduli of the medium. The expectation for positive bulk modulus and positive density is intrinsic. For example, dispersing spherical solid particles in a fluid result in the ratio governed by the specific gravity when interacting with the long acoustic wavelength (sound). Mathematically, it can be proven that βeff and ρeff are definitely positive for natural materials. Negative bulk modulus is achieved through monopolar resonances of the BWS series. Negative mass density is achieved with dipolar resonances of the gold sphere series. Rather than rubber spheres in liquid, this is a solid based material. This is also as yet a realization of simultaneously negative bulk modulus and mass density in a solid based material, which is an important distinction.—that enable acoustic wave manipulation. The Willis moduli couple stress to particle velocity and linear momentum to strain, and are named after J. R. Willis, who predicted them using a dynamic homogenization method. Much of the recent interest in Willis couplings has been driven by their local form (the Milton–Briane–Willis equations). By extending Willis's homogenization method, Pernas-Salomón and Shmuel were the first to show that piezoelectric composites possess an effective coupling between linear momentum and the electric field, which they termed electro-momentum coupling. The electromomentum coupling modulus provides a mechanism for wave manipulation akin to Willis coupling, with the added advantage of electrical tunability. Double C resonators Double C resonators (DCRs) are rings cut in half, which can be arranged in multiple cell configurations, similarly to the SRRS. Each cell consists of a large rigid disk and two thin ligaments, and acts as a tiny oscillator connected by springs. One spring anchors the oscillator, and the other connects to the mass. It is analogous to an LC resonator of capacitance, C, and inductance, L, and resonant frequency √1/(LC). The speed of sound in the matrix is expressed as c = √ρ/μ with density ρ and shear modulus μ. Although linear elasticity is considered, the problem is mainly defined by shear waves directed at angles to the plane of the cylinders. This lens could improve acoustic imaging techniques, since the spatial resolution of the conventional methods is restricted by the incident ultrasound wavelength. This is due to the quickly fading evanescent fields which carry the sub-wavelength features of objects. reported a metamaterial which simultaneously possessed a negative bulk modulus and mass density. A laboratory metamaterial device that is applicable to ultrasound waves was demonstrated in 2011 for frequencies from 40 to 80 kHz. The metamaterial acoustic cloak was designed to hide objects submerged in water, bending and twists sound waves. The cloaking mechanism consists of 16 concentric rings in a cylindrical configuration, each ring having acoustic circuits and a different index of refraction. This causes sound waves to vary their speed from ring to ring. The sound waves propagate around the outer ring, guided by the channels in the circuits, which bend the waves to wrap them around the outer layers. This device has been described as an array of cavities which actually slow the speed of the propagating sound waves. An experimental cylinder was submerged in a tank, and made to disappear from sonar detection. Other objects of various shapes and densities were also hidden from sonar. Quantum-like computing with acoustic metamaterials Researchers have demonstrated a quantum-like computing method using acoustic metamaterials. Recently operations similar to the Controlled-NOT (CNOT) gate, a key component in quantum computing, have been demonstrated. By employing a nonlinear acoustic metamaterial, consisting of three elastically coupled waveguides, the team created classical qubit analogues called logical phi-bits. This approach allows for scalable, systematic, and predictable CNOT gate operations using a simple physical manipulation. This innovation brings promise to the field of quantum-like computing using acoustic metamaterials. ==See also==