Controlling sound with acoustic metamaterials

| Acoustic metamaterials can manipulate and control sound waves in ways that are not possible in conventional materials. Metamaterials with zero, or even negative, refractive index for sound offer new possibilities for acoustic imaging and for the control of sound at subwavelength scales. The combination of transformation acoustics theory and highly anisotropic acoustic metamaterials enables precise control over the deformation of sound fields, which can be used, for example, to hide or cloak objects from incident acoustic energy. Active acoustic metamaterials use external control to create effective material properties that are not possible with passive structures and have led to the development of dynamically reconfigurable, loss-compensating and parity–time-symmetric materials for sound manipulation. Challenges remain, including the development of efficient techniques for fabricating large-scale metamaterial structures and converting laboratory experiments into useful devices. In this Review, we outline the designs and properties of materials with unusual acoustic parameters (for example, negative refractive index), discuss examples of extreme manipulation of sound and, finally, provide an overview of future directions in the field. NATURE REVIEWS | MATERIALS ADVANCE ONLINE PUBLICATION | 1 REVIEWS © 2016 Macmillan Publishers Limited. All rights reserved the propagation of sound in new ways, made possible by the creation of unusual mat erial properties. These efforts have been successful on many fronts. For instance, it is now possible to design acoustic metamaterials that can acoustically conceal an object, acting as cloaks of ‘inaudibility’. Also, acoustic metamaterials with a negative refractive index can be designed to bend sound the ‘wrong’ way when insonified by a loudspeaker, enabling new ways of focusing and shaping sound fields. Over the past 15 years, the field of acoustic metamaterials has branched out in many directions, and it has been shown that acoustic waves can be manipulated and controlled in ways not previously imagined. In this Review, we describe the advances in the field and identify the technical challenges and possible future directions for research. We focus on metamaterials designed to control the propagation of acoustic waves in fluids such as air and water. Beyond this topic, there is ever-expanding research on elastic metamaterials that control vibrations, waves and the motion of solid materials6. Another subject that exceeds the scope of this Review is phononic crystals, materials in which resonant scattering of periodic structures can create wave-band structures with unusual, but useful, properties3. Metamaterials with negative parameters Sound-wave propagation is controlled by the mass density and the bulk modulus of a material (BOX 2). In conventional media, both of these parameters are positive and cannot be easily altered because they are directly associated with the chemical composition and the microstructure of the material. However, if metamaterials are constructed using resonant subwavelength meta-atoms that enhance sound–matter interaction, then it is possible to engineer the wave properties to obtain values of the effective acoustic-material parameters that are not observed in nature. One of the most unusual regimes for acoustic metamaterials arises when the real parts of the effective mass density and bulk modulus are negative in the same frequency range. This regime is analogous to negative-index metamaterials for electromagnetic waves. These materials, developed in the early 2000s, use metallic structures that generate out-of-phase (negative) electric and magnetic dipole responses to incident electro magnetic fields, leading to a negative phase velocity and a negative index of refraction7,8. Materials with tailored parameters are attractive for applications such as steering of waves and superresolution imaging. In particular, there has been a focus on negative parameters and imaging, which has led an initial surge in research into acoustic metamaterials. In what follows, we discuss various illustrative examples in which artificial materials are engineered to have parameters with negative or near-zero values (FIG. 1). These media enable metamaterials designers to construct devices with surprising effects, such as energy flow in the direction opposite to that of the wave vector or sound propagation without phase variations. Such materials allow for the guiding and focusing of acoustic signals at diffraction-unlimited scales. Acoustic metamaterials were initially created for use in sound-attenuating applications4. The first acoustic meta-atoms were spherical metal cores coated with a soft rubber shell packed to a simple-cubic lattice in a host material, which could exhibit a Mie-type resonance frequency far below the wavelength-scale Bragg resonance frequency of the lattice4,9–11. Depending on the underlying mechanical motion in such resonances, negative effective values of the mass density and of the bulk modulus can be obtained. In the context of spherical and cylindrical scatterers, monopolar modes give rise to a resonant response of the bulk modulus, whereas the dipolar modes create resonances in the mass density12. Numerical simulations of rubber spheres suspended in water, which have recently been experimentally verified13, show that these modes can coexist, leading to a band in parameter space characterized by a negative index of refraction13,14. Other architectures for acoustic metamaterials involve segments of pipes and resonators in the form of open and closed cavities. In 1922, a seminal paper by G. W. Stewart15 that discusses lumped acoustic elements for filter applications characterized these structures as simple oscillators. However, these elements were not used to form artificial media until 2006, when metamaterials composed of a waveguide loaded with an Box 1 | Metamaterials The term metamaterial is now broadly applied to engineered materials, usually composites, in which an internal structure is used to induce effective properties in the artificial material that are substantially different from those found in its components. The term originated from the field of electromagnetic materials, in which metamaterials were engineered to control light and radio wave propagation, and is used specifically to indicate materials composed of conducting structures that, by generating controlled electric and magnetic dipole responses to applied fields, result in a negative refractive index. This property is not found in any known natural material. The term metamaterial is not very precisely defined, but a good working definition is: a material with ‘on-demand’ effective properties, without the constraints imposed by what nature provides. For acoustic metamaterials, the goal is to create a structural building block that, when assembled into a larger sample, exhibits the desired values of the key effective parameters — the mass density and the bulk modulus — as discussed in BOX 2. The most common approach to constructing acoustic metamaterials is based on the use of structures whose interaction with acoustic waves is dominated by the internal behaviour of a single unit cell of a periodic structure, often referred to as a meta-atom. To make this internal meta-atom response dominant, the size of the meta-atom generally needs to be much smaller (about ten or more times smaller) than the smallest acoustic wavelength that is being manipulated. By contrast, in so-called phononic (for sound) or photonic (for light) crystals, unusual wave behaviour is created via the mutual interaction (multiple scattering) of unit cells whose dimensions are typically about half of the operating wavelength (although recent work has shown how local and multiple scattering responses can be combined in a single structure to achieve interesting effects, blurring the line between these different classes of artificial media). This subwavelength constraint ensures that the metamaterial behaves like a real material in the sense that the material response is not affected by the shape or boundaries of the sample. This equivalence will not hold for periodic materials in the phononic crystal regime, in which long-range interactions and spatial dispersion dominate the response. Instead, when the material response is determined by the local meta-atom response, effective bulk-material properties can be defined and estimated from simulations or measurements of very small samples. The fact that the effective parameters of a metamaterial composed of thousands or millions of meta-atoms can be determined using simple and efficient methods is one of the most powerful aspects of the metamaterial approach to artificial material design. R E V I E W S 2 | ADVANCE ONLINE PUBLICATION www.nature.com/natrevmats © 2016 Macmillan Publishers Limited. All rights reserved array of coupled Helmholtz resonators were constructed. Helmholtz resonators are closed cavities connected to a waveguide via a narrow channel (FIG. 1b). At their collective resonance frequency, a low-frequency stopband is formed, the origin of which can be traced back to the negative effective bulk modulus K — which occurs when a parcel of fluid compresses under dynamic stretching — of the loaded waveguide16. Altering the volume of the cavity results in a change in its resonance frequency. Thus, attaching a series of open side-branches to the waveguide produces resonators with very low resonance frequency, and sound waves are entirely reflected up to the frequency at which the sign of the bulk modulus changes17. Designing an entire panel of these open sidebranches creates a so-called ‘acoustic double fishnet’ structure that sustains this attenuation band for a wide range of frequencies and angles, and that can provide acoustic shielding to block environmental noise18,19. Insight into the nature of acoustic responses facilitates additional metamaterial design approaches. If a fluid segment accelerates out of phase with respect to the acoustic driving force, then a negative mass density is possible, as implied by equation (2) in BOX 2. This acoustic response can be created using membranes fixed at the rims of a tube or an array of holes20–22 (FIG. 1c). Furthermore, changing the size of the membranes or loading them with a mass makes it possible to alter the resonance over a spectrally extended range. If either the effective bulk modulus K or the mass density ρ are negative, then fully opaque materials with purely imaginary phase velocities are possible. However, in a similar manner to the coexistence of monopolar and dipolar bubble resonances, composing a structure of Helmholtz and membrane units for which ρ and K are simultaneously negative (FIG. 1d) creates a band in which energy can propagate instead of attenuate, as happens when only one of these parameters is negative. This energy propagates with a negative refractive index, which causes energy to flow in the direction opposite to that of the wave23. This counterintuitive effect forces an incident wave impinging on such a structure to refract in the opposite way compared to what happens with natural materials, enabling new ways of controlling sound waves. Several other metamaterial-based approaches for realizing unusual acoustic refraction have been demonstrated. By coiling up space with labyrinthine structures, the sound propagation phase is delayed such that band folding with negative dispersion (ρ < 0 and K < 0) is compressed towards the long-wavelength regime24–26. This approach has the advantage of creating negative refraction with a relatively simple metamaterial structure. Another strategy to obtain negative refraction relies on stacking several holey plates to form an aniso tropic structure with hyperbolic dispersion. Owing to the hyperbolic shape of the dispersion contours, refraction of sound can take place at negative angles for almost any direction of incident sound27,28. Finally, an interesting regime in which the effective mass density is close to zero has recently been explored and tested for advanced phase control and super-squeezing of sound waves in narrow channels29,30. Such media transmit sound waves with no distortion or phase change across the entire length of the material and enable new sound imaging and detection modalities. Most of the acoustic metamaterial designs described above make use of periodic structures. The same is true for the overwhelming majority of acoustic (and electromagnetic) metamaterials, primarily for ease of fabrication. But given that the concept of acoustic metamaterials is based on the local, internal mechanical response of the structure (BOX 2), there is no reason why metamaterials cannot be made from aperiodic architectures, provided the average number of inclusions per unit volume remains fairly uniform on the scale of a wavelength. This idea is beginning to be explored using metamaterials composed of a soft matrix containing an unstructured array of bubbles of a second material13,31,32. Implementing all of these different acoustic metamaterial designs requires techniques to compute the effective acoustic properties of a given structure. Such Box 2 | Acoustics principles and material parameters Acoustics is the science of vibrational wave propagation in fluids such as air or water, including the familiar audio frequency waves in air that we know as sound. For the purposes of controlling sound propagation with acoustic metamaterials, a key step is the identification of the material parameters that control wave propagation. Linear acoustics describes small pressure fluctuations that form a travelling wave of low intensity. One defining equation of acoustics comes from Newton’s second law (F = ma) and connects the acoustic particle perturbation velocity v to the acoustic pressure p as