Phononic crystals and acoustic metamaterials

Phononic crystals and acoustic metamaterials were introduced around three decades ago, and have been attracting growing interest ever since. These terms refer to two classes of synthetic materials, most often artificially structured, with exceptional acoustic properties, unmatched by natural inorganic materials in their bulk state. The phononic crystal concept was proposed in the early 1990s as an acoustic counterpart to the photonic crystals introduced a few years earlier for electromagnetic waves. It is based on the key notion of bandgap, analogous to that of electronics, designating a frequency band in which wave propagation is opposed, whatever the direction of the incident wave vector. Here, the band gap is induced by an artificial two- or three-dimensional periodic grating featuring a unit cell of dimension commensurable with the acoustic wavelength. While the presence of a bandgap in phononic crystals opens up new applications for frequency filtering, it is also possible to use other unusual properties of these structures associated with bandwidths. More generally, this opens the way to the concept of dispersion engineering, which seeks to exploit in a more comprehensive way the possibility of artificially structuring materials to control their properties. Work in this field has led to the emergence of acoustic and elastic metamaterials. The special properties of these artificial materials can be conferred by the existence of local variations in their acoustic properties, or by the use of constituent elements with acoustic or elastic resonances, known as local resonances, at frequencies such that the effective wavelength in the surrounding medium is large compared to the dimensions of these elements. These resonances, which are often quite narrow, are independent of the periodicity of the network. In some contexts, these metamaterials can therefore have characteristic dimensions well below the wavelength. In such cases, they are usually considered as homogeneous propagation media and treated as equivalent media, generally anisotropic, with original physical and mechanical characteristics. In particular, the exploitation of local resonances in metamaterials enables us to act directly on the notion of effective mass, which conditions properties as fundamental as the Young's modulus of the equivalent material.

The physics involved in these phononic crystals and acoustic metamaterials transcend scales. Acoustic or elastic waves are mechanical vibrations propagating from near to near, and can be observed on the macroscopic scale of earthquakes as well as on the nanoscopic scale of atomic vibration in a solid, spanning the entire intermediate spectrum. The immediate corollary of this observation is that the potential scientific and technological impact of these artificial materials ranges...