Acoustic metamaterials and phononic crystals: Towards the total control of the wave propagation

Classical waves, including elastic waves (acoustic waves) and electromagnetic waves (optical waves and microwaves), are described by conventional wave-propagation functions. Elastic waves were the first waveforms to be understood in condensed matter and have a wide range of applications from industry to defense, from healthcare to entertainment. In 1987, the photonic crystal was proposed to describe the propagation of optical waves in refraction index-modulated periodic structures analogous to the propagation of electrons in real crystals. This situation recalls the classical work by Brillouin. Brillouin considered elastic waves in periodic strings, electromagnetic waves in electrical circuits, and electrons in crystals as a system, resulting in some important common concepts, such as the Brillouin zone, band gap, etc., which are generally shared by the various forms of waves: electrons as scalar waves, optical waves as vector waves, and elastic waves as tensor waves. Following on from photonic crystals, the concept of phononic crystals was conceived with elastic waves propagating in periodic structures modulated with periodic elastic moduli and mass densities. These artificially structured materials possess a number of important properties, such as band gaps, band edge states⁷, and the ability to slow the velocity of sound (slow wave effect). Furthermore, by creating artificially designed structures on a deep subwavelength scale, artificial acoustic `atoms´ can be purposely engineered into acoustic metamaterials to dramatically change the excitation and propagation of acoustic waves, and thus give rise to subdiffraction-limited resolution and its related myriad novel effects, such as negative, negative elastic modulus, and negative mass density. Finally, Acoustic metamaterials and phononicc crystal are a newly emerging field, which have inherently abnormal and interesting physical effects that are important to basic research, and offer potential for ap- lications in everyday life that might revolutionize acoustic materials.