Scattering of waves by three-dimensional obstacles in elastic metamaterials with zero index

Abstract

The scattering of elastic waves by three-dimensional obstacles in isotropic elastic zero-index-metamaterials (ZIM) is theoretically investigated. We show that the zero values of each single effective parameter and their various combinations of the elastic ZIM can produce different types of wave propagation. Particularly, there is no mode conversion when either longitudinal ($P$) wave or transverse ($S$) wave is scattered by the obstacles in a specific type of double-ZIM (DZIM), possessing near zero reciprocal of shear modulus and near zero mass density. When the obstacle is off resonance, elastic waves are scarcely scattered; nevertheless, the scattering cross section of the obstacle can be drastically enhanced by orders of magnitude when it is on resonance. While in another type of DZIM possessing near zero reciprocal of bulk modulus and near zero mass density, mode conversion occurs during the scattering process and many other transmission characteristics are also different to the former. Moreover, enhanced transmission can be realized for various types of single-ZIM (SZIM) by introducing obstacles, and numerical analysis shows that the enhanced transmission is due to resonant modes arisen in the embedded obstacles. We expect that our findings could have potential practical application, such as seismic protection and on-chip phononic devices.