Negative refraction and exceptional point with Parity-Time symmetry in a piezoelectric mechanical metamaterial

Abstract

In this work, negative refraction and exceptional point (EP) in piezoelectric mechanical metamaterials are considered, which corporates with the Parity–Time (PT) symmetry. The oblique incidence of anti–plane shear wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes. In periodic layers, propagation characteristics are illustrated by the dispersion relation and transfer matrix method. The normal mode decomposition is developed and time average Poynting vector is used to derive the refraction angle at the interface of piezoelectric metamaterials. The beam splitting is shown with different incident angles, as well as the pure negative refraction is achieved. Due to the mechanical and electric coupling, the complex conjugate of Bloch wave number appears in the dispersion relation and degenerates to the exceptional point. In addition, a defect layer is introduced to study the transmission coefficient of two phononic crystals with different arrangements. When the gain and loss are introduced into the metamaterials, the Parity–Time symmetry system is realized and a complete transmission with a unidirectional zero reflection at exceptional point can be achieved.