In-plane elastic waves in piezoelectric metamaterials with Parity-Time symmetry

The propagation of in-plane waves in piezoelectric metamaterials involves the coupling of longitudinal (i.e. quasi-pressure), transverse (i.e. quasi-shear) and electric potential waves, which can result in different exotic phenomena. In this study, the stiffness matrix method is used to analyze the dispersion relation, which contains anomalous propagation characteristics. With the coupling of electric potential, the frequency spectrum of in-plane wave shows new characteristics. The exceptional point caused by non-Hermitian operator that does not exist before also appears when the vertical wave number is imaginary. The oblique incidence of the in-plane wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes which include the negative refraction. The normal mode decomposition is developed to study the in-plane incidence of piezoelectric metamaterial and then the averaged Poynting vector is applied to obtain the refraction angle. Moreover, the defect layer is introduced into the phononic crystals to study the transmission coefficients with two different symmetrical arrangements. When the balanced gain and loss are considered in the metamaterial, the Parity-Time symmetry appears and brings in pairs of exceptional points to achieve complete transmission with unidirectional zero reflection.