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.

中文翻译：

---

具有宇称-时间对称性的压电超材料中的面内弹性波

压电超材料中面内波的传播涉及纵向波（即准压力）、横向波（即准剪切）和电势波的耦合，这可能会导致不同的奇异现象。在本研究中，采用刚度矩阵方法来分析包含反常传播特性的色散关系。由于电势的耦合，面内波的频谱呈现出新的特征。当垂直波数为虚数时，以前不存在的非厄米算子引起的异常点也会出现。面内波在均匀介质和声子晶体之间的界面处的倾斜入射可以激发包括负折射在内的多种折射模式。法向模式分解被用来研究压电超材料的面内入射，然后应用平均坡印廷矢量来获得折射角。此外，将缺陷层引入声子晶体中，研究两种不同对称排列的传输系数。当超材料中考虑平衡增益和损耗时，宇称-时间对称性出现并带来成对的异常点，以实现单向零反射的完全传输。