“…Due to the existence of BGs and defect states, PCs have many potential applications, which can be widely used in acoustic waveguides, portable devices, wireless sensors, and other devices (Jin et al, 2015; Li and Assouar, 2016; Sun et al, 2022; Taleb and Darbari, 2019). PCs waveguides can transmit sound energy or signals within a specific frequency range, which will be limited to a specified path (Ash et al, 2017; Han and Zhang, 2020; Liu et al, 2020; Piliposyan, 2018). In general, the waveguide is achieved by introducing defects into PCs to obtain propagation mode and changing the geometric parameters or material composition of PCs.…”