Topological rainbow trapping of dual-band valley-locked acoustic waves

The presence of valley-locked waveguides in topological insulators offers innovative possibilities for the modulation of wave propagation, addressing challenges associated with waveguides with limited transmission pathways and the loss of acoustic energy during transmission. In this research, we consider a two-dimensional gradient sonic crystal characterized by a hexagonal lattice structure, which is engineered to achieve acoustic topological rainbow trapping via dual-band valley-locked waveguide mechanisms. By conducting a detailed analysis of unit cells, we investigate the topological phase transitions occurring in the hexagonal lattice. In addition, by utilizing the gradient variation of structural parameters along the topological path, rainbow trapping phenomena can be achieved in dual-band heterostructures featuring valley degrees of freedom. Ultimately, we confirmed that acoustic waves are capable of experiencing lossless transmission within defective or intricate waveguide configurations. This research introduces an innovative design framework for the advancement of dual-band heterostructure acoustic topological rainbow trapping technologies.