Dimensional hierarchy of acoustic topological rainbow trapping in two-dimensional phononic crystals

Rainbow trapping is an important strategy to capture waves of different frequencies at different spatial locations. Combining the topological properties of the phononic crystal (PC), topological rainbow trapping offers a novel way to manipulate the robust transport of acoustic waves. In this paper, a two-dimensional (2D) gradient PC with square lattice is designed to achieve the acoustic topological rainbow trapping of edge and corner states with dimensional hierarchy. Based on the spatial symmetry of the unit cell with different inversion center, the topological phases of the square PCs are investigated. By constructing a sandwiched structure using the two PCs with different topological phase, the coupled one-dimensional (1D) topological edge states and zero-dimensional (0D) corner are obtained. Furthermore, based on a gradient change of the structure parameters along the coupled topological route, the acoustic rainbow trapping phenomena of the edge and corner states are achieved. Finally, we also demonstrate that the width of acoustic field for edge rainbow trapping can be broadened by increasing the coupling layers of PC, and the robustness of the corner states against the defect and disorder are also validated. The proposed structure is simple and easy to manufacture, providing a new route for manipulating and capturing multi-dimensional acoustic signals.