Topological rainbow trapping of elastic waves in two-dimensional valley phononic crystal plates

Rainbow trapping is a significant strategy for capturing waves of different frequencies at different spatial positions. It offers significant potential for multi-frequency on-chip nanophotonic devices in the era of big data and has attracted much interest recently, and topological rainbow trapping that is immune to disorder has been observed in optics and acoustics. Reported here is the topological rainbow trapping of elastic waves using gradient valley phononic crystal plates (PCPs) with a hexagonal lattice, based on valley edge states that are localized at the boundary between two PCPs with opposite valley topological phases. The gradient valley PCPs are achieved by gradually adjusting the height of the scatterers or the thickness of the PCPs. The topological rainbow trapping of elastic waves is shown by applying vertical vibration to the studied gradient PCPs, which are simple in structure and easily fabricated, providing a good solution for manipulating and trapping elastic waves.