Dual-band selective rainbow trapping in two-dimensional gradient valley phononic crystals

The realization of topological rainbow trapping provides significant potential for applications in energy storage and recovery, signal sensing, and related fields. Most studies focus on the first bandgap of valley phononic crystals, which presents a challenge for developing multi-band topological acoustic devices. This study designs a three-legged circular rod valley phononic crystal, where spatial symmetry is broken through rotation to open two Dirac cones. It observes topological edge states within the ranges of the original two bandgaps by combining two valley phononic crystals with different topological phases. In addition, the magnitude of the group velocity is calculated in the supercells at different rod lengths, revealing points with a group velocity of zero at different frequencies, thus realizing rainbow trapping in dual bandgaps. The findings indicated that within bandgap 1, the acoustic waves can only propagate along the waveguide from left to right. The acoustic waves are sequentially trapped at different locations as the frequency increases. In the range of bandgap 2, the acoustic waves can only propagate along the waveguide from right to left. As the frequency decreases, the acoustic waves are trapped at different locations. The designed three-legged circular rod valley phononic crystal facilitates the unidirectional propagation of acoustic waves at specific frequencies, making it suitable for applications in acoustic diodes. The realization of dual-band topological rainbow trapping provides potential application value for energy recovery, signal sensors, and other technological applications.