Dual-band rainbow trapping in higher-order topological insulators

The higher-order topological rainbow trapping effect enables the separation, slowing down, and capture of waves at distinct frequencies, holding significant potential for applications in integrated ultrasonic sensing and energy harvesting technologies. At present, most rainbow trapping schemes predominantly operate within a single frequency range, which restricts the multi-frequency selectivity of corner states and hinders the design of topological acoustic devices. This work proposes a unit cell structure with C3 symmetry, which activates distinct valley-selective corner states by rotating the scatterer angle, thereby achieving higher-order topological states across multi-frequency bands, which can localize the acoustic waves at the zero-dimensional corner and immediate vicinity, rather than at interfaces. Research has revealed that the corner states localized at corners with different geometric configurations are found to be frequency dependent, which offers a viable pathway toward realizing dual-band rainbow trapping. This work demonstrates, through the design of an arrowhead-shaped structure with multiple corner configurations, that locking the corner order (i.e., clockwise or counterclockwise direction) in polygons enables selective excitation of corner states. Furthermore, the introduction of defects confirms their excellent defect-immune robustness. The higher-order topological corner states achieved in this work provide a novel mechanism for multi-band/multi-frequency energy harvesting and signal sensing technologies, while extending the applications of sound-wave-based integrated devices to the realm of higher-order topological insulators.