Visualization of rainbow trapping effect in higher-order topological insulators

The rainbow trapping effect, which enables field amplification of multiple wavelengths in topological insulators, offers unprecedented opportunities for integrated ultrasonic sensors and energy harvesting. However, until now, the realization of the rainbow trapping effect has been limited to a one-dimensional (1D) or 2D interface in the electromagnetic and acoustic systems. Here, we propose a method to realize rainbow trapping based on higher-order topological corner modes (HOTCMs), where the elastic wave is localized at 0D corners rather than at the interface. We strategically design the two-dimensional elastic locally resonant metamaterial plate and construct multiple HOTCMs at the interfacial corners formed by trivial and nontrivial domains. We further investigate the interplay between nearest-neighbor couplings and next-nearest-neighbor couplings. Remarkably, the HOTCMs localized at corners with different geometric configurations are shown to be frequency dependent, providing a platform for trapping elastic waves at different corners. Moreover, we demonstrate rainbow trapping based on the HOTCMs at the corners and show the agreement between the experimental results and theoretical modeling. Our results provide a mechanism to realize the trapping of multiple frequencies and extend the use of elastic integrated devices toward higher order topological insulators.