Tuning rainbow trapping in higher-order topological insulators

Rainbow trapping has garnered significant attention due to its ability to separate, slow, and trap waves of different frequencies at different positions. However, most rainbow devices are limited to operating within a specific frequency band, as the structure of the unit cell and the lattice constant cannot be adjusted after the device is fabricated. In this work, we explore the relationship between higher-order topological corner modes (HOTCMs) and the geometric structures of the corners, using topological phononic crystals as a platform. We also propose a method for frequency-tunable rainbow trapping in higher-order topological insulators (HOTIs). The HOTIs are constructed by varying the heights of the mediums within the crystals, and the frequency tunability of the topological rainbow is achieved by introducing an out-of-plane tunable structural parameter, i.e. the channel height. Numerical simulations show that HOTCMs are strongly dependent on the configurations of corners and HOTCMs can appear sequentially in a particular order. Furthermore, the operating frequency of rainbow trapping increases as the channel height is increased within a certain range. This work offers a possibility for tuning rainbow trapping.