Localising elastic edge waves via the topological rainbow effect

The work combines topological physics with graded metamaterials to create a topological metasurface that steers elastic waves in a perforated elastic plate. The plate is a two-dimensional crystalline structure (square lattice with bore holes) engineered to host symmetry-induced topological edge states. By also varying the elastic substrate depth across space, the authors convert an incoming slow wave into robust modes with different envelope modulations. For larger geometric transitions, the incoming energy behaves differently: it propagates along the interface and is partitioned into two chiral beams. The authors describe this as a “topological rainbow” effect that draws on the valley-Hall concept and an analogy to the rainbow effect in electromagnetic metamaterials. They suggest the directional tunability provided by geometry could support applications such as switches, filters, and energy-harvesters.