Localizing Elastic Edge Waves via the Topological Rainbow Effect

Abstract

We combine two different fields, topological physics and graded metamaterials to design a topological metasurface to control and redirect elastic waves. We strategically design a two-dimensional crystalline perforated elastic plate, using a square lattice, that hosts symmetry-induced topological edge states. By concurrently allowing the elastic substrate to spatially vary in depth, we are able to convert the incident slow wave into a series of robust modes, with differing envelope modulations. This adiabatic transition localises the incoming energy into a concentrated region where it can then be damped or extracted. For larger transitions, different behaviour is observed; the incoming energy propagates along the interface before being partitioned into two disparate chiral beams. This "topological rainbow" effect leverages two main concepts, namely the quantum valley-Hall effect and the rainbow effect usually associated with electromagnetic metamaterials. The topological rainbow effect transcends specific physical systems, hence, the phenomena we describe can be transposed to other wave physics. Due to the directional tunability of the elastic energy by geometry our results have far-reaching implications for applications such as switches, filters and energy-harvesters.

Acoustic Topological Circuitry in Square and Rectangular Phononic Crystals

“…7). This differs from the square structure that possesses only a single unique interface, upon which both even-and oddparity modes reside [48][49][50][51][52]. The asymmetric edges in the rectangular case result in two sets of edge states that do not have a complete frequency overlap (Fig.…”

“…2(a) and 3(a). We chose these structures over their hexagonal lattice counterparts due to their inherent ability to localize energy in unique ways [48][49][50][51][52]; the benefits of this will become more evident in Sec. IV.…”

“…5. The locally quadratic curves in the vicinity of the former Dirac cones carry nonzero Berry curvatures [48][49][50][51][52] that in turn lead to the generation of valley-Hall edge modes. Those regions on opposite sides of the mirror symmetry line (in Fourier space) carry Berry curvatures with opposite signum [48][49][50][51].…”

“…For hexagonal lattice systems, there are two distinct orderings of the media that in turn create two distinct interfaces [16,[19][20][21][22][23][24][25], one of which supports only the even modes and the other the odd modes. The square and rectangular models differ from this, as their interfaces support both the even and odd edge modes [48][49][50][51][52] [Figs. 7(c) and 7(d)].…”

“…Specific to our square and rectangular models is the tunable location of the Dirac cones that result in counterpropagating edge states that have a tunable separation in Fourier space; the size of this separation is directly related to the intervalley scattering and hence to the imperviousness of our edge states to shorter-range defects [63][64][65]. This tunability is an appealing property as it has been found to be useful for optimizing transmission along topological guides as well as for energy harvesters [48,52].…”