- Letter
Dipolar Localization of Waves in Twisted Phononic Crystal Plates
Phys. Rev. Applied 15, L011001 – Published 11 January, 2021
DOI: https://doi.org/10.1103/PhysRevApplied.15.L011001
Abstract
The localization of waves in two-dimensional (2D) clusters of scatterers arranged in relatively twisted lattices is studied by multiple scattering theory. It is found that, for a given frequency, it is always possible to find localized modes for a discrete set of rotation angles, analogous to the so-called “magic angles” recently found in 2D materials such as graphene. Similarly, for small rotations of the lattices, a large number of resonant frequencies is found, the position of which depends strongly on the rotation angle. Moreover, for angles close to those that make the two lattices commensurable, a single mode appears that can be easily tuned by the rotation angle. Unlike other twisted materials, where the properties of the bilayers are mainly explained in terms of the dispersion relation of the individual lattices, the specific angles in these clusters happen because of the formation of dipolar scatterers due to the relative rotation between the two lattices, therefore enhancing their interaction. While the presented results are valid for any type of wave, the specific case of flexural waves in thin elastic plates is numerically studied and the different modes found are comprehensively explained in terms of the interaction between pairs of scatterers. The analysis presented here shows that these structures are promising candidates for the inverse design of tunable wave-trapping devices for classical waves.
