Roton-like dispersion via polarisation change for elastic wave energy control in graded delay-lines

TL;DR

This paper demonstrates that roton-like dispersion relations can be achieved in elastic systems through mode locking, without relying on beyond-nearest-neighbor interactions, enabling novel elastic wave control.

Contribution

It introduces a new method to realize roton dispersion in elastic media using mode locking, bypassing the need for complex interactions.

Findings

Roton dispersion achieved without beyond-nearest-neighbor interactions.

Mode locking enables control of elastic wave dispersion.

Spatial separation of energy fluxes with positive and negative group velocity.

Abstract

While roton dispersion relations had been restricted to correlated quantum systems at low temperature, recent works show the possibility of obtaining this unusual dispersion in acoustic and elastic metamaterials. Such phenomenon has been demonstrated in periodic structures by means of beyond-nearest-neighbor interactions, following the formulation firstly developed by Brillouin in the $'50s$. In this paper, we demonstrate both numerically and experimentally that beyond-nearest-neighbor connections are not a necessary condition to obtain this unusual dispersion relation in elasticity. Leveraging the intrinsic complexity of elastic systems supporting different types of waves, we demonstrate that mode locking can be applied to obtain roton dispersion, without the need of elastic or magnetic interactions between non nearest neighbors. Moreover, the combination of roton dispersion and rainbow physics enables spatial separation of the energy fluxes with positive and negative group velocity.