Stopping and reversing sound via dynamic dispersion tuning in a phononic metamaterial

Slowing down, stopping, and reversing a signal is a core functionality for information processing. Here, we show that this functionality can be realized by tuning the dispersion of a periodic system through a dispersionless, or flat, band. Specifically, we propose a phononic metamaterial based on plate resonators, in which the phonon band dispersion can be modified from an acoustic-like to an optical character by modulating a uniform prestress. The switch is enabled by the change in sign of an effective coupling between fundamental modes, which generically leads to a nearly dispersion-free band at the transition point. We demonstrate how adiabatic tuning of the band dispersion can immobilize and reverse the propagation of a sound pulse in simulations of a one-dimensional resonator chain. Our study relies on the basic principles of thin-plate elasticity independently of any specific material, making our results applicable across varied length scales and experimental platforms. More broadly, our approach could be metamaterials and electronic heterostructures.