Y. Chen, K. Wang, M. Kadic, S. Guenneau, C. Wang, and M. Wegener

Commun. Phys. 6, 75 (2023)

Abstract:

Previous theory and experiment has shown that introducing strong (nonlocal) beyond-nearest-neighbor interactions in addition to (local) nearest-neighbor interactions into rationally designed periodic lattices called metamaterials can lead to unusual wave dispersion relations of the lowest band. For roton-like dispersions, this especially includes the possibility of multiple solutions for the wavenumber at a given frequency. Here, we study the one-dimensional frequency-dependent acoustical phonon transmission of a slab of such nonlocal metamaterial in a local surrounding. In addition to the usual Fabry-Perot resonances, we find a series of bound states in the continuum. In their vicinity, sharp Fano-type transmission resonances occur, with sharp zero-transmission minima next to sharp transmission maxima. Our theoretical discussion starts with a discrete mass-and-spring model. We compare these results with solutions of a generalized wave equation for heterogeneous nonlocal effective media. We validate our findings by numerical calculations on three-dimensional metamaterial microstructures for one-dimensional acoustical wave propagation.