Willis metamaterial on a structured beam

TL;DR

This paper reports the experimental realization of a Willis metamaterial for flexural waves in beams, demonstrating asymmetric reflection and control over wave propagation using loss and non-Hermitian effects.

Contribution

It introduces the first experimental Willis metamaterial for elastic flexural waves, extending wave propagation theory to include Willis coupling in beams.

Findings

Demonstrated asymmetric reflection due to Willis coupling

Controlled asymmetric amplitudes using loss to approach exceptional points

Achieved unidirectional zero reflection in a non-Hermitian system

Abstract

Bianisotropy is common in electromagnetics whenever a cross-coupling between electric and magnetic responses exists. However, the analogous concept for elastic waves in solids, termed as Willis coupling, is more challenging to observe. It requires coupling between stress and velocity or momentum and strain fields, which is difficult to induce in non-negligible levels, even when using metamaterial structures. Here, we report the experimental realization of a Willis metamaterial for flexural waves. Based on a cantilever bending resonance, we demonstrate asymmetric reflection amplitudes and phases due to Willis coupling. We also show that, by introducing loss in the metamaterial, the asymmetric amplitudes can be controlled and can be used to approach an exceptional point of the non-Hermitian system, at which unidirectional zero reflection occurs. The present work extends conventional propagation theory in plates and beams to include Willis coupling, and provides new avenues to tailor flexural waves using artificial structures.