Nonreciprocal controllable Willis longitudinal metasurface

The reciprocity of wave systems refers to the principle that identical responses are obtained for any wave propagation path along forward and backward directions. Recently, there has been a significant breakthrough in breaking reciprocity with specially designed artificial elastic material, Willis metamaterial. From its unique coupling between momentum and stress, Willis metamaterial could provide various non-reciprocal behaviors. Here, we aim to achieve Willis metamaterial with non-reciprocity by using the idea of active metamaterials. The main advantage of the proposed method is extremely high tunability – since it is based on the active metamaterial, any desired parameters of Willis coupling can be easily realized. Theory of artificial springs will be introduced in the presentation to define the Willis parameters with active metamaterials. Also, various numerical examples will be presented.