Acoustic Willis metamaterials beyond the passivity bound

TL;DR

This paper introduces a novel class of acoustic Willis metamaterials that surpass the passivity bound, enabling independent control of constitutive parameters and nonreciprocal wave manipulation through digital inverse design.

Contribution

It develops a virtualized metamaterial framework to break passivity and reciprocity limits, achieving programmable, broadband, and nonreciprocal acoustic responses.

Findings

Experimental demonstration of bianisotropy beyond passive media limits.

Achievement of broadband, flat-response Willis coupling.

Realization of purely nonreciprocal acoustic media.

Abstract

Acoustic bianisotropy, also known as the Willis parameter, expands the field of acoustics by providing nonconventional couplings between momentum and strain in constitutive relations. Sharing the common ground with electromagnetics, the realization of acoustic bianisotropy enables the exotic manipulation of acoustic waves in cooperation with a properly designed inverse bulk modulus and mass density. While the control of entire constitutive parameters substantiates intriguing theoretical and practical applications, a Willis metamaterial that enables independently and precisely designed polarizabilities has yet to be developed to overcome the present restrictions of the maximum Willis bound and the nonreciprocity inherent to the passivity of metamaterials. Here, by extending the recently developed concept of virtualized metamaterials, we propose acoustic Willis metamaterials that break the passivity and reciprocity limit while also achieving decoupled control of all constitutive parameters with designed frequency responses. By instituting basis convolution kernels based on parity symmetry for each polarization response, we experimentally demonstrate bianisotropy beyond the limit of passive media. Furthermore, based on the notion of inverse design of the frequency dispersion by means of digital convolution, purely nonreciprocal media and media with a broadband, flat-response Willis coupling are also demonstrated. Our approach offers all possible independently programmable extreme constitutive parameters and frequency dispersion tunability accessible within the causality condition and provides a flexible platform for realizing the full capabilities of acoustic metamaterials.