  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.
