Acoustic Willis meta-atom beyond the bounds of passivity and reciprocity

Willis metamaterial enables exotic manipulations of acoustic waves with a precise combination of bulk modulus, mass density, and Willis parameters. While the realization of unrestricted and completely decoupled constitutive parameters would extend the horizon of future applications, the restriction of passivity and reciprocity dictate a hard bound in the values of achievable polarizabilities and correlations between them. Here, we break the bound of passivity and reciprocity by instituting a basis and independent kernel for each constitutive polarization in a virtualized metamaterial platform, active metamaterials realizing artificial polarization with the digital convolution. We demonstrate decoupled control of all four constitutive parameters in a nonreciprocal regime, at the same time achieving values of polarizabilities beyond the passivity limit. Broadband, flat-response nonreciprocal Willis coupling is also demonstrated with analytically designed causal frequency dispersion. Our approach will be useful for nonreciprocal wave manipulation and communication for broadband operation. Metamaterials are designed to control unconventional wave properties in acoustic systems with a range of applications such as acoustic cloaking. Here, the authors design an active acoustic Willis metamaterial that can realize decoupled polarizabilities beyond the bound of passivity and reciprocity.