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.

威利斯超材料可以利用体积模量，质量密度和威利斯参数的精确组合实现对声波的奇特操纵。尽管无限制且完全解耦的本构参数的实现将扩展未来应用的范围，但无源性和互易性的限制在可实现的极化率和它们之间的相关性值上规定了一个硬性界限。在这里，我们通过为虚拟超材料平台中的每个本构极化建立基础和独立内核，打破主动性和互惠性的界限，有源超材料通过数字卷积实现人工极化。我们展示了在不可逆状态下对所有四个本构参数的解耦控制，同时获得超过无源极限的极化率值。还通过分析设计的因果频率色散展示了宽带，平坦响应，不可逆的威利斯耦合。我们的方法对于宽带通信的不可逆波操纵和通信将很有用。