Extreme effective material parameters enabled by non-local Willis coupling

While traditional acoustic metamaterial designs based on monopolar and dipolar resonance realize effective densities and bulk moduli that go beyond the those of natural materials, their reliance on local resonance ultimately limits their ability to access extreme effective parameter values. Here, we use an active metamaterial with non-local Willis coupling to drastically extend the accessible range of the effective density and bulk modulus by at least two orders of magnitude compared to a non-Willis metamaterial that relies on local resonance. Our design introduces Willis coupling with two sensor-transducer pairs on both sides of the metamaterial that detects incident waves and superimposes an asymmetric active acoustic signal on an otherwise passive unit cell. The asymmetry of the active signal results from feedback control circuits with unequal gains and/or phases. In our setup, an asymmetric feedback control circuit induces the non-local Willis coupling that potentially increases the effective length of wave propagation and extends the range of effective density and bulk modulus of the metamaterial. Active metamaterials with extreme effective material parameters via non-local Willis coupling will enable improved control over acoustic propagation and yield valuable advancements in biomedical imaging, noise control, and invisibility cloaking technology.