Field depletion using complementary Willis coupling

Complementary media, which employ paired structures with contrasting effective parameters such as compressibility and density in acoustics, have been widely explored as an effective approach to restore wave transmission in disrupted fields. In this study, we introduce complementary Willis couplings between two-layer media that share identical effective compressibility and density. This configuration achieves acoustic field depletion (active local absorption without scattering), mimicking a shadow zone with significant attenuation while maintaining unit transmittance throughout the medium. We formulate the condition for the material parameters of the two layers to achieve such acoustic field depletion in both the reciprocal and nonreciprocal regimes. Furthermore, we experimentally demonstrate field depletion with purely nonreciprocal complementary Willis coupling facilitated by digitally virtualized active meta-atoms. Our results demonstrate that both pressure and velocity fields are minimized at the midpoint of the device but with full transmission. Unlike conventional active acoustic systems, our active material approach allows self-adaptivity to different incident waves, opening up potential applications, such as directional sensing, nonreciprocal communication, and tailored field manipulation.