Controllable nonlocality of acoustic meta-surfaces based on Willis coupling

Significant nonlocality is the principal mechanism enabling superior and versatile functionalities of non-local meta-surfaces with efficiency that goes far beyond conventional designs. Distinct from the design strategy of minimizing the non-local coupling effects in acoustic phase-gradient meta-surfaces, nonlocality has been explored to achieve anomalous wave manipulations with extremely high efficiency. However, the controllable exploitation of non-local coupling effects to intentionally tailor acoustic behavior remains a challenge. Therefore, we proposed a theoretical model for predicting the acoustic performance of finite meta-surfaces using Willis coupling as an additional degree of freedom, in which a coupling index βn is derived to explicitly characterize and leverage the non-local coupling effects. Numerical calculations performed on a random three-meta-atom array confirmed the accuracy of our model and demonstrated the dominant influence of non-local coupling effects on both the scattering strength and directivity of the constituent meta-atoms. Furthermore, the controllability of non-local coupling effects via the derived βn was demonstrated in two sound-isolation meta-surfaces, where the acoustic responses of all meta-atoms were modulated and synchronized, achieving a significant enhancement in transmission loss. This work novelly elevates non-local coupling effects from an inherent phenomenon to a controllable parameter based on Willis coupling for the practical design of high-efficiency non-local meta-surfaces.