Homogenization and design of acoustic Willis metasurfaces

Metasurfaces are ultrathin planar arrays of carefully tailored subwavelength particles that enable agile and flexible manipulation of the impinging waves. Originally introduced in optics, their application to acoustic waves has recently opened exciting opportunities for exotic sound control. In conventional acoustic inclusions, the interactions with the impinging pressure and velocity are decoupled, limiting the functionalities that arrays of them can achieve. While the coupling between these two quantities in symmetry-breaking inclusions, known as Willis coupling, has been discussed for several years, only recently has it been realized that these phenomena can become nonperturbative in suitably tailored resonant scatterers. Here, we explore the opportunities that these Willis meta-atoms open in the context of acoustic metasurfaces, offering additional knobs to manipulate and tailor sound. The general response of Willis metasurface is analytically derived, yielding fundamental bounds and optimal surface responses enabling full control of the impinging acoustic wave front.