Digitally coded bianisotropic metasurface for direction-dependent elastic wave control

Abstract

Willis metamaterials are periodic structures with engineered asymmetries that exhibit Willis coupling, a non-classical constitutive behavior linking stress to velocity and momentum to strain. This coupling gives rise to bianisotropy, a property enabling directional dependence of the reflected wave characteristics, which allows for asymmetric wave control and expanded design flexibility toward compact and tunable systems. In this work, we design, fabricate, and experimentally validate a viscoelastic metasurface that exhibits bianisotropic behavior resulting in direction-dependent wavefront shaping. The metasurface achieves arbitrary wave tailoring in the reflected field for waves incident in a particular direction. This bianisotropic behavior is demonstrated through a dual-focus metasurface, which focuses energy in the transmitted field independent of direction of incidence, and in the reflected field only for incidence in a particular direction. To effectively reduce the size of the large design parameter space, we introduce a digital coding-based design strategy for the bianisotropic metasurface. A 2-bit digitally coded version of the metasurface, utilizing only four discrete unit cell states, is shown to achieve focusing performance comparable to that of a conventional gradient metasurface. Experimental validation confirms strong qualitative agreement with numerical simulations. The proposed digitally coded metasurface architecture offers a promising platform for broadband, directionally selective wavefront control, with potential applications in energy harvesting, signal processing, and beyond.