Metamaterial-enabled asymmetric negative refraction of GHz mechanical waves

Known examples of negative refraction in metamaterials do not distinguish between positive and negative angles of incidence. Here, the authors show that it is possible to break this symmetry using an asymmetric unit cell, and demonstrate it using a mechanical metamaterial working at GHz frequencies. Wave refraction at an interface between different materials is a basic yet fundamental phenomenon, transversal to several scientific realms - electromagnetism, gas and fluid acoustics, solid mechanics, and possibly also matter waves. Under specific circumstances, mostly enabled by structuration below the wavelength scale, i.e., through the metamaterial approach, waves undergo negative refraction, eventually enabling superlensing and transformation optics. However, presently known negative refraction systems are symmetric, in that they cannot distinguish between positive and negative angles of incidence. Exploiting a metamaterial with an asymmetric unit cell, we demonstrate that the aforementioned symmetry can be broken, ultimately relying on the specific shape of the Bloch mode isofrequency curves. Our study specialized upon a mechanical metamaterial operating at GHz frequency, which is by itself a building block for advanced technologies such as chip-scale hybrid optomechanical and electromechanical devices. However, the phenomenon is based on general wave theory concepts, and it applies to any frequency and time scale for any kind of linear waves, provided that a suitable shaping of the isofrequency contours is implemented.