Global phase metasurfaces for sound bending splitter

Recently, by tailoring the local phase, the emergence of acoustic metasurfaces such as gradient-index metasurfaces (GIMs) shows an exotic way of redirecting sound waves. With a lot of effects taken on modulation of local phase, however, the global phase is rarely discussed. Distinguished from the local phase by metasurface's components (meta-units), the global phase is the collective phase response of a whole metasurface. Here, we exploit the global phase of GIMs. We demonstrate that a reflective-type lossless GIM exhibits angularly symmetric behavior in both directivity and efficiency, yet intrinsically supports asymmetry in global phase. Consequently, a GIM engenders equal-strength redirecting waves in angular-symmetry directions under opposite incidences, while encoding distinct phases globally. We exploit the parameters determining the global phases of a GIM, showing these parameters enable complete, independent, and arbitrary tuning of the phase under opposite incidences. We further demonstrate that, by tailoring the global phase, a metasurface made by a junction of two opposite GIMs can function as a bending splitter that combines the advantages of beam-redirecting and beam-splitting metasurfaces, enabling the bisecting line of those split beams to be arbitrarily tuned. Our findings may enrich the study of metasurfaces and provide a hidden degree of freedom on wave field manipulation.