Generalized momentum conservation and Fedorov-Imbert linear shift of acoustic vortex beams at a metasurface

We study the transmission and reflection of a paraxial acoustic vortex beam (AVB) at a metasurface with a prescribed phase gradient. By using a plane-wave decomposition method, we obtain a closed-form expression for the transverse shift of the beam's gravity center. The transverse shift is proportional to the topological charge of the AVB and derives from momentum conservation and the reflection/transmission coefficient modulation. It corresponds to the acoustic Fedorov-Imbert linear shift and represents the orbital Hall effect for spinless longitudinal sound. We develop a generalized momentum conservation relation to understand the phenomena and find that the metasurface induces both linear momentum and angular momentum, which have different dependences on the incident angle. In particular, this mechanism can enable the Fedorov-Imbert linear shift even for normal incidence and total reflection. The results provide deeper insights into the physics underlying the interaction of AVBs with metasurfaces and may help the development of orbital angular momentum based acoustic devices.