Coupled mode theory for acoustic vortex generation and manipulation via phase gradient metasurfaces

Metasurfaces offer a promising platform for controlling acoustic orbital angular momentum (OAM); yet, existing research studies are primarily limited to the qualitative prediction of the vortex diffraction laws, lacking systematic theoretical guidance. In this work, we propose an analytical framework for acoustic metasurfaces based on coupled mode theory (CMT), providing a comprehensive exploration of phase gradient metasurfaces and acoustic OAM. Theoretical calculations demonstrate these phenomena, such as vortex generation and parity-dependent OAM diffraction, with results showing excellent agreement with numerical simulations under both lossless and lossy conditions. Moreover, by applying the genetic algorithm to optimize within the CMT framework, we significantly enhance the efficiency of OAM generation and enable the realization of customized vortex modes. This study provides a solid theoretical framework for exploring the plentiful interactions between acoustic metasurfaces and OAM, and developing OAM-based functional acoustic devices.