Sculpturing sound fields with the real-space structural topology of acoustic cavities

Artificial structures have been widely employed to manipulate sound fields to realize intriguing acoustic phenomena and functionalities. The development of this field requires a thorough understanding of how sound fields depend on the various properties of artificial structures. Although the effects of the material and geometry of artificial structures are known well, the effects of the real-space structural topology on sound field properties remain unclear. To tackle this problem, we present a detailed study of the sound fields inside acoustic cavities with different Euler characteristics and demonstrate that the real-space topology can give rise to topological configurations of the velocity and pressure fields. Specifically, we find that the acoustic cavities can induce topological singularities in the velocity polarization and isopressure line fields. The total topological index of the surface singularities is always equal to the cavities’ Euler characteristic. The mechanism is rooted in the Poincaré-Hopf theorem and is irrelevant to the specific material, geometric details, or excitations. The isopressure line singularities lead to acoustic hotspots and quiet zones. The velocity polarization singularities give rise to nontrivial polarization Möbius strips and skyrmion textures. These topological configurations can be directly manipulated by controlling the cavities’ Euler characteristics. Our work uncovers the fundamental relationship between the topological properties of sound fields and the topological properties of structures. The results enable sound sculpturing with structural topology, and the acoustic cavities can serve as a platform for characterizing the topological properties of sound fields in three-dimensional space. © 2025 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.