Acoustic resonances in non-Hermitian open systems

Acoustic resonances in open systems, which are usually associated with resonant modes characterized by complex eigenfrequencies, play a fundamental role in manipulating acoustic wave radiation and propagation. Notably, they are accompanied by considerable field enhancement, boosting interactions between waves and matter, and leading to various exciting applications. In the past two decades, acoustic metamaterials have enabled a high degree of control over tailoring acoustic resonances over a range of frequencies. Here, we provide an overview of recent advances in the area of acoustic resonances in non-Hermitian open systems, including Helmholtz resonators, metamaterials and metasurfaces, and discuss their applications in various acoustic devices, including sound absorbers, acoustic sources, vortex beam generation and imaging. We also discuss bound states in the continuum and their applications in boosting acoustic wave–matter interactions, active phononics and non-Hermitian acoustic resonances, including phononic topological insulators and the acoustic skin effect. Non-Hermitian acoustic resonances in open systems provide a versatile platform to manipulate sound–matter interaction. This Review article surveys the fundamental physics of various acoustic resonances and their uses in realizing different acoustic wave-based applications. Key points Acoustic resonances in open systems are associated with eigenmodes characterized by complex eigenfrequencies. These resonances arise in various acoustic systems whose features can be precisely engineered, making them promising for advanced sound manipulation with resonant metastructure devices. An emerging class of non-Hermitian resonances is that of acoustic bound states in the continuum, which are exotic resonances with a theoretically unbounded Q -factor, providing a versatile and powerful means of enhancing acoustic wave–matter interactions. By making use of the properties of active metamaterials and metasurfaces, acoustic resonances can be precisely engineered to feature active, nonlinear and non-reciprocal properties, as well as parity–time-symmetric wave phenomena, showing great potential for applications in enhanced acoustic wave control. Non-Hermitian Hamiltonians extend the common Hermitian dispersion to the complex plane, resulting in additional exotic features of the band structure. Among these, exceptional degeneracies and bandgaps with unconventional topologies yield exciting and unusually robust wave