PT -symmetric Helmholtz resonator dipoles for sound directivity

Parity-time ($\mathcal{PT}$)-symmetric or, more generally, non-Hermitian systems have opened a new area for unconventional management of waves, with significant applications, especially in optics. However, fewer proposals are found in acoustics, possibly due to the lack of a simple mechanism for coherent gain. In this paper, we propose a composite non-Hermitian system in acoustics consisting of assemblies of $\mathcal{PT}$-symmetric Helmholtz resonator (HR) dipoles. Like meta-atoms are used as building elements in metamaterials, we propose $\mathcal{PT}$-symmetric dipoles to design non-Hermitian systems intended to engineer complicated directivity fields. We theoretically analyze, numerically confirm, and experimentally show the symmetry breaking in a two-dimensional space of non-Hermitian dipoles consisting of a pair of Helmholtz resonators with different levels of gain and loss. In particular, we explore, as an application, a metastructure to concentrate the sound pressure inside the circular array formed by $\mathcal{PT}$-symmetric dipoles. The proposed HR dipoles may be a convenient composite element for smart control of sound.