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.

中文翻译：

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PT对称的亥姆霍兹共振器偶极子，用于声音指向性

奇偶时间（$\mathcal{PT}$对称的或更普遍的非赫米特系统为非常规的电波管理开辟了一个新领域，尤其是在光学领域，它具有重要的应用。但是，在声学方面发现的建议较少，这可能是由于缺乏用于相干增益的简单机制所致。在本文中，我们提出了一种声学复合非赫米特系统，该系统由以下组件组成：$\mathcal{PT}$对称亥姆霍兹谐振器（HR）偶极子。就像将超原子用作超材料中的构建元素一样，我们建议$\mathcal{PT}$对称偶极子来设计非赫米特系统，以设计复杂的方向性场。我们从理论上进行分析，数值确定并通过实验证明在由一对具有不同增益和损耗水平的亥姆霍兹谐振器组成的非埃尔米特偶极子的二维空间中的对称性破坏。特别是，我们探索了一种作为应用的元结构，以将声压集中在由$\mathcal{PT}$对称偶极子。提议的HR偶极子可能是方便的复合元件，用于智能控制声音。