Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional points or one-dimensional lines of exceptional points. Here, we substantially expand the space of exceptional systems by designing two-dimensional surfaces of exceptional points, and find that symmetries are a key element to protect such exceptional surfaces. We construct them using symmetry-preserving non-Hermitian deformations of topological nodal lines, and analyze the associated symmetry, topology, and physical consequences. As a potential realization, we simulate a parity-time-symmetric 3D photonic crystal and indeed find the emergence of exceptional surfaces. Our work paves the way for future explorations of systems of exceptional points in higher dimensions, and applications in emission control and sensing.

中文翻译：

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出色的表面 $\mathcal{PT}$对称非赫米特光子系统

最近，非厄密系统中的异常点已显示出具有非平凡的拓扑特性，并引起了许多奇异的物理现象。但是，到目前为止，大多数研究都集中在孤立的例外点或例外点的一维线上。在这里，我们通过设计特殊点的二维表面大大扩展了特殊系统的空间，并且发现对称性是保护此类特殊表面的关键要素。我们使用拓扑节点线的保留对称性的非Hermitian变形构造它们，并分析相关的对称性，拓扑结构和物理后果。作为一种潜在的实现，我们模拟一个奇偶时间对称的3D光子晶体，并确实发现了异常表面的出现。