Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, 351-0198, Japan.
Nonlinear Physics Centre, RSPE, The Australian National University, Canberra, ACT, 0200, Australia.
Nat Commun. 2019 Feb 4;10(1):580. doi: 10.1038/s41467-019-08397-6.
Maxwell electromagnetism, describing the wave properties of light, was formulated 150 years ago. More than 60 years ago it was shown that interfaces between optical media (including dielectrics, metals, negative-index materials) can support surface electromagnetic waves, which now play crucial roles in plasmonics, metamaterials, and nano-photonics. Here we show that surface Maxwell waves at interfaces between homogeneous isotropic media described by real permittivities and permeabilities have a topological origin explained by the bulk-boundary correspondence. Importantly, the topological classification is determined by the helicity operator, which is generically non-Hermitian even in lossless optical media. The corresponding topological invariant, which determines the number of surface modes, is a [Formula: see text] number (or a pair of [Formula: see text] numbers) describing the winding of the complex helicity spectrum across the interface. Our theory provides a new twist and insights for several areas of wave physics: Maxwell electromagnetism, topological quantum states, non-Hermitian wave physics, and metamaterials.
麦克斯韦电磁学描述了光的波动特性，它是 150 年前提出的。60 多年前，人们证明了光学介质（包括电介质、金属、负折射率材料）之间的界面可以支持表面电磁波，这些波现在在等离子体、超材料和纳米光子学中起着至关重要的作用。在这里，我们表明，由实介电常数和磁导率描述的各向同性均匀介质界面上的表面麦克斯韦波具有拓扑起源，可以用体边界对应关系来解释。重要的是，拓扑分类由螺旋算子决定，即使在无损耗光学介质中，螺旋算子通常也是非厄米的。确定表面模式数量的相应拓扑不变量是一个 [公式：见正文] 数（或一对 [公式：见正文] 数），它描述了复螺旋谱在界面上的缠绕。我们的理论为波物理的几个领域提供了一个新的视角和见解：麦克斯韦电磁学、拓扑量子态、非厄米波物理和超材料。
