Surface localization of plasmons in three dimensions and convexity
Surface localization of plasmons in three dimensions and convexity
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等离激元在三维和凸度上的表面定位
DOI：
10.1137/20m1373530
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发表时间：
2021
影响因子：
1.9
通讯作者：
Takashi Nakazawa
中科院分区：
文献类型：
--
作者：
Kazunori Ando;Hyeonbae Kang;Yoshihisa Miyanishi;Takashi Nakazawa
定义在光滑曲面上的Neumann-Poincaré算子具有一系列收敛到零的本征值，并且相应的本征函数的单层势，称为等离子体，衰变到零，即随着序列的指数趋于无穷大，局域化在曲面上。我们从三维角度定量研究了等离子体激元的表面局域化。结果有三个方面。我们首先证明了在一般形状的光滑有界域上，等离子体序列几乎必然以更快的速度收敛到边界面外的零。然后，我们证明了如果区域是严格凸的，则收敛速度变得；也就是说，它比任何整数都快。因此，我们证明了在三维严格凸光滑区域上不会发生反常局域共振伪装。然后通过数值计算研究了Clifford环面上等离子体激元的表面局域化。以Clifford环面为例，给出了非凸曲面的一个例子。计算结果表明，环面表现出与严格凸域完全不同的光谱性质。特别是，他们提出，环面上有一个等离子体激元的子序列，它的衰减比序列的其他条目慢得多。
The Neumann--Poincaré operator defined on a smooth surface has a sequence of eigenvalues converging to zero, and the single-layer potentials of the corresponding eigenfunctions, called plasmons, decay to zero, i.e., are localized on the surface, as the index of the sequencetends to infinity. We investigate quantitatively the surface localization of the plasmons in three dimensions. The results are threefold. We first prove that on smooth bounded domains of general shape, the sequence of plasmons converges to zero off the boundary surface almost surely at the rate faster thanas. We then prove that if the domain is strictly convex, then the convergence rate becomes; namely, it is faster thanfor any integer. As a consequence, we prove that cloaking by anomalous localized resonance does not occur on three-dimensional strictly convex smooth domains. We then look into the surface localization of the plasmons on the Clifford torus by numerical computations. The Clifford torus is taken as an example of nonconvex surfaces. The computational results show that the torus exhibits spectral properties completely different from strictly convex domains. In particular, they suggest that there is a subsequence of plasmons on the torus which has much slower decay than other entries of the sequence.