论文标题
等离子在三个维度和凸度中的表面定位
Surface localization of plasmons in three dimensions and convexity
论文作者
论文摘要
在光滑表面上定义的Neumann-Poincaré操作员具有一系列特征值趋于零，并且相应的特征函数的单层电势（称为等离子子，称为零），即零至零，即，作为序列$ j $ tosex $ j $倾向于Infinity。我们在定量地研究了等离子在三个维度中的表面定位。结果是三倍。我们首先证明，在一般形状的平滑界面域上，等离子的序列几乎肯定地以$ j^{ - 1/2} $的速率收敛到边界表面。然后，我们证明，如果域严格凸出，则收敛速率变为$ j^{ - \ infty} $，即，对于任何整数$ n $，它都比$ j^{ - n} $快。结果，我们证明，在三维严格凸平光平滑域中不会出现异常的局部共振。然后，我们通过数值计算来研究等离子在Clifford圆环上的表面定位。克利福德圆环被视为非凸表面的一个例子。计算结果表明，圆环表现出与严格凸域完全不同的光谱特性。特别是，他们表明，圆环上有一个子等离子，比序列的其他条目要慢得多。
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 sequence $j$ tends 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 of $j^{-1/2}$. We then prove that if the domain is strictly convex, then the convergence rate becomes $j^{-\infty}$, namely, it is faster than $j^{-N}$ for any integer $N$. 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 non-convex surfaces. The computational results show that the torus exhibits the spectral property 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.
