Surface localization of plasmons in three dimensions and convexity
| Autor: | Yoshihisa Miyanishi, Kazunori Ando, Takashi Nakazawa, Hyeonbae Kang |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Surface (mathematics)
Physics Applied Mathematics Operator (physics) Mathematical analysis Spectrum (functional analysis) Mathematics::Spectral Theory Eigenfunction 01 natural sciences Neumann–Poincaré operator Convexity Functional Analysis (math.FA) 35J47 (primary) 35P05 (secondary) 010101 applied mathematics Mathematics - Functional Analysis Mathematics - Spectral Theory Mathematics - Analysis of PDEs FOS: Mathematics 0101 mathematics Spectral Theory (math.SP) Plasmon Eigenvalues and eigenvectors Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.2007.16157 |
| Popis: | The Neumann--Poincar\'e 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. Comment: 14 pages, 13 figures |
| Databáze: | OpenAIRE |
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