论文标题
曲线纳米棒的等离子体共振的数学分析
Mathematical analysis of plasmon resonances for curved nanorods
论文作者
论文摘要
我们研究了呈现各向异性几何形状的弯曲纳米棒的等离子共振。我们分析了等离子体共振的定量特性及其与纳米棒的超材料构型和各向异性几何形状的关系。基于对层电位运算符的精致和微妙的渐近和光谱分析，尤其是与各向异性几何形状相关的Neumann-Poincaré算子，我们得出了准静态状态中相应散射场的急剧渐近公式。通过仔细分析渐近公式，我们建立了尖锐的条件，可以确保等离子共振的发生。共振条件以复杂但优雅的方式将超材料参数，波频和纳米棒的几何形状融为一体。我们通过研究纳米棒内外的波场来提供彻底的共振分析。此外，我们的定量分析表明，纳米棒的不同部分会诱导不同程度的共振。具体而言，弯曲纳米棒的两个端部的谐振强度比纳米棒的立面零件要出色。本文介绍了关于各向异性几何形状内纳米结构的等离子共振的第一项理论研究。
We investigate plasmon resonances for curved nanorods which present anisotropic geometries. We analyze quantitative properties of the plasmon resonance and its relationship to the metamaterial configurations and the anisotropic geometries of the nanorods. Based on delicate and subtle asymptotic and spectral analysis of the layer potential operators, particularly the Neumann-Poincaré operators, associated with anisotropic geometries, we derive sharp asymptotic formulae of the corresponding scattering field in the quasi-static regime. By carefully analyzing the asymptotic formulae, we establish sharp conditions that can ensure the occurrence of the plasmonic resonance. The resonance conditions couple the metamaterial parameters, the wave frequency and the nanorod geometry in an intricate but elegant manner. We provide thorough resonance analysis by studying the wave fields both inside and outside the nanorod. Furthermore, our quantitative analysis indicates that different parts of the nanorod induce varying degrees of resonance. Specifically, the resonant strength at the two end-parts of the curved nanorod is more outstanding than that of the facade-part of the nanorod. This paper presents the first theoretical study on plasmon resonances for nanostructures within anisotropic geometries.
