弯曲纳米棒等离子体共振的数学分析
Mathematical analysis of plasmon resonances for curved nanorods
摘要：
我们研究了弯曲纳米棒的等离子体共振呈现各向异性的几何形状。我们分析了等离子体共振的定量性质及其与超材料结构和纳米棒各向异性几何形状的关系。基于对各向异性几何中的层势算子，特别是Neumann-Poincaré算子的精细渐近和谱分析，我们导出了准静态散射场的精确渐近公式.通过仔细分析渐近公式，我们建立了尖锐的条件，可以确保等离子体共振的发生。共振条件以复杂但优雅的方式耦合超材料参数、波频率和纳米棒几何形状。我们通过研究纳米棒内部和外部的波场来提供彻底的共振分析。此外，我们的定量分析表明，纳米棒的不同部分诱导不同程度的共振。具体地，弯曲纳米棒的两个端部处的共振强度比纳米棒的正面部分的共振强度更突出。本文首次对各向异性几何结构中纳米结构的等离子体共振进行了理论研究。
英文摘要：
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.
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