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.

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体共振。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配置和各向异性几何形状的关系。基于与各向异性几何相关的层势算子，特别是 Neumann-Poincaré 算子的微妙和微妙的渐近和光谱分析，我们推导出准静态区域中相应散射场的尖锐渐近公式。通过仔细分析渐近公式，我们建立了可以确保等离子体共振发生的尖锐条件。共振条件以一种复杂而优雅的方式耦合了超材料参数、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引起不同程度的共振。具体而言，弯曲纳米棒两端的共振强度比纳米棒正面部分的共振强度更突出。