细长纳米环的等离子体共振
Plasmonic resonances of slender nanometallic rings
摘要：
我们发展了一个近似的准静态理论来描述细长纳米环及其结构的低频等离子体共振。首先，我们使用渐近参数减少等离子体激元本征值问题的几何（材料和频率无关）模式的一个给定的环结构的一维周期积分微分问题，其中本征函数表示与每个环的方位角电压和极化电荷配置文件。其次，我们得到封闭形式的解决方案，减少本征值问题的方位不变的环（包括圆环形的环，但也允许非圆形的横截面形状），以及同轴二聚体和链等环。对于更一般的几何形状，涉及方位非均匀环和非同轴结构，我们解决了减少本征值问题，使用半解析方案的基础上减少本征函数的傅立叶展开。第三，我们使用的渐近近似模式，结合准静态谱理论的等离子体共振，研究和解释的频率响应的范围广泛的纳米细长环结构下的平面波照明。
英文摘要：
We develop an approximate quasi-static theory describing the low-frequency plasmonic resonances of slender nanometallic rings and configurations thereof. First, we use asymptotic arguments to reduce the plasmonic eigenvalue problem governing the geometric (material- and frequency-independent) modes of a given ring structure to a 1D-periodic integro-differential problem in which the eigenfunctions are represented by azimuthal voltage and polarization-charge profiles associated with each ring. Second, we obtain closed-form solutions to the reduced eigenvalue problem for azimuthally invariant rings (including torus-shaped rings but also allowing for non-circular cross-sectional shapes), as well as coaxial dimers and chains of such rings. For more general geometries, involving azimuthally non-uniform rings and non-coaxial structures, we solve the reduced eigenvalue problem using a semi-analytical scheme based on Fourier expansions of the reduced eigenfunctions. Third, we used the asymptotically approximated modes, in conjunction with the quasi-static spectral theory of plasmonic resonance, to study and interpret the frequency response of a wide range of nanometallic slender-ring structures under plane-wave illumination.
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