Yang Yujia, Hobbs Richard G, Keathley Phillip D, Berggren Karl K
Opt Express. 2020 Sep 14;28(19):27405-27414. doi: 10.1364/OE.401835.
We theoretically investigated electron energy loss spectroscopy (EELS) of ultraviolet surface plasmon modes in aluminum nanodisks. Using full-wave Maxell electromagnetic simulations, we studied the impact of the diameter on the resonant modes of the nanodisks. We found that the mode behavior can be separately classified for two distinct cases: (1) flat nanodisks where the diameter is much larger than the thickness and (2) thick nanodisks where the diameter is comparable to the thickness. While the multipolar edge modes and breathing modes of flat nanostructures have previously been interpreted using intuitive, analytical models based on surface plasmon polariton (SPP) modes of a thin-film stack, it has been found that the true dispersion relation of the multipolar edge modes deviates significantly from the SPP dispersion relation. Here, we developed a modified intuitive model that uses effective wavelength theory to accurately model this dispersion relation with significantly less computational overhead compared to full-wave Maxwell electromagnetic simulations. However, for the case of thick nanodisks, this effective wavelength theory breaks down, and such intuitive models are no longer viable. We found that this is because some modes of the thick nanodisks carry a polar (i.e., out of the substrate plane or along the electron beam direction) dependence and cannot be simply categorized as radial breathing modes or angular (azimuthal) multipolar edge modes. This polar dependence leads to radiative losses, motivating the use of simultaneous EELS and cathodoluminescence measurements when experimentally investigating the complex mode behavior of thick nanostructures.
我们从理论上研究了铝纳米盘紫外表面等离子体模式的电子能量损失谱(EELS)。通过全波麦克斯韦电磁模拟,我们研究了直径对纳米盘共振模式的影响。我们发现,模式行为可分为两种不同情况:(1)直径远大于厚度的扁平纳米盘;(2)直径与厚度相当的厚纳米盘。虽然扁平纳米结构的多极边缘模式和呼吸模式此前已使用基于薄膜堆栈表面等离子体激元(SPP)模式的直观分析模型进行解释,但已发现多极边缘模式的真实色散关系与SPP色散关系有显著偏差。在此,我们开发了一种改进的直观模型,该模型使用有效波长理论来准确模拟这种色散关系,与全波麦克斯韦电磁模拟相比,计算开销显著减少。然而,对于厚纳米盘的情况,这种有效波长理论失效,此类直观模型不再可行。我们发现这是因为厚纳米盘的一些模式具有极化(即垂直于衬底平面或沿电子束方向)依赖性,不能简单地归类为径向呼吸模式或角向(方位角)多极边缘模式。这种极化依赖性导致辐射损耗,这促使在实验研究厚纳米结构的复杂模式行为时同时使用EELS和阴极发光测量。