An equilateral triangular prism is used as the fundamental building block to construct additive Sierpiński fractals, enabling new surface plasmon resonances (SPR) in the first three generations of Sierpiński triangles, as well as topological intermediaries between generations. The modes are characterized using electron energy loss spectroscopy accompanied by eigenmode calculations and optical finite-difference time-domain simulations. The complex fractal geometries present a predictable hierarchy of new resonances, each arising from the previous generational building blocks used to construct the fractal. Intermediate structures break the polarization degeneracy of the equilateral fractals while maintaining a rich multiband spectral response. Engineering defects in the narrow conductive channels of the fractal allows further manipulation of the SPR response, emphasizing higher order SPR modes over the lowest energy peak. The knowledge gained is used to develop guidelines for engineering the response of more complex fractal-based structures, including the spectral response and hotspot distribution.

中文翻译：

---

分形结构中的等离激元共振

等边三角形棱镜被用作构建加性Sierpiński分形的基本构建块，从而在Sierpiński三角形的前三代以及几代之间的拓扑中介中实现了新的表面等离振子共振（SPR）。这些模式使用电子能量损失谱进行表征，并伴有本征模计算和光学有限差分时域仿真。复杂的分形几何形状呈现出可预测的新共振层次，每个共振都来自用于构造分形的前几代构造块。中间结构打破了等边形分形的极化简并性，同时保持了丰富的多频带光谱响应。分形的狭窄导电通道中的工程缺陷允许对SPR响应进行进一步处理，从而强调了最低能量峰值上的高阶SPR模式。所获得的知识用于开发指导工程，以设计更复杂的基于分形的结构的响应，包括光谱响应和热点分布。