AI 中文总结
本文以现代本征模式形式主义为基础，构建第一性原理分析描述，统一等离子体傅里叶表面的SPP带隙与qBIC现象，并通过本征模式工程提升SPP折射率灵敏度，揭示了浅、深波纹间本征模式的演化机制。
AI 中文摘要
支撑表面等离激元极化激元（SPPs）的周期性波纹金属界面属于最早的纳米等离子体平台。即使是由少量谐波描述的最简单结构——等离子体傅里叶表面，其远场特征也会因波纹深度和对称性呈现显著差异：浅波纹在两个杂化SPP驻波之间表现出等离子体带隙（PBG），而深波纹则支持由不对称性诱导的单尖锐共振，过去十年中被称为准连续谱束缚态（qBICs）。尽管这些光谱特征长期以来在实验中被观测到并得到经验处理，但连接浅波纹与深波纹 regime 的本征模式演化机制在很大程度上仍未被探索。本文通过现代本征模式形式主义重新审视这一长期存在的问题，从瑞利假设出发，构建了简洁的第一性原理分析描述，明确揭示了一个本征模式如何从暗束缚态转变为可观测的qBIC，而另一个则从亮态转变为过耦合、不可观测的状态，从而在同一本征模式框架内统一了具有PBG和qBIC的SPP表现形式。最后，通过展示精确的本征模式工程如何增强SPP的折射率灵敏度，证明了该理论的实际相关性。
英文摘要
Periodically corrugated metal interfaces supporting surface plasmon polaritons (SPPs) belong to the earliest nanoplasmonic platforms. Even simplest reliefs described by a few harmonics - plasmonic Fourier surfaces - display markedly different far-field signatures depending on the corrugation depth and symmetry: shallow reliefs exhibit a plasmonic bandgap (PBG) between two hybridized SPP standing waves, while deeper reliefs support asymmetry-induced single sharp resonances, termed over the last decade as quasi-bound states in the continuum (qBICs). Although these spectral features have long been observed experimentally and treated empirically, the underlying eigenmode evolution connecting the shallow and deep corrugation regimes has remained largely unexplored. Here we revisit this long-standing problem by analyzing it in terms of modern eigenstate formalism. Starting from the Rayleigh hypothesis, we develop a concise first-principle analytical description that explicitly captures how one eigenmode transforms from a dark bound state into an observable qBIC, while the other turns from bright into an overcoupled, unobservable state - thus unifying the SPP manifestations featuring PBG and qBIC within the same eigenmode framework. Finally, we demonstrate the practical relevance of the theory by showing how precise eigenstate engineering can enhance the SPP refractive index sensitivity.
