We investigate the Fano resonance in grating structures using coupled resonators. The grating consists of a perfectly conducting slab with periodically arranged subwavelength slit holes, where inside each period, a pair of slits sit very close to each other. The slit holes act as resonators and are strongly coupled. It is shown rigorously that there exist two groups of resonances corresponding to poles of the scattering problem. One sequence of resonances has imaginary part in the order of ε, where ε is the size of the slit aperture, while the other sequence has imaginary part in the order of ε2. When coupled with the incident wave at resonant frequencies, the narrow-band resonant scattering induced by the latter will interfere with the broader background resonant radiation induced by the former. The interference of these two resonances generates the Fano-type transmission anomaly, which persists in the whole radiation continuum of the grating structure as long as the slit aperture size is small compared to the incident wavelength.

中文翻译：

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通过强耦合亚波长谐振器在金属光栅中的 Fano 谐振

我们使用耦合谐振器研究光栅结构中的 Fano 谐振。光栅由具有周期性排列的亚波长狭缝孔的完美导电板组成，在每个周期内，一对狭缝彼此非常靠近。狭缝孔充当谐振器并且强耦合。严格证明，存在两组对应于散射问题极点的共振。一个共振序列具有虚部，顺序为ε， 在哪里ε是狭缝孔径的大小，而另一个序列具有虚部，顺序为ε2. 当与共振频率的入射波耦合时，后者引起的窄带共振散射会干扰前者引起的更宽的背景共振辐射。这两个共振的干涉产生了 Fano 型透射异常，只要狭缝孔径尺寸与入射波长相比较小，这种异常就会持续存在于光栅结构的整个辐射连续体中。