We derive the formulas for the resonance frequencies and their sensitivity when the nano-slit structures are used in the detection of thin layers. For a thin layer with a thickness of |$H$| deposited over the nanostructure, we show quantitatively that for both single and periodic slit structures with slit aperture size |$\delta $|⁠, the sensitivity of resonance frequency reduces as |$H$| increases. Specifically, the sensitivity is of order |$O(\delta /H)$| if |$H>\delta $| and of order |$O(1+\ln H/\delta )$| otherwise. The evanescent wave modes are present along the interface between the thin dielectric film and ambient medium above. From the mathematical derivations, it is observed that the sensitivity of the resonance frequency highly depends on the effect of evanescent wave modes on the tiny slit apertures.

中文翻译：

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纳米狭缝结构检测薄层时的共振频率敏感性

当纳米缝结构用于检测薄层时，我们得出了共振频率及其灵敏度的公式。对于厚度为| $ H $ |的薄层 沉积在纳米结构上，我们定量地表明，对于狭缝孔径尺寸为| $ \ delta $ |⁠的单个和周期性狭缝结构，共振频率的敏感度随| $ H $ |而降低。增加。具体来说，灵敏度约为| $ O（\ delta / H）$ | 如果| $ H> \ delta $ | 和顺序| $ O（1+ \ ln H / \ delta）$ |除此以外。van逝波模式沿着薄介电膜与上方环境介质之间的界面存在。从数学推导中可以看出，谐振频率的灵敏度高度取决于of逝波模式对微小狭缝孔径的影响。