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 δ, the sensitivity of resonance frequency reduces as H increases. Specifically, the sensitivity is of order O(δ/H) if H>δ and of order O(1+ln H/δ) $ 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.
|Original language||English (US)|
|Number of pages||19|
|Journal||IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)|
|State||Published - Feb 1 2021|
Bibliographical noteFunding Information:
National Science Foundation (DMS-1719851 and DMS-2011148 to J.L.); Hong Kong Research Grants Council (GRF 16304517 and GRF 16306318 to H.Z.).
- Sensitivity analysis
- Slit structure