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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 ε 2 . 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. 

Abstract 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.