Fano resonance in metallic grating via strongly coupled subwavelength resonators

We investigate the Fano resonance in grating structures by 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 have imaginary part on the order of $\varepsilon$, where $\varepsilon$ is the size of the slit aperture, while the other sequence have imaginary part on the order of $\varepsilon^2$. 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.