  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.
