  Using the Fourier modal method (FMM) we report our analysis of the
transmission resonances of a plasmonic grating with sub-wavelength period and
extremely narrow slits for wavelengths of the incoming, transverse magnetic
(TM)-polarized, radiation ranging from 240nm to 1500nm and incident angles from
0 degree to 90 degree. In particular, we study the case of a silver grating
placed in vacuo. Consistent with previous studies on the topic, we highlight
that the main mechanism for extraordinary transmission is a TM-Fabry-Perot (FP)
branch supported by waveguide modes inside each slit. The TM-FP branch may also
interact with surface plasmons (SPs) at the air/Ag interface through the
reciprocal lattice vectors of the grating, for periods comparable with the
incoming wavelength. When the TM-FP branch crosses a SP branch, a band gap is
formed along the line of the SP dispersion. The gap has a Fano-Feshbach
resonance at the low frequency band edge and a ridge resonance with extremely
long lifetime at the high frequency band edge. We discuss the nature of these
dispersion features, and in particular we describe the ridge resonance in the
framework of guided-mode resonances (GMRs). In addition, we elucidate the
connection of the coupling between the TM-FP branch and SPs within the Rayleigh
condition. We also study the peculiar characteristics of the field localization
and the energy transport in two topical examples.
