Lamellar gratings are investigated via temporal coupled-mode theory and numerical simulations. Total absorption can be achieved by an optimized grating with shallow grooves under normal incidence and the full width at half-maximum (FWHM) is only 0.4 nm. For certain wavelengths, the structure shows high absorption only within an ultra-narrow angle, which suggests that it can be used as a highly directional thermal emitter according to Kirchhoff's law. Besides, the resonant wavelength is sensitive to the refractive index of the environmental dielectric. The large sensitivity (1400 nm/RIU) and simultaneous small FWHM result in a huge figure-of-merit of 2300/RIU, which enables the structure to have great potential in plasmonic sensing.