Resonance diffraction of THz hidrogen cyanide laser radiation on a semiconductor (InSb) grating is studied both experimentally and theoretically. The specular reflectivity suppression due to the resonance excitation of the THz surface plasmon-polariton is observed on a pure semiconductor grating and on semiconductor gratings covered with a thin dielectric layer. The dielectric coating of the grating results in the resonance shift and widening depending both on the layer thickness and dielectric properties. A simple analytical theory of the resonance diffraction on rather shallow gratings covered with a dielectric layer is presented, and the results are in a good accordance with the experimental data. Analytical expressions for the resonance shift and broadening are essential for the resonance properties understanding and useful for sensing data interpretation of the agents deposited on the grating surface.PACS: 42.25.Fx Diffraction and scattering.Keywords: plasmon-polariton, semiconductor, resonance, diffraction, grating.The terahertz band (0.3-10 THz) is a very promising frequency range of the electromagnetic spectrum due to a wide variety of possible applications such as imaging, nondestructive evaluation, biomedical analysis, chemical characterization, remote sensing (including detection of agents associated with illegal drugs or explosives), communications, etc [1][2][3]. Therefore, in spite of the lack of cheap and compact THz sources and detectors, fundamental and applied researches in the THz area are a problem of today.Imaging and sensing capabilities of the THz radiation can be substantially enhanced by employing the surface plasmon-polariton (SPP) owing to its high field concentration near a metal-dielectric interface. SPPs are transverse magnetic waves that propagate along the boundary between the conducting and dielectric media and are coupled to the collective oscillations of free electrons in a conductor [4]. In the visible and IR ranges metals are usually considered as standard SPP supported media. In contrast to this, in the THz region metals behave as approximately perfect conductors that results in a weak SPP localization within the adjacent dielectric and a huge free path length. Actually, the terahertz SPP at a flat metal loses its surface nature and its existence calls into question.Meanwhile, many semiconductors possess optical properties allowing efficient THz SPP excitation, propagation and manipulation without any additional treatment [5][6][7][8]. It is due to the fact that the dielectric permittivity of these semiconductors in THz is analogous to that of metals in the visible spectrum range. So, all effects observed in optics and associated with SPP, in particular, total suppression of the specular reflection [9,10], resonance polarization transformation [11][12][13], enhanced transmission through optically thick structured metal layers [14,15], and its counterpart, suppressed transmission through optically thin structured metal films [16][17][18][19], can be realized in the THz region...