Resonance radiation of electromagnetic waves by a diffraction grating filled with metamaterial

We consider the diffraction of a plane inhomogeneous $H$-polarized wave, generated by a modulated sheet electron beam, on a periodic reflective grating with rectangular grooves filled by a metamaterial with the effective permittivity characterized by a frequency dispersion. The problem is solved using the method of reexpansion. The phenomenon of resonance radiation of electromagnetic waves by the grating is discovered and the conditions for its manifestation are established.