Quasi-optical eigenmodes of the resonator with the corrugated mirror

Quasi-optical resonators (QORs) with a periodical structure placed on the mirror surface are used in different devices of the millimeter and submillimeter ranges, for instance, in orotrons. In the present paper we intend to discuss the results of a numerical investigation of the QOR with a periodical structure (a grating) used for the relativistic orotron. Electron beams with energy up to several keV are used in the millimeter wavelength orotron. In this case the period of the grating is far shorter than the wavelength. To obtain operation in the submillimeter wavelength range (the wavelengths from 20-30 microns up to 1 mm) it is possible to use an electron beam with a greater energy up to several MeV. A periodic structure with the period close to the wavelength must be used for the relativistic electron beams. For an adequate eigenmode representation of the QOR with such periodical structures, we must take into account the diffraction harmonics propagating at small angles to the periodical surface. From the results it that the losses increase abruptly when the wavelength becomes close to the period of the grating. This effect depends both on the mirror size and the depth of the grating