Within the coupled waves method complemented by quasi-optical approach, we investigate a possibility of diffraction mode selection with respect to the transverse mode index in lasers with planar Bragg resonators. Allowable values of the Fresnel parameter are determined which provide for establishment of stationary single-mode oscillation regime with narrow angle spectrum due to diffraction losses from the edges of the Bragg structure. We show that at larger values of the Fresnel parameter, oscillation stability can be improved by shifting the operating transition frequency to the eigenfrequency of the highest-Q longitudinal mode of the Bragg resonator.

Novel scheme of Bragg resonators implementing three-dimensional distributed feedback is proposed. The study of their electrodynamic characteristics in the framework of the coupled wave approach has been carried out and high selective properties for the three mode indices have been demonstrated under conditions of substantial oversize. The results of the theoretical analysis are corroborated by the 3D simulations. The prospects of using these resonators in the project of a super-power terahertz-band free electron laser, which is currently being developed at the BINP RAS (Novosibirsk) in collaboration with the IAP RAS (Nizhny Novgorod), are discussed.