On the condition of total backward reflection for a diffraction grating on a mirror operating in Littrow mounting

Optical properties of a structure consisting of a diffraction grating operating in the Littrow geometry, a plane-parallel dielectric layer, and a mirror that completely reflects the incident radiation are considered. A condition is obtained that is imposed on the scattering matrix elements of a diffraction grating, under which, by choosing the thickness of the dielectric layer, it is possible to obtain total backward reflection, i.e., to direct all the energy of the incident wave to the –1st reflected diffraction order. The results of numerical simulations within the framework of the electromagnetic theory of diffraction completely confirm the obtained theoretical results.