Computations with the rigorous differential method show that single gratings made by ion implantation have a diffraction efficiency in the +1 transmitted order under TE illumination of only 0.78%. The insertion of such gratings into multilayer dielectric Fabry-Perot cavities leads to an enhancement of the free-space diffraction efficiency. Different designs for the multilayer are considered. An 18.8% efficiency is reached with 11-layer mirrors. This result is obtained by optimization of the thickness of the spacer of the Fabry-Perot cavity that contains the grating and centering of the wavelength of the mirrors. The dependence of optical properties of the structure on the various optogeometrical parameters of the structure is discussed.