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We propose a setup for measuring visible and near-visible internalSmith-Purcell radiation and Cherenkov Diffraction Radiation, based on silicaand silicon, and perform quantitative numerical analysis of its radiationefficiency. We calculate the total radiated energy per electron and thespectral distribution of different radiation orders, taking into accountmaterial dispersion and absorption. For an optimized silica grating of 200micrometer length, the total radiated energy reaches 2~eV per electron for 2MeV electrons. Above the Cherenkov threshold, in most cases the energy ofCherenkov diffraction radiation is several times higher than the energy ofinternal Smith-Purcell radiation, but for some geometries and frequency rangesfirst or second order radiation may dominate over Cherenkov radiation (zerothorder). Radiation up to the 4th order is detected in the simulation. Thespectrum of Cherenkov radiation is highly resonant, with local minima forfrequencies where maxima of the other radiation orders occur. The spectrum ofCherenkov radiation takes a frequency comb-like shape for a uniform layer of Sion SiO2 substrate, due to a Fabry-Perot effect occurring for the evanescentfield of the moving electron. The proposed setup could become a prototype of anon-invasive particle beam monitor for both conventional and laser particleaccelerators.

Efficiency of gratings for silica fiber-coupled internal Smith-Purcell  radiation and Cherenkov diffraction radiation -- a quantitative numerical  study