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

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