Optical readout of Gas Electron Multipliers (GEM) provides very interesting performances and has been proposed for different applications in particle physics. In particular, thanks to its good efficiency in the keV energy range, it is being developed for low-energy and rare event studies, such as Dark Matter search. So far, the optical approach exploits the light produced during the avalanche processes in GEM channels. Further luminescence in the gas can be induced by electrons accelerated by a suitable electric field. The CYGNO collaboration studied this process with a combined use of a triple-GEM structure and a grid in an He/CF\(_4\) (60/40) gas mixture at atmospheric pressure. Results reported in this paper allow to conclude that with an electric field of about 11~kV/cm a photon production mean free path of about 1.0~cm was found.