along a periodically deformed surface; the latter playing the role of a diffraction grating. This is known as the Smith-Purcell effect [@SmithPurcell] and it can be applied, for instance, for the generation of teraherz radiation, which finds considerable interest in physics, chemistry, and biology [@Williams2006]. Closely related to the Smith-Purcell effect is the generation of coherent frequency combs of radiation in the scenario in which electrons (or other charged particles) interact with a train of strong laser pulses. In such case the pulse train acts as a diffraction grating in the time domain [@K1; @F1]. Note that the coherent frequency combs of radiation generated from Compton or Thomson scattering offer a possibility for the diagnosis of relativistically intense and short laser pulses [@K2]. Moreover, similar combs have been observed for matter waves. Specifically, the multislit interference and diffraction pattern, as the one predicted by Eq. , has been observed in the momentum and energy distributions of particles emitted via the Breit-Wheeler electron-positron pair creation [@K3] or in photoionization [@K5; @K6]. These selected examples show that the Fraunhofer formula  is universal, as it can be applied across different areas of classical and quantum physics.

The aim of this paper is to 