RESUMEN
We investigate the possibility of frequency conversion in time-varying metasurfaces, composed of graphene microribbon arrays (GMRAs) with time-periodic modulation of their conductivity. We present a quasi-static model for the interaction of light with a temporally modulated metasurface, as well as an accurate analytical treatment of the problem of time-varying GMRAs. Results coming from numerical simulations are also available. We provide corrections to a previous related proposal for frequency conversion and refute the possibility of attaining frequency shifts not equal to an integral multiple of modulation frequency. Contrary to the preceding results, our findings show that efficient frequency conversion demands more requisites than single-layer GMRAs can supply and that its requirements can be addressed successfully by a multi-layer design.