▎ 摘　　要

In a periodic arrangement of equally-doped graphene monolayers the electromagnetic wave propagation is described by band theory. We have found that the photonic response of this system enriches when the doping level is sequentially-modulated acquiring periodic, quasi-periodic or harmonic profiles along the superlattice axis. Because the dielectric background that supports the graphene layers is homogeneous, it is the doping modulation superimposed on the graphene layers that produces a particular photonic band structure. We report that the fixed separation between the layers generates a persistent structural band gap which is tunable by gating. We also demonstrate that doping modulations following continuous cosine or semi-continuous square envelope functions give place to frequency mini-bands. In our calculations the doping levels correspond to chemical potentials within the range 0.2 eV < mu < 1.2 eV and the model for the graphene conductivity is valid in the limit of low temperatures in the THz spectrum. (C) 2017 Elsevier Ltd. All rights reserved.