Massless Dirac fermions in a laser field as a counterpart of graphene superlattices

We establish an analogy between spectra of Dirac fermions in laser fields and an electron spectrum of graphene superlattices formed by static one-dimensional periodic potentials. The general relations between a laser-controlled spectrum where electron momentum depends on the quasienergy and a superlattice miniband spectrum in graphene are derived. As an example we consider two spectra generated by a pulsed laser and by a steplike electrostatic potential. We also calculate the graphene excitation spectrum in continuous strong laser fields in the resonance approximation for linear and circular polarizations. Some physical phenomena, including an anomalous energy-gap anisotropy, related to the peculiar graphene energy spectrum in the strong electromagnetic field are discussed.