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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 1D periodic potentials. The general relations between a laser-controlled spectrum where electron momentum depends on the quasi-energy and a superlattice mini-band spectrum in graphene are derived. As an example we consider two spectra generated by a pulsed laser and by a step-like electrostatic potential. We also calculate the graphene excitation spectrum in continuous strong laser fields in the resonance approximation for linear and circular polarizations and show that circular polarized laser fields cannot be reduced to any graphene electrostatic superlattice. Some physical phenomena related to the peculiar graphene energy spectrum in the strong electromagnetic field are discussed.