Graphene exhibits excellent ultrafast optical properties due to its unique electronic structure. In this paper we investigate theoretically the ultrafast dynamic optical properties of graphene based on the Bloch-equations, and introduce the theoretical model of graphene. First, we give the energy which has a linear relationship with the wave vector k. The behavior of electrons in the vicinity of the two Dirac points can be described by the massless Dirac-equation, thus we have the Dirac equation of graphene. Second, we discuss the interaction between graphene and light field. The Bloch-equations of graphene are obtained through the Heisenberg equation and then we discuss the photon carriers ,electric polarization and optical current change over time by analyzing the Bloch-equations. It is found that the nonequilibrium carriers in graphene induced by a terahertz field can be built in 20–200 fs due to the Pauli blocking and the conservation of energy principle. The photon carrier density will increase with the frequency of enhanced light field. Thus an optical current can be created rapidly within 1 ps. A graphene system responds linearly to the external optical field for √2evFE0t≪~ω, while the graphene systems respond nonlinearly to the external optical field, where E0 andωare respectively the intensity and the frequency of the light, t is the time and vF the Dirac velocity in graphene. The electric polarization and optical current increase with increasing photon energies. These theoretical results are in agreement with recent experimental findings and indicate that graphene exhibits important features and has practical applications in the ultrafast optic filed, especially in terahertz field.
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