  We theoretically investigate the ultrafast terahertz(THz) properties of
monolayer graphene. The analytical formulations of the photon carrier, electric
polarization and optical current are obtained by solving the Bloch-equations in
present of the ultrafast THz Gaussian pulse. Graphene shows a large nonlinear
and ultrafast optical response at THz frequencies due to the gapless and
relativistic Dirac particles with nearly linear energy dispersion. It is found
that the photon carrier density, electric polarization and optical current
density increase with increasing the frequency of the THz pulse. These
theoretical results are in agreement with recent experimental findings. This
study confirms further that graphene exhibits important features and is
relevant to the applications in the ultrafast THz fields.
