  In this work, we present numerical results for the second and third order
conductivities of the plain graphene and gapped graphene monolayers associated
with the second and third harmonic generation, the optical rectification and
the optical Kerr effect. The frequencies considered here range from the
microwave to the ultraviolet portion of the spectrum, the latter end of which
had not yet been studied. These calculations are performed in the velocity
gauge and directly address the components of the conductivity tensor. In the
velocity gauge, the radiation field is represented by a power series in the
vector potential, and we discuss a very efficient way of calculating its
coefficients in the context of tight-binding models.
