  We apply a circularly and linearly polarized terahertz field on a monolayer
of graphene taking into account spin-orbit interactions of the intrinsic and
Rashba type. It turns out that the field can not only be used to induce a gap
in the energy spectrum, but also to close an existing gap due to the different
reaction of the spin components on circularly polarized light. Signatures of
spin-orbit coupling on the density of states of the driven system can be
observed even for energies where the static density of states is independent of
spin-orbit interactions. Furthermore it is shown that the time evolution of the
spin polarization and the orbital dynamics of an initial wave packet can be
modulated by varying the ratio of the spin-orbit coupling parameters. Assuming
that the system acquires a quasi stationary state, the optical conductivity of
the irradiated sample is calculated. Our results confirm the multi step nature
of the conductivity obtained recently, where the number of intermediate steps
can be changed by adjusting the spin-orbit coupling parameters and the
orientation of the field.
