  Pump-probe techniques with high temporal resolution allow one to drive a
system of interest out of equilibrium and at the same time, probe its
properties. Recent advances in these techniques open the door to studying new,
non-equilibrium phenomena such as Floquet topological insulators and
superconductors. These advances also necessitate the development of theoretical
tools for understanding the experimental findings and predicting new ones. In
the present work, we provide a theoretical foundation to understand the
non-equilibrium behavior of a Dirac system. We present detailed numerical
calculations and simple analytic results for the evolution of a Dirac system
irradiated by light. These results are framed intuitively by appealing to the
recently revitalized notion of side-bands. We find that, under the application
of circularly polarized light, a Dirac point only ever splits into two copies
of sidebands. Meanwhile, the application of linearly polarized light leaves the
Dirac point intact while producing side bands. Our immediate interest in this
work is in connection to time and angle resolved photoemission experiments,
where we find excellent qualitative agreement between our results and those in
the literature. However, our results are general and may prove useful beyond
this particular application and should be relevant to other pump-probe
experiments.
