We examine Floquet engineering in strongly correlatec systems with
spin-orbit coupling. Our approximation for heating
processes, which arise from doublon-holon propagation, suggests that compounds with stronger
Hund's-rule coupling are less prone to heating. We then discuss the possibility of Floquet engineering in the
three candidate Kitaev materials Na2IrO3,
a-Li2IrO3 and a-RuCl3.
Focusing on a-RuCl3, we describe the influence of arbitrary polarization and
the limiting cases of linear and circular polarization. The
corresponding model is derived via perturbation theory up to fourth
order. Starting from linear and circular polarization, we bridge the
gap between those two limiting cases. We then study more complex
Lissajous figures and general trends arising for them. In theory these
Lissajous figures should inherit effects from both linear and circular
polarized light and therefore yield tuning possibilities not yet
explored in the context of candidate Kitaev materials.