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This paper discusses Floquet engineering with arbitrary polarization in$\alpha$-RuCl$_3$. We describe the influence of arbitrary polarization and thelimiting cases of linear and circular polarization. The corresponding model isderived via perturbation theory up to fourth-order. Starting from linear andcircular polarization we bridge the gap between those two limiting cases. Wethen we study more complex Lissajous figures and general trends arising forthem.

From linear to circular polarized light -- Floquet engineering in Kitaev-Heisenberg materials with Lissajous figures