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Fig. 2 "Laser parameters" a) two examples from ARPES ARPES b) parameter scans with Flquet theory c) stepping of the switch off phase. d) with Floquet theory.  3. In the case that the frequency of the pump field is on resonance with the equilibrium quasiparticle gap, the observed features are known as the ac-Stark effect. We discuss how this follows from Floqeut theory and explain the limits in which the well known formula for the shift as a function of energy holds. Among others, this gives a systematic explanation of the mechanism behind recently observerd optical Stark effects in TMDs. TMDs\cite{sie_valley-selective_2014}.  Fig. 3. "beyond ac-Stark" scaling and dependence of shift on pump parameters