Fig. 1. Energy bands and laser models used in numerical simulation. (a) 2D four-band model of graphene; (b) time delay scheme between the infared pump laser and X-ray probe pulse

Fig. 2. Numerical simulation results of ATAS. (a) X-ray response functions of graphene without and with infrared pump laser field of td=0; (b) according ATAS at td=0; (c) ATAS dependent on the time delay near point M

Fig. 3. Simplified band model and numerical simulation result of ATAS. (a) One-electron model in one-dimensional two-band structure; (b) numerically ATAS simulated based on the single-electron model

Fig. 4. Comparison of the offset time between the numerical simulation and analytical theory

Fig. 5. Comparison between the numerical and analytical calculated offset time for different laser wavelengths and periods. (a) Offset time as function of the laser wavelength; (b) offset time as function of the laser period