Probing subcycle spectral structures and dynamics of high-order harmonic generation in crystals

Subcycle spectral structures and dynamics of high-order harmonic generation(HHG)processes of atoms and molecules driven by intense laser fields on the attosecond time scale have been originally studied theoretically and ex-perimentally.However,the time scale of HHG dynamics in crystals is in the order of sub-femtosecond,and the carrier dynamics of HHG in crystals driven by subcycle laser pulses are largely unexplored.Here we perform a theoretical study of subcycle structures,spectra,and dynamics of HHG of crystals in mid-infrared laser fields subject to excitation by a subcycle laser pulse with a time delay.The HHG spectra as a function of time delay between two laser fields are cal-culated by using a single-band model for the intra-band carrier dynamics in crystal momentum space and by solving the time-dependent Schr?dinger equation in velocity gauge for the treatment of multi-band crystal systems.The results exhibit a complex time-delay-dependent oscillatory pattern,and the enhancement and suppression of the HHG related to subcycle pulse are observed at the given time delay in either single-band or multi-band crystal systems.To understand oscillation structures with respect to the dependence for the subcycle laser fields,the time-frequency characteristics of the HHG as well as the probability density distribution of the radiation are analyzed in detail.