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 experimentally. 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 calculated by using a single-band model for the intra-band carrier dynamics in crystal momentum space and by solving the time-dependent Schrodinger 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.