Time-dependent population imaging for high-order-harmonic generation in solids

We propose an intuitive method, called the time-dependent population imaging (TDPI) method, to map the dynamical processes of high-order-harmonic generation (HHG) in solids by solving the time-dependent Schr\"odinger equation. It is shown that the real-time dynamical characteristics of HHG in solids, such as the instantaneous photon energies of emitted harmonics, can be read directly from the energy-resolved population oscillations of electrons in the TDPI picture. Meanwhile, the short and long trajectories of solid HHG are illustrated clearly from the TDPI picture. By using TDPI, we investigate the effects of the carrier-envelope phase in few-cycle pulses and demonstrate intuitively the HHG dynamics driven by two-color fields. Our results show that TDPI provides a powerful tool to study the ultrafast dynamics in strong fields for various laser-solid configurations and to gain insight into HHG processes in solids.