Spatial coherence in high-order-harmonic generation from periodic solid structures

We theoretically investigate the high-harmonic generation (HHG) from periodical structures driven by an intense laser pulse. Including the full bands, the single electron time-dependent Schr\"odinger equation is numerically solved in the velocity gauge using Bloch states to obtain the emission spectra. The contributions from different crystal sites are identified using the localized Wannier functions and time-frequency analysis. It is found that the cutoff energy of harmonics is depending on the migration distance of the electron and the instantaneous laser field strength when the electron transports into the related sites. We show that the coherence among different sites during electron propagation is crucial for HHG from solids which can be taken advantage to control the individual site contribution to the certain frequency range of the total harmonic spectra.