Interference Between Harmonics Of Different Crystal Momentum Channels In Solid High-Order Harmonic Generation

We theoretically investigate high-order harmonic generation (HHG) in one-dimensional model solids with linearly polarized laser pulses. By identifying crystal-momentum-resolved contributions, we show that the reason behind the odd-order harmonics-dominated harmonic spectrum originates from the interferences between harmonics generated by different crystal momentum channels. Symmetry analysis show that constructive interferences between odd-order harmonics and destructive interferences between even-order harmonics are determined by the inversion symmetry of the band dispersion and the time translation symmetry of the laser field. We also propose and numerically demonstrate a method to select the short and long trajectories for HHG in solids. It is shown that the classical trajectories predicted by quasiclassical model are associated with the quantum orbits that originate from a single crystal momentum channel. However, the classical trajectories predicted by the recollision model are associated with all of the crystal momentum channels in the entire first Brillouin zone, and the interferences between harmonics generated by different crystal momentum channels play a key role in the formation of recollision quantum orbits. Moreover, we find that the effect of dephasing time is the damping of the current rather than changing the harmonic phases. The present results may contribute to disentangling the underlying mechanism of HHG in solids.