Role of trajectory symmetry in solid high-order harmonic generation

High-order harmonic generation (HHG) from ZnO crystal with two-band model has been investigated theoretically driven by a few-cycle laser pulse. It is observed that the harmonics in the cut-off region exhibit periodic frequency shifts with changes in carrier envelope phase (CEP) of the laser field. When the CEP of the laser pulse is an integer multiple of π, the cut-off region is dominated by even-order harmonics rather than odd-order harmonics. To illustrate the physical mechanism of even-order harmonics, we track the trajectories of electron and hole between two successive half-cycles by performing the time-frequency analysis and recollision model. The results show that the maximum electron displacement is symmetric between two successive half-cycles for odd-order harmonics. However, the half-cycle symmetry of the maximum displacement is broken in the case of even-order harmonics.