Dependence of high-order-harmonic generation on dipole moment in Si O2 crystals

High-order-harmonic generation in α-quartz SiO2 is theoretically investigated under a strong laser field by solving the extended semiconductor Bloch equations. The accurate band structures as well as dipole moments between different bands are obtained from state-of-the-art first-principles calculations. We find that the shapes of k-space-dependent dipole moments play an important role in harmonic generation. The calculated results show that harmonic conversion efficiency is significantly enhanced and the cutoff energy is distinctly increased when the dipole moments change greatly along a valley in the k direction in the solid. Based on that dependence on the dipole moment, we also show that symmetry groups greatly affect the harmonic spectra from the solid materials. Moreover, a two-color synthesized field is used to achieve a supercontinuum harmonic spectrum near the cutoff region, and isolated attosecond pulses can be obtained directly by filtering out the harmonic radiation. We hope the contribution presented in this work provides a useful reference for future studies on laser-crystal interactions.