Robust retrieval method of crystal transition dipole moments by high-order harmonic spectrum

According to the three-step model for solid high-order harmonic generation, there is a one-to-one correspondence between the emitted photon energy and the band gap where the electron-hole pair is annihilated. In the tunneling excitation regime, as the electron-hole pair is mostly created in the vicinity of the minimum band gap, the conversion efficiency of the high-energy photon should be approximately proportional to the square of the transition dipole moment at the k point where the high-harmonic photon is emitted. Based on this picture we propose that a high-order harmonic spectrum could be a strong tool to reconstruct the shape of k-dependent transition dipole moments with the band dispersion and the laser field known. Two real systems, e.g., MgO and ZnO, are taken as samples to verify our idea. The reconstructed shape of the transition dipole moments shows small variation as the laser parameters, such as intensity, wavelength, and pulse duration, are tuned in wide ranges, which proves this scheme is robust.