Two-dimensional imaging of energy bands from crystal orientation dependent higher-order harmonic spectra in h−BN

High-order harmonic generation (HHG) from hexagonal boron nitride is simulated by solving extended multiband semiconductor Bloch equations under strong laser fields. By changing the angle of the laser polarization with respect to the crystal orientation, we find that harmonic spectra present a double-plateau structure and HHG is dominantly emitted along \ensuremath{\Gamma}-M direction in the first plateau, but special anisotropic distribution is observed in the secondary plateau. In-depth analyses reveal that two plateaus originate from different pair of conduction band and valence band, and the shapes of band dispersion and transition dipole moment determine anisotropic harmonic emission in $h$-BN crystal. Furthermore, we show that band energies of high-lying unoccupied bands and low-lying occupied ones can be directly extracted from laser polarization dependent high harmonic spectra. This paves a way to image the two-dimensional band information of solid materials by using laser-induced HHG.