Probing periodic potential of crystals via strong-field re-scattering

Strong-field ionization and re-scattering phenomena have been used to image angstrom-scale structures of isolated molecules in the gas phase. These methods typically make use of the anisotropic response of the participating molecular orbital. Recently, an anisotropic strong-field response has also been observed in high-order harmonic generation (HHG) from bulk crystals (2016 Nat. Phys. 13 345). In a (100) cut magnesium oxide crystal, extreme ultraviolet high-harmonics are foud to depend strongly on the crystal structure and inter-atomic bonding. Here, we extend these measurements to other two important crystal orientations: (111) and (110). We find that HHG from these orientations is also strongly anisotropic. The underlying dynamics is understood using a real-space picture, where high-harmonics are produced via coherent collision of strong-field driven electrons from the atomic sites, including from the nearest neighbor atoms. We find that harmonic efficiency is enhanced when semi-classical electron trajectories connect to the concentrated valence charge distribution regions around the atomic cores. Similarly, the efficiency is suppressed when the trajectories miss the atomic cores. These results further support the real-space picture of HHG with implications for retrieving the periodic potential of the crystal, if not the wavefunctions in three-dimensions.