Theory of HHG in solids: band structure, orientation dependence, and time profiles

Over the past several years we have explored the theory of high harmonic generation (HHG) in solids, using a momentum space model. We have shown that the HHG process can be described as a three-step process that involves tunneling from the valence to the conduction band(s), acceleration on one or multiple conduction bands, and radiation via coherence with the valence band. We have also shown that in a given system this dynamics can be described using a multi-level system that originates as the Gamma-point band structure of that system. We will discuss how this points to a close connection between the band structure and a number of properties of the harmonic radiation such as: (i) the cutoff energy and yield of the often multiple plateaus that can be observed in the harmonic spectrum, (ii) the dependence of the harmonic yield on the relative orientation of the crystal and the laser polarization, and (iii) the sub-cycle time structure of the harmonic radiation. We will discuss the comparison of our predictions to several recent experimental results.