High harmonic generation in solids: Real versus virtual transition channels

A closed-form formalism for modeling high harmonic generation (HHG) in solids is derived; its validity is tested for one-dimensional two-band inversion symmetric model solids; excellent agreement with the exact von Neumann equation is found. From the closed-form expressions, a diagnostic method is developed that allows one to separate resonant from nonresonant processes in nonlinear optics. This opens a deeper view into the dominant laser- and material-dependent mechanisms of high harmonic generation in solids. Midinfrared-driven HHG in semiconductors is dominated by the resonant interband current. As a result of the dynamic Stark shift, virtual processes gain in importance in near-infrared-driven HHG in dielectrics. Finally, comparison to experiments indicates the potential importance of little-explored processes, such as dephasing of the strong-field dynamics from coupling to the many-body environment of solids.