Onset of Bloch oscillations in the almost-strong-field regime

In the field of high-order harmonic generation from solids, the electron motion typically exceeds the edge of the first Brillouin zone. In conventional nonlinear optics, on the other hand, the excursion of band electrons is negligible. Here, we investigate the transition from conventional nonlinear optics to the regime where the crystal electrons begin to explore the first Brillouin zone. It is found that the nonlinear optical response changes abruptly already before intraband currents due to ionization become dominant. This is observed by an interference structure in the third-order harmonic generation of few-cycle pulses in a non-collinear geometry. Although approaching Keldysh parameter γ = 1, this is not a strong-field effect in the original sense, because the iterative series still converges and reproduces the interference structure. The change of the nonlinear interband response is attributed to Bloch motion of the reversible (or transient or virtual) population, similar to the Bloch motion of the irreversible (or real) population which affects the intraband currents that have been observed in high-order harmonic generation. There are many possible mechanisms of high-harmonic generation from crystals. Here the authors discuss the role of the Bloch oscillation to nonlinear response of the crystal and harmonic radiation from it.