Generation and propagation of high-order harmonics in crystals

The observation of nonperturbative high-order-harmonic generation in periodic solids has been interpreted in terms of a two step process comprising tunnel ionization and radiation from electrons undergoing frequency modulated Bloch oscillations in a strong laser field [Ghimire et al., Nat. Phys. 7, 138 (2011)]. Here we extend the model to include propagation effects. We show that the predicted efficiency is limited by phase velocity mismatch for emission below the band gap and by absorption above the band gap. The efficiency of harmonics scales with the square of the carrier density, suggesting that direct seeding could lead to higher yield. The emitted harmonics should have a temporal profile consisting of a train of subcycle pulses with duration on the order of 650 as depending on the crystal thickness.