We study the generation of high-harmonic radiation by Bloch electrons in a model transparent solid driven by a strong midinfrared laser field. We solve the single-electron time-dependent Schrödinger equation (TDSE) using a velocity-gauge method [M. Korbman, New J. Phys. 15, 013006 (2013)NJOPFM1367-263010.1088/1367-2630/15/1/013006] that is numerically stable as the laser intensity and number of energy bands are increased. The resulting harmonic spectrum exhibits a primary plateau due to the coupling of the valence band to the first conduction band, with a cutoff energy that scales linearly with field strength and laser wavelength. We also find a weaker second plateau due to coupling to higher-lying conduction bands, with a cutoff that is also approximately linear in the field strength. To facilitate the analysis of the time-frequency characteristics of the emitted harmonics, we also solve the TDSE in a time-dependent basis set, the Houston states [J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986)PRBMDO1098-012110.1103/PhysRevB.33.5494], which allows us to separate interband and intraband contributions to the time-dependent current. We find that the interband and intraband contributions display very different time-frequency characteristics. We show that solutions in these two bases are equivalent under a unitary transformation but that, unlike the velocity-gauge method, the Houston state treatment is numerically unstable when more than a few low-lying energy bands are used.
Publication Source (Journal or Book title)
Physical Review A - Atomic, Molecular, and Optical Physics
Wu, M., Ghimire, S., Reis, D., Schafer, K., & Gaarde, M. (2015). High-harmonic generation from Bloch electrons in solids. Physical Review A - Atomic, Molecular, and Optical Physics, 91 (4) https://doi.org/10.1103/PhysRevA.91.043839