Role of Van Hove singularities and effective mass anisotropy in polarization-resolved high harmonic spectroscopy of silicon

Nonlinear optical response of materials exposed to strong nonresonant light fields leads to production of high energy photons whose spectra contain fingerprints of the coherent electron dynamics in the material. In this paper we investigate how the high harmonic spectra generated in crystalline silicon are linked to specific properties of its band structure. By comparing the polarization anisotropy of high harmonic spectra for two distinct frequencies of the driving pulses we show that the anisotropy has two sources. When driven by mid-infrared light, the signal at specific photon energies is enhanced by the presence of Van Hove singularities in the joint density of states of silicon. With near-infrared driving pulses, in contrast, the high harmonic yield is mainly influenced by the anisotropy of the reduced mass of electron-hole pair, which is related to the nonresonant excitation probability. The experimental results are compared with numerical calculations using time-dependent density functional theory. High harmonic generation in solids has been intensively studied for compact extreme ultraviolet light sources and for understanding of the inner workings of solids. In this study, the authors conducted polarization-resolved nonlinear spectroscopy of silicon with numerical calculations and uncovered the significant influence of van Hove singularities on the processes of high harmonic generation.