Electron Scattering and Static Field Effects in High-order Harmonic Generation in Solid Systems

Abstract

The strong non-linear light emission induced by a high-intensity laser in solid systems has become a research topic of immense interest over the last few years. Under such a strong laser, electrons from the material will generate photons with energy being integer multiple of that of the input laser photon. This specific light emission process is addressed as high-order harmonic generation (HHG) and has been widely studied in systems of atomic or molecular gas. With the great understanding of the mechanisms of the photon emission process, several powerful applications based on the gas-phase HHG are developed, enabling the generation of isolated short pulses, atomic or molecular orbital tomography, and real-time observation of electron dynamics. Recently HHG has also been observed in solid systems using a semiconductor as a target. Considering many useful applications utilizing HHG from gas systems have been developed and widely utilized in various scientific fields, adaptation of the applications based on gas-phase HHG to the realm of solid-phase HHG has been pursued by many researchers. Whether the adaptation could be carried out highly depends on what physicists know about solid-phase HHG. As a result, a deep understanding of the dynamics and development of theoretical models are highly demanded in the community of solid-phase HHG.

In this thesis we investigate solid-phase HHG under the influence of electron scattering or an additional static field in an attempt to achieve a better understanding of the underline dynamics. For the studies of electron scattering, we integrate Umklapp scattering into the generalized three-step model and compare the results from this modified model with those from quantum simulations. This leads to our publication showing that in HHG power spectra each of the multi-plateau, which originates from the band climbing, is dominated by the light emission from electron-hole pairs experiencing a specific number of scattering; An electron-hole pair with zero, one, and two scattering before emitting a photon mainly contributes to the first, second, and third plateaus of an HHG power spectrum, respectively. In addition, we also consider another simple modification to the generalized three-step model for treating general scattering effects in solids based on a mean-free-path approach. We find that such a simple modification could reproduce the wavelength independence of cutoff energy for solid-phase HHG, suggesting such behavior is directly related to scattering processes in solids. As for the studies on the effect of an additional static field, we add a static electric field on top of a driving laser for HHG based on a simple two-band parabolic quantum model. The resulting HHG power spectra yield an overall lower emission intensity and static-field-dependent cutoff energy. When increasing the static field from zero, the cutoff energy will increase, reach a maximum, and then decrease to the band gap when the static field becomes as strong as the oscillating driving laser. This static-field-dependence of the cutoff energy could be described by the two competing mechanisms induced by a static field: reduced probability for overall electron-hole recombination and increased chances for recombination for some high-energy electron-hole pairs when the static field happens to align with the driving laser pushing the pairs together.

In addition to the studies on dynamics of solid-phase HHG, we also present a preliminary investigation of the core electron absorption for bulk aluminum under X-ray by time-dependent density functional theory (TDDFT). The aim was to verify whether the underline theoretical model could capture the well-known absorption saturation in aluminum so as to estimate the applicability of the simulation framework for solid-phase HHG driven by X-ray pulses. From our simulations, the absorption saturation is indeed reproduced qualitatively. This suggests the first step of solid-phase HHG in the three-step model, namely the excitation of electrons, could be captured by ab initio simulations based on TDDFT.