We revisit the mechanism of high-harmonic generation (HHG) from solids by comparing HHG in laser fields with different ellipticities but a constant maximum amplitude. It is shown that the cutoff of HHG is strongly extended in a circularly polarized field. Moreover, the harmonic yield with large ellipticity is comparable to or even higher than that in the linearly polarized field. To understand the underlying physics, we develop a reciprocal-space-trajectory method, which explains HHG in solids by a trajectory ensemble from different ionization times and different initial states in the reciprocal space. We show that the cutoff extension is related to an additional preacceleration step prior to ionization, which has been overlooked in solids. By analyzing the trajectories and the time-frequency spectrogram, we show that the HHG in solids cannot be interpreted in terms of the classical recollision picture alone. Instead, the radiation should be described by the electron-hole interband polarization, which leads to the unusual ellipticity dependence. We propose a new four-step model to understand the mechanism of HHG in solids.

The selection rules of high harmonic generation (HHG) are investigated using three-dimensional time-dependent density functional theory (TDDFT). From the harmonic spectra obtained with various real molecules and different forms of laser fields, several factors that contribute to selection rules are revealed. Extending the targets to stereoscopic molecules, it is shown that the allowed harmonics are dependent on the symmetries of the projections of molecules. For laser fields, the symmetries contributing to the selection rules are discussed according to Lissajous figures and their dynamical directivities. All the phenomena are explained by the symmetry of the full time-dependent Hamiltonian under a combined transformation. We present a systematic study on the selection rules and propose an intuitive method for the judgment of allowed harmonic orders, which can be extended to more complex molecules and various forms of laser pulses.

We propose an intuitive method, called the time-dependent population imaging (TDPI) method, to map the dynamical processes of high-order-harmonic generation (HHG) in solids by solving the time-dependent Schrödinger equation. It is shown that the real-time dynamical characteristics of HHG in solids, such as the instantaneous photon energies of emitted harmonics, can be read directly from the energy-resolved population oscillations of electrons in the TDPI picture. Meanwhile, the short and long trajectories of solid HHG are illustrated clearly from the TDPI picture. By using TDPI, we investigate the effects of the carrier-envelope phase in few-cycle pulses and demonstrate intuitively the HHG dynamics driven by two-color fields. Our results show that TDPI provides a powerful tool to study the ultrafast dynamics in strong fields for various laser-solid configurations and to gain insight into HHG processes in solids.

We investigate the high-order-harmonic generation (HHG) in doped semiconductors. The HHG is simulated with the single-electron time-dependent Schrödinger equation. The results show that the high-order harmonics in the second plateau generated from the doped semiconductors is about one to three orders of magnitude higher than those from the undoped semiconductor. The results are explained based on the analysis of the energy-band structure and the time-dependent population imaging. Our paper indicates that doping can effectively control the HHG in semiconductors.

We propose and theoretically demonstrate a method to generate attosecond XUV pulses with tunable ellipticity from aligned molecules irradiated by a bichromatic counterrotating circularly polarized (BCCP) driving laser field. By rotating the BCCP field, the attoseond XUV pulse varies from being left elliptically polarized to right elliptically polarized. The rotation of the BCCP field can be easily achieved by adjusting the relative phases between the two circularly polarized components. This scheme will benefit a broad range of applications, including the exploration of chiral-sensitive properties of the light–matter interaction and time-resolved imaging of magnetic structures.

High harmonic generation (HHG) from gas-phase atoms (or molecules) has opened up a new frontier in ultrafast optics, where attosecond time resolution and angstrom spatial resolution are accessible. The fundamental physical pictures of HHG are always explained by the laser-induced recollision of particle-like electron motion, which lay the foundation of attosecond spectroscopy. In recent years, HHG has also been observed in solids. One can expect the extension of attosecond spectroscopy to the condensed matter if a description capable of resolving the ultrafast dynamics is provided. Thus, a large number of theoretical studies have been proposed to understand the underlying physics of solid HHG. Here, we revisit the recollision picture in solid HHG and show some challenges of current particle-perspective methods, and present the recently developed wave-perspective Huygens–Fresnel picture for understanding dynamical systems within the ambit of strong-field physics.