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.

Electron migration in molecules is the progenitor of chemical reactions and biological functions after light-matter interaction. Following this ultrafast dynamics, however, has been an enduring endeavor. Here we demonstrate that, by using machine learning algorithm to analyze high-order harmonics generated by two-color laser pulses, we are able to retrieve the complex amplitudes and phases of harmonics of single fixed-in-space molecules. These complex dipoles enable us to construct movies of laser-driven electron migration after tunnel ionization of N₂and CO₂molecules at time steps of 50 attoseconds. Moreover, the angular dependence of the migration dynamics is fully resolved. By examining the movies, we observe that electron holes do not just migrate along the laser polarization direction, but may swirl around the atom centers. Our result establishes a general scheme for studying ultrafast electron dynamics in molecules, paving a way for further advance in tracing and controlling photochemical reactions by femtosecond lasers.

Molecules constituted by different isotopes are different in vibrational modes, making it possible to elucidate the mechanism of a chemical reaction via the kinetic isotope effect. However, the real-time observation of the vibrational motion of isotopic nuclei in molecules is still challenging due to its ultrashort time scale. Here we demonstrate a method to monitor the nuclear vibration of isotopic molecules with the frequency modulation of high-order harmonic generation (HHG) during the laser-molecule interaction. In the proof-of-principle experiment, we report a red shift in HHG from H₂ and D₂. The red shift is ascribed to dominant HHG from the stretched isotopic molecules at the trailing edge of the laser pulse. By utilizing the observed frequency shift, the laser-driven nuclear vibrations of H₂ and D₂ are retrieved. These findings pave an accessible route toward monitoring the ultrafast nuclear dynamics and even tracing a chemical reaction in real time.

We propose an all-optical method to directly reconstruct the band structure of semiconductors. Our scheme is based on the temporal Young’s interferometer realized by high harmonic generation with a few-cycle laser pulse. As a time-energy domain interferometer, temporal interference encodes the band structure into the fringe in the energy domain. The relation between the band structure and the emitted harmonic frequencies is established. This enables us to retrieve the band structure from the spectrum of high harmonic generation with a single-shot measurement. Our scheme paves the way to study matters under ambient conditions and to track the ultrafast modification of band structures.

We demonstrate an angular high-harmonic spectroscopy method to probe the spinning dynamics of a molecular rotation wave packet in real time. With the excitation of two time-delayed, polarization-skewed pump pulses, the molecular ensemble is impulsively kicked to rotate unidirectionally, which is subsequently irradiated by another delayed probe pulse for high-order harmonic generation (HHG). The spatiotemporal evolution of the molecular rotation wave packet is visualized from the time-dependent angular distributions of the HHG yields and frequency shift measured at various polarization directions and time delays of the probe pulse. The observed frequency shift in HHG is demonstrated to arise from the nonadiabatic effect induced by molecular spinning. Different from the previous spectroscopic and Coulomb explosion imaging techniques, the angular high-harmonic spectroscopy method can reveal additionally the electronic structure and multiple orbitals of the sampled molecule. All the experimental findings are well reproduced by numerical simulations. Further extension of this method would provide a powerful tool for probing complex polyatomic molecules with HHG spectroscopy.

Elliptically polarized high-order harmonics opens a path toward the study of ultrafast dynamics in circular dichroism of magnetic materials, chiral molecules, and electronic spin motion. Recently, efficient high-order harmonic generation with controllable ellipticity has attracted considerable attention in experiment and theory. Here, we experimentally demonstrate a scenario using cross-linearly-polarized two-color fields consisting of a fundamental field and its second harmonic (SH). Through adjusting the relative phase, crossing angle, and intensity ratio of the cross-linearly-polarized two-color field, we obtain ellipticity-tunable high-order harmonics, with ellipticity up to $\varepsilon =0.73$. Meanwhile, the elliptically polarized high-order harmonics preserve high efficiency. Furthermore, when the intensity of the SH field is stronger than that of the fundamental field, the even order harmonics will become several times stronger than the odd order harmonics with opposite helicity.