We introduce a quasi-classical model in the k space combined with the energy band structure of solids to understand the mechanisms of high-order harmonic generation (HHG) process occurring in a subcycle timescale. This model interprets the multiple plateau structure in HHG spectra well and the linear dependence of cutoff energies on the amplitude of vector potential A₀ of the laser fields. It also predicts the emission time of HHG, which agrees well with the results by solving the time-dependent Schrödinger equation (TDSE). It provides a scheme to reconstruct the energy dispersion relations in Brillouin zone and to control the trajectories of HHG by varying the shape of laser pulses. This model is instructive for experimental measurements.

We theoretically study high-order harmonic generation (HHG) from solid-phase systems in spatially inhomogeneous strong laser fields originated by resonant plasmons within a metallic nanostructure. The intensity of the second plateau in HHG may be enhanced by two to three orders and be comparable with the intensity of the first plateau. This is due to bigger transition probabilities to higher conduction bands. It provides us with a practical way to increase the conversion efficiency of HHG with laser intensity below the damage threshold. It presents a promising way to triple the range of HHG spectra in experimental measurements. It also allows us to generate intense isolated attosecond pulses from solids driven by few-cycle laser fields.

We studied the ultrafast dynamics of high-order harmonic generation (HHG) from solids numerically. It is found that a superposition of Bloch oscillation in the same band and Zenner tunneling to its neighboring conduction band (i.e., Bloch-Zener oscillation effect) play significant roles in HHG when the Bloch electrons cross the boundary of the first Brillouin zone. It increases the number of the harmonic emission channels. These multichannel signals extend the cutoff energy of the plateau in the HHG spectra and enhance both the intra- and interband contributions. The interference of different channels makes the structure of the HHG spectra complex. The multichannel dynamics in the monochromatic and two-color laser fields are demonstrated in a periodic potential model and single-crystal MgO, respectively. It provides an alternative way to control the ultrafast electron dynamics and HHG emission processes in solids.

For the high-order harmonic generation (HHG) from solids, the dephasing process induced by many-body interactions has been discussed extensively in the studies of using the semiconductor Bloch equations (SBEs). However, the role of dephasing in solid HHG is always ignored in the simulations of using a time-dependent Schrödinger equation under the independent electron approximation. To solve this problem, we introduce the imaginary potential to phenomenologically depict the dephasing process in the solid HHG. Compared with the results of experiment and SBEs, the validity of this approach has been verified by the laser intensity- and wavelength-dependent HHG spectra. Diffusion of the quantum wave packet controls the time-frequency characteristic in solid HHG. To obtain semiclassical trajectories whose predictions are consistent with the quantum simulations, we propose an open-trajectory model by relaxing the zero displacement condition in the tunneling and recollision steps. In addition, the quantum decoherence adjusts the chirp of the emission time profile via modulating the coherent overlap between recombined wave packets, which further paves a way to generate an attosecond pulse from solids and probe the dephasing time via the high-harmonic spectroscopy.

High-order harmonic generation (HHG) in solid and gaseous targets has been proven to be a powerful avenue for the generation of attosecond pulses, whereas the influence of electron-phonon scattering on HHG is a critical outstanding problem. Here we first introduce a temperature-dependent lattice vibration model by characterizing the spacing fluctuation. Our results reveal that (i) structural disorder induced by lattice vibration does not lead to generation of even-order harmonics; (ii) dephasing of HHG occurs as the lattice temperature is growing; (iii) an open-trajectory picture predicts the maximal photon energy in the temperature-dependent HHG spectra. Moreover, a formula assessing dephasing time with lattice temperature is proposed to identify the timescale of electron-phonon scattering. This work paves the way to study the non-Born-Oppenheimer effect in solids driven by a strong field.