The time-dependent Schrödinger equation (TDSE) is usually treated in the real space in the textbook. However, it makes the numerical simulations of strong-field processes difficult due to the wide dispersion and fast oscillation of the electron wave packets under the interaction of intense laser fields. Here we demonstrate that the TDSE can be efficiently solved in the momentum space. The high-order harmonic generation and above-threshold ionization spectra obtained by numerical solutions of TDSE in momentum space agree well with previous studies in real space, but significantly reducing the computation cost.

We propose a simple pump-coupling-seed scheme to examine the optical X²Σ_g⁺-A²Π_u coupling in N₂⁺ lasing. We produce the N₂⁺ lasing at 391 nm, corresponding to the B²Σ_u⁺(v'=0)-X²Σ_g⁺(v=0) transition, by externally seeding the N₂⁺ gain medium prepared by irradiation of N₂ with an intense pump pulse. We then adopt a weak coupling pulse in between the pump and seed pulses, and show that the intensity of the 391-nm lasing can be efficiently modulated by varying the polarization direction of the coupling pulse with respect to that of the pump pulse. It is found that when the polarization directions of the pump and coupling pulses are perpendicular, the 391-nm lasing intensity is more sensitive to the coupling laser energy, which reflects the inherent nature of the perpendicular X²Σ_g⁺-A²Π_u transition.

We macroscopically investigate the effect of the laser intensity and gas density on quantum trajectories in the high-order harmonic generation of Ne atoms irradiated by few-cycle, 800-nm laser pulses. The time-frequency profile of the harmonics shows that the long quantum trajectory is dominant at both lower and higher gas densities for a low laser intensity. At high laser intensities, the long quantum trajectory plays an important role for lower gas densities, while the short quantum trajectory is dominant at higher gas densities. An analysis of the phase mismatch for high-order harmonic generation shows that the primary emission of the quantum trajectories is determined by dynamic changes in the laser electric field during the propagation process.

The high-order harmonic generation from a model solid structure driven by an intense laser pulse is investigated using the semiconductor Bloch equations (SBEs). The main features of harmonic spectrum from SBEs agree well with the result of the time-dependent Schrödinger equation (TDSE), and the cut-off energy can be precisely estimated by the recollision model. With increasing the field strength, the harmonic spectrum shows an extra plateau. Based on the temporal population of electron and the time-frequency analysis, the harmonics in the extra plateau are generated by the Bloch oscillation. Due to the ultrafast time response of the Bloch electron, the generated harmonics provide a potential source of shorter isolated attosecond pulse.

According to the frequency-domain theory, we investigate the asymmetric structure of above-threshold ionization (ATI) spectrum of an atom in two-color elliptically polarized (EP) laser fields. When both laser fields are linearly polarized (LP), the spectrum shows that the multi-plateau structure is symmetric about the emitted angle of electron at π/2, while the spectrum becomes asymmetric and shifts rightwards with the increase of the EP degree of the IR laser field. Since the total ATI process is regarded as including direct ATI and the rescattering ATI, we analyze the spectrum structure of direct ATI and rescattering ATI separately. Using the saddle-point approximation, we find that for direct ATI, the fringes on the spectrum are mainly attributed to the fact that the ionization probability becomes very small when the direction of emitted electrons is perpendicular to the direction of the XUV laser polarization; while for the rescattering ATI, the interference fringes on the spectrum mainly come from the superposition of the waist structures on the spectra of all sub-channels.

High-order harmonic generation below ionization threshold of He atom in the laser field is investigated by solving the three-dimensional time-dependent Schrödinger equation. An angular momentum-dependent model potential of He atom was used for getting the accurate energy levels of singlet states. The satellite-peak structures of the below-threshold harmonic generation (BTHG) of He are observed. We analyze the emission properties of the BTHG by employing a synchrosqueezing transform technique. We find that the satellite-peak structures have two types related to two kinds of transitions. One is the transition of the dressed states of the excited states, the other is the transition between the excited states and the ground state in the field-free case. Furthermore, our results show that the maximum Stark shift of the 2p state is about 0.9U_p (penderomotive energy), and that of the 4p state is about 1.0U_p. It indicates that the energy difference between some satellite- and main-peaks of the BTHG can be used to measure the maximum Stark shift of the excited states of He atom in the laser field.

We investigate experimentally multi-orbital effects in high-order harmonic generation (HHG) from aligned CO₂ and N₂O molecules by intense femtosecond laser fields with linear and elliptical polarizations. For either of the aligned molecules, a minimum in the harmonic spectrum is observed, the position of which shifts to lower-order harmonics when decreasing the intensity or increasing the ellipticity of the driving laser. This indicates that the minimum originates from the dynamic interference of different channels, of which the tunneling ionization and recombination are contributed via different molecular orbitals. The results show that both the highest occupied molecular orbital (HOMO) and low-lying HOMO-2 in CO₂ (or HOMO-1 in N₂O) contribute to the molecular HHG in both linearly and elliptically polarized strong laser fields. Our study would pave a way for understanding multi-electron dynamics from polyatomic molecules irradiated by strong laser fields.

We ab initio investigate the interaction between the hydrogen atom and the inhomogeneous field which is induced by resonant plasmons within a metal nanostructure. Same as normal laser pulse (homogeneous field), only odd-harmonic generation occurs when the bow-tie nanostructure is utilized. For the single nanotip case, the even-harmonic generation can be distinctly found in the harmonic emission spectrum. By investigating the symmetry and trajectories of different inhomogeneous fields, we demonstrate that the breaking symmetry of system can enable even high harmonic generations.

Bichromatic circularly polarized fields provide a useful tool to probe the ionization dynamics. In this work, we compare the photoelectron momentum distribution in few-cycle bichromatic field of different helicities. The spectral features are analyzed with semiclassical trajectories derived from the strong field approximation. In particular, the interference fringes in momentum distribution are investigated by tracking the ionization time and tunneling exits of released photoelectrons. Different types of trajectories that contribute to the interference fringes are elucidated.

We experimentally investigate Coulomb exploded directional double ionization of N₂O molecules in elliptically polarized femtosecond laser pulses. The denitrogenation and deoxygenation channels are accessed via various pathways. It leads to distinct asymmetries in directional breaking of the doubly ionized N₂O molecules versus the instantaneous laser field vector, which is revealed by tracing the sum-momentum spectra of the ionic fragments as a recoil of the ejected electrons. Our results demonstrate that the accessibility of the Coulomb exploded double ionization channels of N₂O molecules are ruled by the detailed potential energy curves, and the directional emission of the fragments are governed by the joint effects of the electron localization-assisted enhanced ionization of the stretched molecules and the profiles of the molecular orbitals.