Analysis on the minimum structure of harmonic spectra from MgO crystals.

Recent theoretical and experimental findings have demonstrated the minimum characteristic in the harmonic spectrum of bulk MgO crystals subjected to intense laser pulses. However, the dominant mechanism behind this minimum structure is still under debate. This study simulates the harmonic spectrum from a MgO crystal in a linearly polarized laser pulse by solving multi-band semiconductor Bloch equations. The results show that the minimum feature at 20 eV in the MgO harmonic spectra from 1700 and 800 nm laser pulses is due to band dispersion and interference between interband harmonics. Notably, the disappearance of the minimum structure at 14 eV in the harmonic spectrum from the 800 nm laser is attributed to the intensity suppression of higher energy harmonics, caused by decreased electron population at the boundary of the first Brillouin zone in the multi-band case. These findings offer insights into the spectral structure of solid-state harmonics, contributing to the all-optical reconstruction of the crystal band based on its harmonic spectrum.

Enhancing harmonic brightness near the cutoff region by using laser pulses with a small positive chirp.

Efficient enhancement of harmonic brightness near the cutoff region is achieved by employing laser pulses with a small positive chirp in theory, where the laser intensity and frequency near the peak of the laser pulse are almost unchanged relative to the chirp-free field. The improvement of harmonic brightness is achieved under the condition that the ionization probability is almost unchanged. Through the analysis of the harmonics contributed by the rising and falling parts of the laser pulse, we have uncovered a "frequency compensation" mechanism that leads to an enhanced harmonic brightness near the cutoff region. Under appropriate chirp parameters, the harmonics contributed by the rising and falling parts can be constructively interfered in a smaller frequency range with greater intensity, thereby obtaining harmonics with good monochromaticity and high brightness. This study explains the mechanism of harmonic brightness enhancement from a new perspective, and provides a new idea for harmonic regulation without changing the ionization.

Circularly polarized attosecond light generation from OCS molecules irradiated by the combination of linear polarized infrared and orthogonal terahertz fields.

Researching ultrafast dynamics and creating coherent light sources will both benefit significantly from the establishment of polarization control in high-order harmonic generation (HHG). By employing the time-dependent density functional theory method, we investigate HHG of carbonyl sulfide molecules using a combination of a linear polarized infrared (IR) laser and a weaker orthogonal Terahertz (THz) field. Our findings show that by adjusting the amplitude of the THz field, the movement scale of electrons in the THz direction can be tuned, thereby one can control the harmonic intensity in the IR laser direction. This method allows for the creation of near-circularly polarized attosecond pulses. Furthermore, the ellipticity of the attosecond pulse may be changed by modifying the carrier-envelope phase of the IR laser pulse.

Minimum structure of high-order harmonic spectrum from molecular multi-orbital effects involving inner-shell orbitals.

The spectral features of high-order harmonic spectra can provide rich information for probing the structure and dynamics of molecules in intense laser fields. We theoretically study the high harmonic spectrum with the laser polarization direction perpendicular to the N2O molecule and find a minimum structure in the plateau region of the harmonic spectrum. Through analyzing the time-dependent survival probability of different electronic orbitals and the time-dependent wave packet evolution, it is found that this minimum position is caused by the harmonic interference of HOMO a, HOMO-1, and HOMO-3 a orbitals. Moreover, this interference minimum is discovered over a wide frequency range of 0.087 a.u. to 0.093 a.u., as well as a range of driving laser intensities with peak amplitudes between 0.056 a.u. and 0.059 a.u.. This study sheds light on the multi-electron effects and ultrafast dynamics of inner-shell electrons in intense laser pulses, which are crucial for understanding and controlling chemical reactions in molecules.

Effect of pulse duration on the above-threshold ionization of a hydrogen atom irradiated by a 400 nm intense laser.

The photoelectron emission spectra generated by the interaction between ultrashort intense laser pulses and atoms can reveal the ultrafast dynamics of electrons. By using the numerical solution of the time-dependent Schrödinger equation in momentum space, the photoelectron emission spectra of atoms irradiated by 400 nm intense lasers with different durations of the pulse has been investigated. In the photoelectron emission spectrum, in addition to the above-threshold ionization peaks due to ionization interference in multiple cycles and the sideband peaks mainly due to the interference of ionized electrons at different moments along the rising edge of the laser pulse envelope, additional peaks of photoelectron emission whose intensity appears to oscillate with the increasing duration of the laser pulse can also be observed. Based on strong-field approximation and the population's analysis of the bound state, it is found that these photoelectron peaks originate from the ionization of the excited state and the oscillations of these peaks are due to the superposition of their peak energy positions with the sideband energy positions. Furthermore, it is demonstrated that the energy positions of the maximum intensity of the photoelectron emission spectra move towards the higher energy end as the duration of the driving laser pulse extends. This phenomenon can be attributed to the fact that the main moment of ionization of atoms changes with the increasing duration of the driving laser pulse, thus allowing the real-time ionization of atoms to be probed using photoelectron emission spectra.

Calculation of high-order harmonic generation of atoms and molecules by combining time series prediction and neural networks.

High-order harmonic generation (HHG) from the interaction of ultra-intense laser pulses with atoms is an important tabletop short-wave coherent light source. Accurate quantum simulations of it present large computational difficulties due to multi-electron multidimensional effects. In this paper, the time-dependent response of hydrogen atoms is calculated using a time-series prediction scheme, the HHG spectrum is reconstructed very accurately. The accuracy of the forecasting is further improved by using a neural network scheme. This scheme is also applied to the simulation of the harmonic emission on multi-electron systems, and the applicability of the scheme is confirmed by the harmonic calculation of complex systems. This method is expected to simulate the nonlinear dynamic process of multi-electron atoms and molecules irradiated by intense laser pulses quickly and accurately.

All-optical reconstruction of three-band transition dipole moments by the crystal harmonic spectrum from a two-color laser pulse.

When a bulk solid is irradiated by an intense laser pulse, transition dipole moments (TDMs) between different energy bands have an important influence on the ultra-fast dynamic process. In this paper, we propose a new all-optical method to reconstruct the k-dependent TDMs between multi-bands using a crystal high-order harmonic generation (HHG). Taking advantage of an obvious separation of bandgaps between three energy bands of an MgO crystal along the <001 > direction, a continuous harmonic spectrum with two plateaus can be generated by a two-color laser pulse. Furthermore, the first harmonic platform is mainly dominated by the polarization between the first conduction band and the valence band, and the second one is largely attributed to the interband HHG from the second conduction band and the valence band. Therefore, the harmonic spectrum from a single quantum trajectory can be adopted to map TDMs between the first, second conduction bands, and the valence one. Our work is of great significance for understanding the instantaneous properties of solid materials in the strong laser field, and will strongly promote the development of the HHG detection technology.

Effect of interband polarization on a solid's high-order-harmonic generation just belowthe band gap.

A series of theoretical and experimental results has proved that harmonics below/above the band gap are produced mainly by the intraband current/interband polarization for solids in strong mid-infrared laser pulses. However, which mechanism dominates the harmonic process is still debated. In this work, based on simulating high-order-harmonic generation from an MgO crystal in a linearly polarized mid-infrared laser by solving semiconductor Bloch equations, we demonstrate that harmonics just below the band gap originate from the interference between intraband and interband currents. Furthermore, it is found that intensities of harmonics just below the band gap are apparently enhanced with an increase in the incident laser's strength. By analyzing the band dispersion and the transition dipole moment of the 001-cut MgO crystal, this can be attributed to the interband polarization between two conduction bands.

All-optical reconstruction of k-dependent transition dipole moment by solid harmonic spectra from ultrashort laser pulses.

Band structure and transition dipole moment play important roles in high-order harmonic generation from solid materials. In this work we provide a new all-optical technique to reconstruct the momentum-dependent transition dipole moment using the harmonic spectrum from MgO crystal driven by an ultrashort mid-infrared laser pulse. Under the influence of the ultrashort laser pulse, the emitted photon energy and the crystal momentum form a one-to-one match, in the same way between the intensity of the harmonic above the minimum bandgap and the square of the amplitude of the transition dipole moment, resulting in a realization of directly probing the transition dipole moment. Our all-optical method paves a way to image the two-dimensional transition dipole moment of crystals with the inversion symmetry.

Role of the Transition Dipole Amplitude and Phase on the Generation of Odd and Even High-Order Harmonics in Crystals.

Since the first observation of odd and even high-order harmonics generated from ZnO crystals in 2011, the dependence of the harmonic yields on the orientation of the laser polarization with respect to the crystal axis has never been properly interpreted. This failure has been traced to the lack of a correct account of the phase of the transition dipole moment between the valence band and the conduction band. Using a simple one-dimensional two-band model, here we demonstrate that the observed odd harmonics is directly related to the orientation dependence of the magnitude of the transition dipole, while even harmonics is directly related to the phase of the transition dipole. Our result points out the essential role of the complex transition dipole moment in understanding harmonic generation from solids that has long been overlooked so far.

Chirp-free isolated attosecond pulse generation from an atom irradiated by a fundamental terahertz pulse synchronizing an infrared laser pulse.

We theoretically study high-order harmonic generation (HHG) and attosecond pulses from an atom irradiated synchronically by a terahertz (THz) pulse and an infrared laser pulse. For the HHG spectrum from the THz pulse alone and the combined pulse, an apparent peak-valley structure appears the platform region. Specially, for the periodic structure generated by an atom under the action of the combined pulse is originated from the interference between the electrons ionized at different instants in the laser field, which undergo many recollision and return to the core at the same time. Therefore, continuum harmonics with few chirps from the interference enhancement region can be achieved, which result in a chirp-free isolated attosecond pulse.

Propagator for the Fokker-Planck equation with an arbitrary diffusion coefficient.

We consider a general diffusion process that is force-free and the corresponding Fokker-Planck equation with an arbitrary diffusion coefficient. A propagator for the Fokker-Planck equation of the Stratonovich form is obtained based on random walks. The characteristics of the solution are analyzed.