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We develop a model potential to simulate the effective potential of a single active electron in monolayer graphene by taking the electron energy band structure calculated by the density functional theory (DFT) as a reference. Based on the single-electron Schr\"odinger equation, the model potential is used to calculate not only the energy band structure but also the transition dipole moment, charge density, and other physical quantities of graphene. These quantities are compared with results from DFT and a good consistency is achieved. The simulation of laser-graphene interaction with the same laser parameters as Yoshikawa et al. [Science 356, 736 (2017)] is performed with the time-dependent Schr\"odinger equation. The obtained driving laser ellipticity scaling, the harmonic ellipticity, and the harmonic major-axis angle can well reproduce the experimental results. It is found that the carrier-envelope phase and chirp effects are capable of regulating high-order harmonic generation in monolayer graphene. The model potential method can be extended to field-free calculations and dynamic simulations in other materials as long as the corresponding model potential is constructed.

The electron scattering process has been investigated by analyzing the interference structure in the photoelectron momentum distribution (PMD) of a hydrogen atom exposed to a single-cycle linearly polarized near-infrared laser field, based on the numerical solution of the full-dimensional time-dependent Schr\"odinger equation and the Coulomb correlative classical trajectory simulation. The interference pattern in the PMD is closely related to the form of the ultrashort pulse which is dominated by the carrier-envelope phase. A fish-bone-like pattern appears in the PMD using the sine electric field and a spider-like pattern appears using the cosine electric field. These interference structures reflect the scattering process. It is found that the stripe density of the spider-like pattern is mainly dominated by the recollision time of scattering electron trajectories, i.e., the longer the recollision time, the greater the stripe density. Therefore, the photoelectron interference pattern can be used to understand the ionization and scattering processes, and identify these processes on the attosecond time scale.

As a potential high-efficiency XUV light source, high-order harmonic generation (HHG) in solids contains the dynamic information of electrons. The interactions among many particles in solids are ubiquitous and, to some extent, modulate the motion of electrons. However, the role of electron-electron interaction (EEI) effect in solid HHG has not been well understood. In this paper, we study the laser-intensity-dependent EEI effect under the given laser pulse durations. By comparing the finite chain model with the infinite extension model, we find that, if the electric field is strong enough, the induced electric field caused by EEI is nontrivial for the finite chain model. We also find that EEI only can enhance HHG spectra in a limited frequency range under some specific intensities of the laser field in both models, and the EEI effect is related to the configuration of the system. This study can provide a reference for whether EEI can be ignored when simulating the interaction between one-dimensional solids and lasers.

High-order harmonic generation (HHG) is expected to produce high-quality coherent ultrashort light sources. We propose a scheme similar to laser mode locking to selectively enhance and compress HHG in crystals through nonuniform illuminations and phase matching. The selective enhancement of harmonics reflects attosecond-resolved electron dynamics. And these harmonic characteristics originate from the interference of harmonics from different lattices. It paves the way for the practical application of solid HHG with high conversion efficiencies and the detection of electron-hole dynamics with ultrahigh spatial-temporal resolution.

High harmonic generation (HHG) from gases and solids has been studied extensively. Whereas for liquids, it is far more challenging to understand the ultrafast dynamics with conventional methods. From a statistical perspective, we investigate the liquid-phase HHG theoretically by using a disordered linear chain. Our results reveal that (i) the harmonic spectra are characterized by a transition energy that separates the spectra into a low-energy region containing only odd harmonics and a high-energy region containing both even and odd harmonics with low yields; (ii) the transition energy depends on the fluctuation of structure and the field strength, but independent of the laser wavelength; (iii) the occurrence of dephasing is a natural result of the electron dynamics modulated by the long-range disorder. Furthermore, a simple formula is proposed to identify the transition energy, from which we correctly reproduce the experimental cutoff energies of HHG from liquid ethanol. Our results pave the way to better understand and control the HHG in liquids as another compact HHG source.

We theoretically investigate the quantum path interferences in interband transitions in solid high-order harmonic generation. The field strength scaling of the 19th harmonic yield from MgO crystal driven by 1600-nm lasers exhibits a sharp minimum. By solving the semiconductor Bloch equation, we separate the short and long trajectories. Our numerical calculation shows that this minimum originates from the coherent interferences between the short and long trajectories. We also illustrate that the interference minimum depends sensitively on the band dispersion, which can be used to retrieve the band structure accurately. We further report that the two-color fields can select the short or long quantum path effectively by controlling the phase. The yield at the plateau or cutoff region of the harmonic spectra can be enhanced by around one order of magnitude by adding a third harmonic with an intensity of only $10%$ of the fundamental field. Moreover, an isolated attosecond pulse (IAP) is synthesized by controlling the harmonic trajectories in the two-color scheme. The yield of this IAP is enhanced by one order of magnitude compared with the IAP generated by the single-color scheme.

The above-threshold ionization (ATI) of argon atoms in intense circularly polarized laser fields has been investigated by numerically solving the three-dimensional time-dependent Schr\"odinger equation and the classical Newton-Lorentz equation. There are obvious angular shifts of the photoelectron momentum distribution corresponding to the peaks in the ATI spectrum. They have little dependence on the external field and are mainly determined by the final kinetic energy. It is found that the angular shift is monotonically increasing as a function of the photoelectron final kinetic energy. Based on the classical simulations, the initial kinetic energy of electrons can be obtained by separating the contribution of the external field and Coulomb potential from the final kinetic energy. We conclude that the stronger the laser field, the bigger the initial velocity of electrons for a definite final kinetic energy. Then, based on the final kinetic energy and the laser parameters, the initial velocity can be evaluated.

We report the control of tunnel ionization in lithium niobate (${\mathrm{LiNbO}}_{3}$) using phase-controlled two-color laser fields. Through a macroscopic observable of high contrast, we disclose the crucial contribution of the microscopic spontaneous polarization of the ferroelectric material to the ionization rate: as the relative two-color phase is varied, the ablated area of ${\mathrm{LiNbO}}_{3}$ is modulated by 35% when the laser and crystal polarization directions are parallel. Rotating the sample by ${180}^{\ensuremath{\circ}}$ around the laser propagation axis leads to an out-of-phase modulation. We use a two-band model to highlight the key contribution of the material's spontaneous polarization for the symmetry breaking of the ionization rate. Our results open new perspectives for the direct control of ionization dynamics in solids by tailoring the electric field of femtosecond laser pulses.

Physical review / B 101(21), 214311 (1-6) (2020). doi:10.1103/PhysRevB.101.214311, Laser micromachining techniques using femtosecond laser pulses are employed for the fabrication of a wide range of devices, from optical waveguides and fiber Bragg gratings to microfluidic systems. In this perspective, it is important to characterize how transparent materials respond to the high-intensity laser field in order to fully understand and control the strong-field ionization process at the core of such techniques. Here, we characterize the laser polarization dependence of $y$-cut and $x$-cut ferroelectric lithium niobate (LiNbO$_3$) upon ionization. Using linearly polarized 1800-nm femtosecond pulses, we perform single-shot laser-induced ablation measurements to obtain a macroscopic observable with a large contrast compared to all-optical techniques. In the tunnel ionization regime, the crystal orientation can be correlated with the structural symmetry/asymmetry of the material. This is revealed through a variation of the ablated area when the laser polarization is rotated with respect to the c axis of the crystal. It is further found that ablation is more pronounced when the laser polarization is oriented towards angular regions containing Nb-O bonds of the unit cell, identifying the main chemical bonds contributing to the ionization of the material. The experimental results are supported by numerical simulations based on a two-band model for LiNbO$_3$., Published by Inst., Woodbury, NY

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., Previous studies on high harmonic generation from molecules have been used to identify the spectral properties and orbital contributions. Here the authors measure the isotopic effects in the energy shift of the HHG spectra caused by the nuclear motion of the molecules.

High harmonic generation (HHG) in solids provides us compact and coherent extreme ultraviolet sources. However, the low yield of HHG is the bottleneck restricting its wide applications. We propose a pump-probe scheme to selectively enhance the yield of HHG. Our simulations illustrate abnormal harmonic yield dependence on the intensity of driving or preexcitation pulses. A multielectron interference model is proposed to reveal the mechanism of the extreme nonlinear optical phenomena. We find that the $k$-resolved intraband harmonic demonstrates different symmetry, phase, and amplitude, which can be observed by using a resonant preexcitation pulse. The position of the interference minimum obtained by solving the semiconductor Bloch equations agrees well with that obtained by our $k$-resolved semiclassical model. This interference model can help us probe the $k$-resolved band structure and optimize the ultrafast electron-hole dynamics for solid harmonic processes.

The polarization of high-order harmonic generation in ${\mathrm{H}}_{2}{}^{+}$ driven by a counterrotating bichromatic $\ensuremath{\omega}/3\ensuremath{\omega}$ circularly polarized laser field is investigated theoretically. The elliptically polarized harmonics are characterized by ellipticity and rotation angle, where the latter is expanded to $[\ensuremath{-}\ensuremath{\pi}/2,\ensuremath{\pi}/2]$ by an optimized definition. We find a critical alignment angle where the ellipticity of high-energy harmonics is almost the same, so an attosecond pulse train with a high degree of polarization can be synthesized. In addition, we find that the rotation angle is always different from the alignment angle by ${90}^{\ensuremath{\circ}}$ with a small deflection. Thus, we propose a scheme to control the harmonic polarization state by the molecular alignment angle.

Laser-induced high harmonic generation (HHG) in solids strongly depends on the band structure of the target. In this work, we studied the band structure of bulk wurtzite ZnO under different strains. The changes of band structure induced by shear, uniaxial, biaxial, and isotropic strains are compared. It is found that the band gap can be narrowed or widen by modulating the external conditions, which offers an efficient way to engineer the wide-gap crystals to produce HHG. The strain effects on HHG are investigated by numerically solving the semiconductor Bloch equations. Our calculations show that the HHG yield depends sensitively on the change of band structure caused by stress- and temperature-induced strains. In addition, we found that the emission times of HHG and the ratio between inter and intraband contributions to the total solid HHG spectra can be controlled by the magnitude of strain imposed on the solid targets.

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 introduce a concise methodology to detect the parity of atomic and molecular orbitals based on photoelectron holography, which is more general than the existing schemes. It fully accounts for the Coulomb distortions of electron trajectories, does not require sculpted fields to retrieve phase information and, in principle, is applicable to a broad range of electron momenta. By comparatively measuring the differential photoelectron spectra from strong-field ionization of ${\mathrm{N}}_{2}$ molecules and their companion atoms of Ar, some photoelectron holography patterns are found to be dephased for both targets. This is well reproduced by the full-dimensional time-dependent Schr\"odinger equation and the Coulomb quantum-orbit strong-field approximation (CQSFA) simulation. Using the CQSFA, we trace back our observations to different parities of the $3p$ orbital of Ar and the highest-occupied molecular orbital of ${\mathrm{N}}_{2}$ via interfering Coulomb-distorted quantum orbits carrying different initial phases. This method could in principle be used to extract bound-state phases from any holographic structure, with a wide range of potential applications in recollision physics and spectroscopy.

We present a systematic investigation of the depolarization properties of a supercontinuum accompanied with femtosecond laser filamentation in barium fluoride (BaF2) crystal. It is found that the depolarization of the supercontinuum depends strongly on the crystal orientations with respect to the incident laser polarization. At most crystal orientations, the depolarization of the supercontinuum rises with the increase of the input laser energies and finally saturates. While at 45°, the depolarization of the supercontinuum is not changed and keeps nearly negligible with the increase of the input laser energies. These peculiar depolarization properties of the supercontinuum can be ascribed to the orientation dependence of the cross-polarized wave (XPW) generation and ionization-induced plasma scattering in the BaF2 crystal.

Different from the high-order harmonic generation (HHG) from gases, we find that the yield of HHG from solids exhibits unexpected modulations as a function of the driving laser intensity and wavelength. Its mechanism can be unraveled by the interference between currents inside the solids induced by two adjacent Zener tunneling events. Our simulations agree well with the experimental measurements of HHG from ZnSe and solid Ar. We also find that the dephasing time plays a key role in this subcycle interference and can turn it on or off by controlling the overlap between the channels. It provides an avenue to optimize the ultrafast electron dynamics and HHG emission processes in solids, which will be useful for the compact ultrafast EUV light sources. We also propose an experimental scheme by using ultrashort lasers to explore this interference in other solid materials.

We studied the high-order harmonic generation (HHG) from 2D solid materials in circularly and bichromatic circularly polarized laser fields numerically by simulating the dynamics of single-active-electron processes in 2D periodic potentials. Contrary to the absence of HHG in the atomic case, circular HHGs below the bandgap with different helicities are produced from intraband transitions in solids with C4 symmetry driven by circularly polarized lasers. Harmonics above the bandgap are elliptically polarized due to the interband transitions. High-order elliptically polarized harmonics can be generated efficiently by both co-rotating and counter-rotating bicircular mid-infrared lasers. The cutoff energy, ellipticity, phase, and intensity of the harmonics can be tuned by the control of the relative phase difference between the 1ω and 2ω fields in bicircularly polarized lasers, which can be utilized as an ultrafast optical tool to image the structure of solids.

We investigate theoretically interference effects between inter- and intraband currents in high-order harmonic generation (HHG) from solids by numerically solving the one-dimensional time-dependent Schr\"odinger equation (TDSE) for a model crystal and the semiconductor Bloch equation (SBE) for a real material zinc oxide (ZnO). The TDSE method is used to extract the explicit dynamic process of interference. We find that the contribution from constructive interference dominates the harmonic spectrum when the interband current and intraband current have good synchronism. When they lose synchronism, destructive interference counteracts contributions from inter- and intraband currents. The phase differences between intra- and interband harmonics are close to zero and $\ensuremath{\pi}$ when constructive and destructive interferences occur, respectively. In $k$ space, constructive (destructive) interference occurs near a moment when electrons at most transit to a higher (lower) energy band. Interference effects create fine structures in harmonic spectra and lead to suppression of harmonic signals which can be directly measured in experiments. The interference effect is also investigated by using the SBE method in HHG from ZnO.

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.

We study numerically the Bloch electron wave-packet dynamics in periodic potentials to simulate laser-solid interactions. We introduce an alternative perspective in the coordinate space combined with the motion of the Bloch electron wave packets moving at group and phase velocities under the laser fields. This model interprets the origins of the two contributions (intra- and interband transitions) in the high-order harmonic generation (HHG) processes by investigating the local and global behaviours of the wave packets. It also elucidates the underlying physical picture of the HHG intensity enhancement by means of carrier-envelope phase, chirp, and inhomogeneous fields. It provides a deep insight into the emission of high-order harmonics from solids. This model is instructive for experimental measurements and provides an alternative avenue to distinguish mechanisms of the HHG from solids in different laser fields.

We investigated the high-order harmonic generation (HHG) process of diatomic molecular ion $\mathrm{H}_2^+$ in non-Born-Oppenheimer approximations. The corresponding three-dimensional time-dependent Schrodinger equation is solved with arbitrary alignment angles. It is found that the nuclear motion can lead to spectral modulation of HHG. Redshifts are unique in molecular HHG which decrease with the increase of alignment angles of the molecules and are sensitive to the initial vibrational states. It can be used to extract the ultrafast electron-nuclear dynamics and image molecular structure.

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 Schrodinger 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 use differential holography to overcome the forward scattering problem in strong-field photoelectron holography. Our differential holograms of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ molecules exhibit a fishbonelike structure, which arises from the backscattered part of the recolliding photoelectron wave packet. We demonstrate that the backscattering hologram can resolve the different nuclear dynamics between ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ with subangstrom spatial and subcycle temporal resolution. In addition, we show that attosecond electron dynamics can be resolved. These results open a new avenue for ultrafast studies of molecular dynamics in small molecules.

We investigate the high harmonic generation (HHG) from solids by simulating the dynamics of a single active electron in periodic potentials. The corresponding time-dependent Schr\"odinger equations (TDSE) are solved numerically by using B-spline basis sets in coordinate space. The energy band structure and wave vectors can be directly retrived from the eigenfunctions. The harmonic spectra obtained agree well with the results simulated by TDSE in $k$ space using Bloch states and show a two-plateau structure. Both of the cutoff energies of the two plateaus in the harmonic spectrum scale linearly with the field strength. We also study HHG driven by intense few-cycle laser pulses and find that the cutoff energy of the harmonic spectrum is as sensitive to the changes of the carrier envelope phase, as to HHG from gas samples, which suggests recollision pictures in HHG as found by recent experiments (Nature {\bf 522}, 462 (2015)).

We studied the multi-plateau high-order harmonic generation (HHG) from solids numerically. It is found that the HHG spectra in the second and higher plateaus are redshifted in short laser pulses due to the nonadiabatic effect. The corresponding FWHMs also increase as a function of the harmonic order, suggesting the step-by-step excitation of higher conduction bands in the HHG process. Although the system is symmetric in the coordinate space, even-order harmonics are present. It is due to the fact that the symmetry of electron motions and the population in the higher conduction bands is broken in the k space and time domain based on the indirect step-by-step excitation model. Our numerical results are in good agreement with recent experimental measurements of Ndabashimiye et al. [Nature 534, 520 (2016)].