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We theoretically investigate the high-order harmonic generation (HHG) from ZnO crystals driven by orthogonally polarized two-color (OTC) laser fields. By solving the semiconductor Bloch equation (SBE) in two dimensions, it is found that the HHG yields show a high sensitivity to the relative phase between the two fields. By changing the laser intensity, the yields of HHG show two maxima in the high-order region. To reveal the physical origin of these phenomena, we analyze the behavior of the electron-hole pair in the real and reciprocal spaces by the recollision model, respectively. It could qualitatively interpret the results by SBE simulations. Our analysis demonstrates that the OTC laser fields could control the electron-hole dynamics and HHG processes efficiently.

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.

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.

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.

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.

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 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.

High-order harmonic generation (HHG) is a nonlinear nonperturbative process in ultrashort intense laser-matter interaction. It is the main source of coherent attosecond (1 as = 10−18 s) laser pulses to investigate ultrafast electron dynamics. HHG has become an important table-top source covering a spectral range from infrared to extreme ultraviolet (XUV). One way to extend the cutoff energy of HHG is to increase the intensity of the laser pulses. A consequence of HHG in such intense short laser fields is the characteristic nonadiabatic red and blue shifts of the spectrum, which are reviewed in the present work. An example of this nonperturbative light-matter interaction is presented for the one-electron nonsymmetric molecular ion HeH2+, as molecular systems allow for the study of the laser-molecule orientation dependence of such new effects including a four-step model of MHOHG (Molecular High-order Harmonic Generation).

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.

Laser-solid interaction was investigated numerically by simulating the Bloch electron wave-packet dynamics in periodic potentials. We introduce a quasi-classical model in the k space combined with the energy band structure to reveal the mechanisms of high-order harmonic generation (HHG) processes occurring in a sub-cycle timescale. We also propose an efficient way to enhance the yield of HHG in inhomogeneous laser fields below the damage threshold.

Molecular high-order harmonic generation (MHOHG) in a non-Born-Oppenheimer treatment of H(2)(+), D(2)(+), is investigated by numerical simulations of the corresponding time-dependent Schrödinger equations in full dimensions. As opposed to previous studies on amplitude modulation of intracycle dynamics in MHOHG, we demonstrate redshifts as frequency modulation (FM) of intercycle dynamics in MHOHG. The FM is induced by nuclear motion using intense laser pulses. Compared to fixed-nuclei approximations, the intensity of MHOHG is much higher due to the dependence of enhanced ionization on the internuclear distance. The width and symmetry of the spectrum of each harmonic in MHOHG encode rich information on the dissociation process of molecules at the rising and falling parts of the laser pulses, which can be used to retrieve the nuclear dynamics. Isotope effects are studied to confirm the FM mechanism.

Orientation-dependent photoelectron holography from the one-electron polar molecular ion HeH2+ in linearly polarized few-cycle laser fields is studied numerically. We identify four dominant holography patterns simultaneously with one shot of lasers and show that these are sensitive to the molecular structure and the orientation angle between the molecular axis and laser polarization direction. Due to the preferential enhanced ionization from one direction of the molecular axis, two kinds of forward photoelectron holography and two backward holography interference patterns predicted by a semiclassical model showup simultaneously for parallel orientation. Coulomb focusing effects are shown to be crucial for the backward scattering holography and a weak forward scattering holography channel with relatively small overlap. In contrast, after increasing the orientation angle, the backward scattering patterns disappears gradually because of the smaller scattering cross sections. Only one forward scattering holography can be clearly identified in the perpendicular orientation. Ultrashort and intense laser pulses are shown to be preferred for photoelectron holography. Intercycle interference rings in the above-threshold ionization are suppressed and consequently the intracycle rescattering signals are enhanced.

Dynamic imaging of the molecular structure of ${\mathrm{H}}_{2}^{+}$ is investigated by attosecond photoelectron holography. The interference between direct (reference) and backward rescattered (signal) photoelectrons in attosecond photoelectron holography reveals the birth time of both channels and the spatial information of molecular structure. This is confirmed by simulations with a semiclassical model and numerical solutions of the corresponding time-dependent Schr\"odinger equation, suggesting an attosecond time-resolved way of imaging molecular structure obtained from laser induced rescattering of ionized electrons. It is shown that both short and long rescattered electron trajectories can be imaged from the momentum distribution.

Time-resolved photoelectron holography from atoms using midinfrared laser pulses is investigated by solving the corresponding time-dependent Schr\"odinger equation (TDSE) and a classical model, respectively. The numerical simulation of the photoelectron angular distribution of Xe irradiated with a low-frequency free-electron laser source agrees well with the experimental results. Different types of subcycle interferometric structures are predicted by the classical model. Furthermore with the TDSE model it is demonstrated that the holographic pattern is sensitive to the shape of the atomic orbitals. This is a step toward imaging by means of photoelectron holography.

Molecular high-order harmonic generation (MHOHG) from the polar diatomic molecule HeH${}^{2+}$ in short intense laser fields is studied numerically. Due to the nonadiabatic response of the molecular dipole to the rapid change of laser intensity, a spectral redshift is predicted in high-intensity and ultrashort laser pulses, contrary to the blueshift observed in the harmonics generated from atoms in long laser pulses. The MHOHG temporal structures are investigated by a wavelet time-frequency analysis, which shows that the enhanced excitation of localized long lifetime excited states shifts the harmonic generation spectrum in the falling part of short laser pulses, due to the presence of a permanent dipole moment, and thus is unique to polar molecules.

Multichannel molecular high-order harmonic generation (MHOHG) from the asymmetric diatomic molecule HeH${}^{2+}$ in two-color laser fields is investigated from numerical simulation of the corresponding time-dependent Schr\"odinger equation (TDSE). It is found that the laser-induced electron transfer (LIET) plays a crucial role in MHOHG, which leads to the multichannel harmonic generation from the ground and long-lifetime excited states. LIET is sensitive to the phase differences of the two-color laser pulses, which can be used to control the enhanced excitation (EE) and enhanced ionization (EI) of the system. Both EE and EI have a strong influence on the overall intensity of the MHOHG spectrum, and there may be four orders of magnitude difference in the MHOHG intensity between the enhanced and suppressed cases. In addition, owing to the asymmetry of the two-color laser fields and the recombination of electron with the neighboring ion, multiple cutoff energies are observed. The mechanism of these effects are confirmed by classical simulations.

We introduce the exterior complex scaling transformed B-spline basis sets into the Floquet theory to study the ionization dynamics of symmetric and asymmetric linear molecular ion H(3)2+ in dc and intense low-frequency laser fields. For several lowest electronic states, the double-peak structure of the ionization rate as a function of the internuclear distance is observed. We explore the insights of the charge-resonance-enhanced multiphoton ionization of the symmetric and asymmetric H(3)2+ at some critical internuclear distances R(c) by the Floquet theory. A detailed analysis of the behavior of the quasienergy states corresponding to the lowest three electronic states is presented. For the purpose of comparison, the total ionization rate is also calculated by numerically solving the full-dimensional time-dependent Schrodinger equation. Very good agreement is achieved between the results obtained by these two different methods.