Terahertz radiation induced by shift currents in liquids.

Considerable progress has been made in the experimental studies on laser-induced terahertz (THz) radiation in liquids. Liquid THz demonstrates many unique features different from the gas and plasma THz. For example, the liquid THz can be efficiently produced by a monochromatic laser. Its yield is maximized with a longer driving-pulse duration. It is also linearly dependent on the excitation pulse energy. In two-color laser fields, an unexpected unmodulated THz field was measured, and its energy dependence of the driving laser is completely different from that of the modulated THz waves. However, the underlying microscopic mechanism is still unclear due to the difficulties in the description of ultrafast dynamics in complex disordered liquids. Here we propose a shift-current model. The experimental observations could be reproduced by our theory successfully. In addition, our theory could be further utilized to investigate the nuclear quantum effect in the THz radiation in H2O and D2O. This work provides fundamental insights into the origin of the THz radiation in bulk liquids.

Trajectory-controlled high-order harmonic generation in ZnO crystals.

We experimentally and theoretically study high-order harmonic generation in zinc oxide crystals irradiated by mid-infrared lasers. The trajectories are mapped to the far field spatial distribution of harmonics. The divergence angles of on-axis and off-axis parts exhibit different dependences on the order of the harmonics. This observation can be theoretically reproduced by the coherent interference between the short and long trajectories with dephasing time longer than 0.5 optical cycle. Further, the relative contribution of the short and long trajectories is demonstrated to be accurately controlled by a one-color or two-color laser on the attosecond time scale. This work provides a reliable method to determine the electron dephasing time and demonstrates a versatile control of trajectory interference in the solid high-order harmonic generation.

Multichannel High-Order Harmonic Generation from Fractal Bands in Fibonacci Quasicrystals.

High-order harmonic generation (HHG) in solids was expected to be efficient due to their high density. However, the strict transition laws in crystals restrict the number of HHG channels. Quasicrystals with fractal band structures could solve this problem and produce multichannel HHG emissions, which has been rarely studied. We simulate the Fibonacci quasicrystal (FQ) HHG for the first time and investigate the electron dynamics on the attosecond timescale. Our results reveal that (i) the acceleration theorem is approximately applicable in FQ, which provides us a valuable tool to analyze the electron trajectories. (ii) Fractal bands lead to more excitation channels, analogous to the forbidden nonvertical electron transitions in crystals. (iii) The broken symmetry results in more frequent backscattering of electrons. (iv) Compared with crystals, multichannel HHG in FQ has a higher yield and wider spectral range. Our results pave the way to understand and control the HHG in quasicrystals and shed light on a potential shorter and stronger attosecond light source based on compact solids.

Impact of Statistical Fluctuations on High Harmonic Generation in Liquids.

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.

Ultrafast intraband electron dynamics of preexcited SiO2.

Intraband high-order harmonics in solids reflect the nonlinear motion of carriers in the energy bands and have important applications. In general, multiple energy bands contribute to the intraband harmonics. We reveal the interference mechanism of intraband harmonics between electrons and holes by using the k-resolved semiclassical intraband model. The model gives a quantitative relationship between the intraband radiation yield, the energy band dispersion, and the laser parameters. Based on a preexcitation scheme, we present a method to reconstruct energy bands by using the intraband harmonics. We simulate the intraband harmonics of photo-carriers polarized by a bias field. The variation of harmonic yields as a function of a delay time results from the k-resolved energy band dispersion and reflects the Bloch oscillation of photo-carriers driven by the bias field.

Nonlinear THz radiation investigated by quantum simulations.

Terahertz (THz) waves can be generated by the nonlinear interaction between ultrashort laser pulses and air. The semiclassical photocurrent model is widely used. It is simple, but neglects the quantum effects. Some theoretical works are based on solving the time-dependent Schrödinger equation. However, it meets the difficulty of prohibitively large boxes in long-time evolution. Here we adopted the wave-function splitting algorithm to fully contain the information of photoelectrons. The contributions of the excited states and interference effects in electron wavepackets to THz radiation are studied numerically. We also theoretically investigated the THz generation from nitrogen molecules in a biased electric field. It is found that the THz yield enhancement as a function of the static field strength in experiments can be reproduced well by our method. In addition, the restriction of wavelength and phase difference in the two-color laser fields is less strict in the presence of the static field.

High-order harmonic generation from 2D periodic potentials in circularly and bichromatic circularly polarized laser fields.

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 C 4 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.

Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics.

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.

Nonadiabatic redshifts in high-order harmonic generation from solids.

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)].

Quasi-classical analysis of the dynamics of the high-order harmonic generation from solids: erratum.

Figure 2Opt. Express25, 151 (2017)] was labeled with wrong tags. Here we publish the revised figure.

Alignment dependent ultrafast electron-nuclear dynamics in molecular high-order harmonic generation.

We investigated the high-order harmonic generation (HHG) process of diatomic molecular ion H2+ in non-Born-Oppenheimer approximations (NBOA). The corresponding three-dimensional time-dependent Schrödinger equation is solved with arbitrary alignment angles. It is found that the nuclear motion can lead to spectral modulation of HHG in both the tunneling and multiphoton ionization regimes. The universal redshifts of the whole spectrum are unique in molecular HHG. The spectral width of HHG increases in NBOA. We calculated possible influences on redshifts of HHG in real experimental conditions and found that redshifts 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. It will be instructive to related experiments.

Quasi-classical analysis of the dynamics of the high-order harmonic generation from 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 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.

Probing Molecular Dynamics by Laser-Induced Backscattering Holography.

We use differential holography to overcome the forward scattering problem in strong-field photoelectron holography. Our differential holograms of H_{2} and 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 H_{2} and 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.

Probing nuclear motion by frequency modulation of molecular high-order harmonic generation.

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.

Attosecond time-resolved imaging of molecular structure by photoelectron holography.

Dynamic imaging of the molecular structure of 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 Schrödinger 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.

Multichannel molecular high-order harmonic generation from asymmetric diatomic molecules.

Multichannel molecular high-order harmonic generation (MHOHG) from a single electron asymmetric molecular ion HeH2+ is investigated numerically. It is found that considerable resonant excitation occurs by laser induced electron transfer (LIET) to neighboring ions and multiple frequency (fractional-order) harmonics are observed from the excited states shifted by some energy Δ from the main Nω energy harmonics. A time series analysis is used to confirm this MHOHG channel which is created by initial ionization from the excited state prepared by LIET and recombination to the neighboring ion at specific field phases, resulting in interference between recombination pathways from ground and excited states.