Probe of Multielectron Dynamics in Xenon by Caustics in High-Order Harmonic Generation

Highly versatile, two-color setup for high-order harmonic generation using spatial light modulators

We present a novel, interferometric, two-color, high-order harmonic generation setup based on a turn-key Ytterbium-doped femtosecond laser source and its second harmonic. Each interferometer arm contains a spatial light modulator with individual capabilities to manipulate the spatial beam profiles and to stabilize the relative delay between the fundamental and the second harmonic. In addition, separate control of the relative power and focusing geometries of the two color beams is implemented to conveniently perform automated scans of multiple parameters. A live diagnostics system gives continuous information during ongoing measurements.

Coulomb-induced emission time shifts in high-order harmonic generation from H2

Accurate emission times of high-order harmonic generation (HHG) are vital for high-precision ultrafast detection in attosecond science, but a quantitative analysis of Coulomb effects on this time is absent in the molecular HHG. Here, we investigate the Coulomb-induced emission-time shift in HHG of H2+ with two different internuclear distances R, where the times obtained via the Gabor transform of numerical data from solving the time-dependent Schrödinger equation are used as simulation experiment results. Based on the molecular strong-field approximation, we develop a trajectory-resolved classical model that takes into account the molecular two-center structure. By selecting appropriate electron trajectories and including Coulomb interactions, the classical trajectory method can reproduce Gabor emission times well. This consistence reveals that Coulomb tails cause an emission-time shift of ∼35 as at the R = 2.0 a.u. case and of ∼40-60 as at the R = 2.6 a.u. case under the present laser parameters when compared to the Coulomb-free quantum-orbit model. Our results are of significance to probe the attosecond dynamics via two-center interference.

High-Harmonic Generation Spectroscopy of Gas-Phase Bromoform

High-Harmonic Generation (HHG) spectra of randomly aligned bromoform (CHBr3) molecules have been experimentally measured and theoretically simulated at various laser pulse intensities. From the experiments, we obtained a significant number of harmonics that goes beyond the cutoff limit predicted by the three-step model (3SM) with ionization from HOMO. To interpret the experiment, we resorted to real-time time-dependent configuration interaction with single excitations. We found that electronic bound states provide an appreciable contribution to the harmonics. More in detail, we analyzed the electron dynamics by decomposing the HHG signal in terms of single molecular-orbital contributions, to explain the appearance of harmonics around 20-30 eV beyond the expected cutoff due to HOMO. HHG spectra can be therefore explained by considering the contribution at high energy of HOMO-6 and HOMO-9, thus indicating a complex multiple-orbital strong-field dynamics. However, even though the presence of the bromoform cation should be not enough to produce such a signal, we could not exclude a priori that the origin of harmonics in the H29-H45 to be due to the cation, which has more energetic ionization channels.

Quantitative performance analysis and comparison of optimal-continuum Gaussian basis sets for high-harmonic generation spectra

Quantum-chemistry methods in the time domain with Gaussian basis sets are increasingly used to compute high-harmonic generation (HHG) spectra of atomic and molecular systems. The quality of these approaches is limited by the accuracy of Gaussian basis sets to describe continuum energy states. In the literature, optimal-continuum Gaussian basis sets have been proposed: Kaufmann et al. [J. Phys. B: At., Mol. Opt. Phys. 22, 2223 (1989)], Woźniak et al. [J. Chem. Phys. 154, 094111 (2021)], Nestmann and Peyerimhoff [J. Phys. B: At., Mol. Opt. Phys. 23, L773 (1990)], Faure et al. [Comput. Phys. Commun. 144, 224 (2002)], and Krause et al. [J. Chem. Phys. 140, 174113 (2014)]. In this work, we have compared the performances of these basis sets to simulate HHG spectra of H atom at different laser intensities. We have also investigated different strategies to balance basis sets with these continuum functions, together with the role of angular momentum. To quantify the performance of the different basis sets, we introduce local and global HHG descriptors. Comparisons with the grid and exact calculations are also provided.

Role of Inner Molecular Orbitals in High-Harmonic Generation Spectra of Aligned Uracil

In this work, we decompose the high-harmonic generation (HHG) signal of aligned gas-phase uracil into single molecular-orbital (MO) contributions. We compute HHG spectra for a pulse linearly polarized perpendicular to the molecular plane, with an intensity of 0.6 and 0.85 × 1014 W/cm2 and a wavelength of 800 nm. We use the real-time time-dependent Configuration Interaction with singles method, coupled to a Gaussian-based representation of the time-dependent wavefunction. The strong-field dynamics is affected by the energy of the ionization/recombination channels and by the coupling between the orbital symmetry and laser polarization. In the configuration studied here, we expect that π-type MOs favorably couple with the incoming pulse and play a substantial role in generating the HHG spectrum. Indeed, we show that HOMO, HOMO - 1, and HOMO - 4, which all are π-like, determine the intensity of harmonic peaks at different energies, while HOMO - 2 and HOMO - 3 provide a smaller contribution. It is worth mentioning that HOMO - 4 produces a stronger signal than that from HOMO - 1, even though the corresponding ionization energy, in an one-electron picture, is around 2.5 eV larger and more than 4 eV larger than the HOMO one.

Resonance absorption of the inner shell during high-order harmonic generation

In this work, we report the observation of resonance absorption of the inner shell during the high-order harmonic generation (HHG) from xenon (Xe) and krypton (Kr). The absorption peaks show a periodic variation with the change of carrier-envelope phase of driving laser pulses and the delay of two-color laser field, which indicates the absorption peaks come from the collective multielectron effects during the HHG. With the increase of gas pressure, the depth of absorption peak will continue to increase, while due to the phase matching effect, there will be an optimal pressure for the intensity of harmonic signal. Our experimental results pave the way to uncover the physical mechanism of the collective multielectron effects involving inner-shell electrons in the HHG process.

Time-dependentab initioapproaches for high-harmonic generation spectroscopy

High-harmonic generation (HHG) is a nonlinear physical process used for the production of ultrashort pulses in XUV region, which are then used for investigating ultrafast phenomena in time-resolved spectroscopies. Moreover, HHG signal itself encodes information on electronic structure and dynamics of the target, possibly coupled to the nuclear degrees of freedom. Investigating HHG signal leads to HHG spectroscopy, which is applied to atoms, molecules, solids and recently also to liquids. Analysing the number of generated harmonics, their intensity and shape gives a detailed insight of, e.g., ionisation and recombination channels occurring in the strong-field dynamics. A number of valuable theoretical models has been developed over the years to explain and interpret HHG features, with the three-step model being the most known one. Originally, these models neglect the complexity of the propagating electronic wavefunction, by only using an approximated formulation of ground and continuum states. Many effects unravelled by HHG spectroscopy are instead due to electron correlation effects, quantum interference, and Rydberg-state contributions, which are all properly captured by anab initioelectronic-structure approach. In this review we have collected recent advances in modelling HHG by means ofab initiotime-dependent approaches relying on the propagation of the time-dependent Schrödinger equation (or derived equations) in presence of a very intense electromagnetic field. We limit ourselves to gas-phase atomic and molecular targets, and to solids. We focus on the various levels of theory employed for describing the electronic structure of the target, coupled with strong-field dynamics and ionisation approaches, and on the basis used to represent electronic states. Selected applications and perspectives for future developments are also given.

Spectral caustics of high-order harmonics in one-dimensional periodic crystals

We theoretically investigate the spectral caustics of high-order harmonics in solids. We analyze the one-dimensional model of high-order harmonic generation (HHG) in solids and find that apart from the caustics originating from the van Hove singularities in the energy band structure, another kind of catastrophe enhancement also emerges in solids when the different branches of electron-hole trajectories generating high-order harmonics coalesce into a single branch. We solve the time-dependent Schrödinger equation in terms of the periodic potential and demonstrate the control of this kind of singularity in HHG with the aid of two-color laser fields. The diffraction patterns of the harmonic spectrum near the caustics agree well with the interband electron-hole recombination trajectories predicted by the semiconductor semiclassical equation. This work is expected to improve our understanding of the HHG dynamics in solids and enable us to manipulate the harmonic spectrum by adjusting the driving field parameters.

Time-frequency analysis of high harmonic generation using a probe XUV pulse

Interpretation of strong-field phenomena is mostly based on the analysis of classical electron trajectories in an intense laser field, whose specific properties determine general features of nonlinear laser-matter interaction. Currently, the visualization of closed electron trajectories contributing to high harmonic generation (HHG) of the laser field is the prerogative of a theoretical analysis based on the time-frequency spectrogram of the induced dipole acceleration. Here, we propose a method for direct reconstruction of the HHG time-frequency spectrogram using a time-delayed probe XUV pulse. Our analytical theory and ab initio numerical simulations demonstrate that the XUV-assisted HHG yield as a function of time delay and harmonic energy mimics the short-time Fourier transform of the dipole acceleration induced by the laser field, thereby providing possible in-situ experimental access for tracing electron dynamics in strong-field phenomena.

Application of optimized waveforms for enhancing high-harmonic yields in a three-color laser-field synthesizer

We apply the optimization method suggested by Jin et al. [Nat. Commun.5, 4003 (2014)24873949] to a three-color laser-field synthesizer in a recent experiment by Burger et al. [Opt. Express25(25), 31130 (2017)29245790] for efficient high-order harmonic generation (HHG). With the experimental laser parameters being precisely tuned according to those returned by the genetic optimization, the three-color waveform composed by a 790-nm laser with its second and third harmonic fields, can enhance the macroscopic HHG yields by one to two orders with only 80% pulse energy compared to the fundamental single-color field. We check that this enhancement can be realized for He or Ne gas at both low and high gas pressures. The optimized waveform enables the short-trajectory emissions dominant to facilitate the buildup of the harmonic field, which is revealed by analyzing the behaviors of electron trajectories and the time-frequency pictures of the single-atom and macroscopic HHG. We also optimize the two-color waveform consisting of the fundamental laser and its third harmonic field for the flexible choice in the experiment. This study provides with a practical route to implement the optimization technique in the experiment for the high-flux harmonic generation from the extreme ultraviolet to the X-rays.

HHG probing of atomic dipoles by electronic wave-packet caustics

We exploit high-order harmonic generation spectroscopy at the caustics of the recombining electron wave-packet as a method for directly comparing experimental spectra with ab-initio theories. Experimental results in xenon and comparison with ab-initio time-dependent configuration-interaction singles calculations allowed to assess the role of the wave-packet enhancement during the giant resonance. Results in argon show that this technique can also be applied to other targets.

Harmonic Generation from Neutral Manganese Atoms in the Vicinity of the Giant Autoionization Resonance

High harmonics from laser-ablated plumes are mostly generated from ionic species. We demonstrate that with ultrashort infrared (∼1.82  μm) driving lasers, high harmonics from laser-ablated manganese are predominantly generated from neutral atoms, a transition metal atom with an ionization potential of 7.4 eV. Our results open the possibility to advance laser-ablation technique to study the dynamics of neutral atoms of low ionization potential. Moreover, as manganese contains giant autoionizing resonance, intense and broadband high harmonics have been demonstrated from this resonance at energies from 49 to 53 eV. This opens the possibility to generate intense attosecond pulses directly from the giant resonances, as well as to study these resonances using high-harmonic spectroscopy.

Enhanced high-harmonic generation up to the soft X-ray region driven by mid-infrared pulses mixed with their third harmonic

We systematically study the efficiency enhancement of high-harmonic generation (HHG) in an Ar gas cell up to the soft X-ray (SXR) range using a two-color laser field composed of 2.1 μm (ω) and 700 nm (3ω) with parallel linear polarization. Our experiment follows the recent theoretical investigations that determined two-color mid-infrared (IR) pulses, mixed with their third harmonic (ω + 3ω), to be close to optimal driving waveforms for enhancing HHG efficiency in the SXR region [Jin et al., Nature Comm. 5, 4003 (2014)]. We observed sub-optical-cycle-dependent efficiency enhancements of up to 8.2 of photon flux integrated between 20 - 70 eV, and up to 2.2 between 85 - 205 eV. Enhancement of HHG efficiency was most pronounced for the lowest tested backing pressure (≈ 140 mbar), and decreased monotonically as the pressure was increased. The single-color (ω)-driven HHG was optimal at the highest backing pressure tested in the experiment (≈ 375 mbar). Our numerical simulations based on single-atom response and 3D pulse propagation show good qualitative agreement with experimental observations. The lower enhancement at high pressure and higher photon energy indicates that phase matching of two-color-driven HHG is more sensitive to ionization rate and pulse propagation effects than the single-color case. We show that with further improvements to the relative phase jitter and the spatio-temporal overlap of the two beams, the efficiency enhancement could be further improved by at least a factor of ≈ 2.

Robust enhancement of high harmonic generation via attosecond control of ionization

High-harmonic generation (HHG) is a powerful tool to generate coherent attosecond light pulses in the extreme ultraviolet. However, the low conversion efficiency of HHG at the single atom level poses a significant practical limitation for many applications. Enhancing the efficiency of the process defines one of the primary challenges in the application of HHG as an advanced XUV source. In this work, we demonstrate a new mechanism, which in contrast to current methods, enhances the HHG conversion efficiency purely on a single particle level. We show that using a bichromatic driving field, sub-optical-cycle control and enhancement of the tunnelling ionization rate can be achieved, leading to enhancements in HHG efficiency by up to two orders of magnitude. Our method advances the perspectives of HHG spectroscopy, where isolating the single particle response is an essential component, and offers a simple route toward scalable, robust XUV sources.