Laser-induced Electron Diffraction Research Articles

Exploring valence-electron dynamics of xenon through laser-induced electron diffraction

Exploring valence-electron dynamics of xenon through laser-induced electron diffraction

Laser-Induced Electron Diffraction in Chiral Molecules

Laser-Induced Electron Diffraction in Chiral Molecules

Tailoring quantum trajectories for strong-field imaging

Strong-field imaging techniques such as laser-induced electron diffraction (LIED) provide unprecedented combined picometer spatial and attosecond temporal resolution by “self-imaging” a molecular target with its own rescattering electrons. Accessing the rich information contained in these experiments requires the ability to accurately manipulate the dynamics of these electrons—namely, their ionization amplitudes, and times of ionization and rescattering—with attosecond to femtosecond precision. The primary challenge is imposed by the multitude of quantum pathways of the photoelectron, reducing the effective measurement to a small range of energies and providing very limited spatial resolution. Here, we show how this ambiguity can be virtually eliminated by manipulating the rescattering pathways with a tailored laser field. Through combined experimental and theoretical approaches, a phase-controlled two-color laser waveform is shown to facilitate the selection of a specific quantum pathway, allowing a direct mapping between the electron’s final momentum and the rescattering time. Integrating attosecond control with Ångstrom-scale resolution could advance ultrafast imaging of field-induced quantum phenomena.

New perspectives in time-resolved laser-induced electron diffraction

Imaging the microscopic world in real space and real time is a grand challenge of science. In the landscape of time-resolved imaging techniques, laser-induced electron diffraction (LIED) has recently shown to be a promising candidate to push the frontiers of ultrafast molecular imaging. In this work, we review the main achievements of LIED research in terms of experimental results and advanced modelling. We also envision interesting perspectives toward the future advancement of time-resolved LIED imaging.

Generation of synchronized x-rays and mid-infrared pulses by Doppler-shifting of relativistically intense radiation from near-critical-density plasmas

It is shown that when relativistically intense ultrashort laser pulses are reflected from the boundary of a plasma with a near-critical density, the Doppler frequency shift leads to generation of intense radiation in both the high-frequency (up to the x-ray) and low-frequency (mid-infrared) ranges. The efficiency of energy conversion into the wavelength range above 3 µm can reach several percent, which makes it possible to obtain relativistically intense pulses in the mid-infrared range. These pulses are synchronized with high harmonics in the ultraviolet and x-ray ranges, which opens up opportunities for high-precision pump–probe measurements, in particular, laser-induced electron diffraction and transient absorption spectroscopy.

Laser-induced electron diffraction in the over-the-barrier-ionization regime

Large polyatomic molecules typically exhibit low ionization potentials, ${I}_{\mathrm{p}}$, leading to over-the-barrier ionization (OBI) already at relatively low intensities ($\ensuremath{\sim}{10}^{13}$ W/${\mathrm{cm}}^{2}$). We revisit laser-induced electron diffraction (LIED) in the over-the-barrier-ionization (OBI) regime and answer the question of whether imaging of molecular structure is still possible with LIED. We employ a hydrogenlike model system mimicking a molecule with low ${I}_{\mathrm{p}}$ using a classical trajectory-based model that incorporates the Coulomb potential; we also use the numerical solution to the time-dependent Schr\"odinger equation. Specifically, we adopt the Fourier transform variant of LIED to show that even a significant contribution of short trajectories in the OBI regime does not preclude structure retrieval from strong-field diffractive patterns. This theoretical investigation shows that LIED can be well described by the classical recollision model even when ionization occurs within the OBI regime. This study paves the way towards strong-field imaging of chemical transformations of large polyatomic molecules in real time based on strong-field electron recollision.

Effect of two-cutoff structure in laser-induced recollision dynamics

We theoretically identify a two-cutoff structure in the recollision energy distribution of the third-return recollision trajectories whose contribution is dominant in the high-energy part of the above-threshold ionization (ATI) spectrum. The additional second cutoff in the recollision energy distribution, resulted from the acceleration of Coulomb field to specific recollision trajectories, induces an extension of the Two-dimensional (2D) photoelectron momentum spectrum and will affect the differential cross-sections (DCS) extracted in laser-induced electron diffraction (LIED) scheme. Both the position and relative yield of the second cutoff decrease with increasing laser intensity. Therefore, the effect of the second cutoff should be taken into account when the laser intensity is not so high.

Machine learning for laser-induced electron diffraction imaging of molecular structures

Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gas-phase molecules with combined picometre spatial and attosecond temporal resolution. However, structural retrieval becomes progressively difficult with increasing structural complexity, given that a global extremum must be found in a multi-dimensional solution space. Worse, pre-calculating many thousands of molecular configurations for all orientations becomes simply intractable. As a remedy, here, we propose a machine learning algorithm with a convolutional neural network which can be trained with a limited set of molecular configurations. We demonstrate structural retrieval of a complex and large molecule, Fenchone (C10H16O), from laser-induced electron diffraction (LIED) data without fitting algorithms or ab initio calculations. Retrieval of such a large molecular structure is not possible with other variants of LIED or ultrafast electron diffraction. Combining electron diffraction with machine learning presents new opportunities to image complex and larger molecules in static and time-resolved studies.

Two-dimensional retrieval methods for ultrafast imaging of molecular structure using laser-induced electron diffraction.

Molecular structural retrieval based on electron diffraction has been proposed to determine the atomic positions of molecules with sub-angstrom spatial and femtosecond temporal resolutions. Given its success on small molecular systems, in this work, we pointout that the accuracy of structure retrieval is constrained by the availability of a wide range of experimental data in the momentum space in all molecular systems. To mitigate the limitations, for laser-induced electron diffraction, here we retrieve molecular structures using two-dimensional (energy and angle) electron momentum spectra in the laboratory frame for a number of small molecular systems, which have previously been studied with 1D methods. Compared to the conventional single-energy or single-angle analysis, our 2D methods effectively expand the momentum range of the measured data. Besides utilization of the 2D data, two complementary methods are developed for consistency check on the retrieved results. The 2D nature of our methods also offers a way of estimating the error from retrieval, which has never been explored before. Comparing with results from prior experiments, our findings show evidence that our 2D methods outperform the conventional 1D methods. Paving the way to the retrieval of large molecular systems, in which their tunneling ionization rates are challenging to obtain, we estimate the error of using the isotropic model in place of including the orientation-dependent ionization rate.

Classical backpropagation for probing the backward rescattering time of a tunnel-ionized electron in an intense laser field

We present a method to estimate the backward rescattering time of a tunnel-ionized electron in an intense laser pulse. The idea of the classical backpropagation method is applied to determine the backward rescattering time and its dependence on various parameters such as the ionization potential of the parent ion, its spatial profile and the peak intensity and wavelength of the driving laser field. The accurate estimation of the rescattering time would provide critical information in analyzing ultrafast rescattering dynamics in applications such as high-order harmonic generation, above-threshold ionization, and laser-induced electron diffraction experiments. We find that the backward rescattering time is significantly affected by the peak intensity of the laser pulse. The rescattering time changes by a few hundred attoseconds when the peak intensity varies from $1\ifmmode\times\else\texttimes\fi{}{10}^{14}$ to $5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2}$.

Publisher's Note: “Laser-induced electron diffraction of the ultrafast umbrella motion in ammonia” [Struct. Dyn. 8, 014301 (2021)

Publisher's Note: “Laser-induced electron diffraction of the ultrafast umbrella motion in ammonia” [Struct. Dyn. <b>8</b>, 014301 (2021)

Molecular structure retrieval directly from laboratory-frame photoelectron spectra in laser-induced electron diffraction

Ubiquitous to most molecular scattering methods is the challenge to retrieve bond distance and angle from the scattering signals since this requires convergence of pattern matching algorithms or fitting methods. This problem is typically exacerbated when imaging larger molecules or for dynamic systems with little a priori knowledge. Here, we employ laser-induced electron diffraction (LIED) which is a powerful means to determine the precise atomic configuration of an isolated gas-phase molecule with picometre spatial and attosecond temporal precision. We introduce a simple molecular retrieval method, which is based only on the identification of critical points in the oscillating molecular interference scattering signal that is extracted directly from the laboratory-frame photoelectron spectrum. The method is compared with a Fourier-based retrieval method, and we show that both methods correctly retrieve the asymmetrically stretched and bent field-dressed configuration of the asymmetric top molecule carbonyl sulfide (OCS), which is confirmed by our quantum-classical calculations.

Strong-field ionization of complex molecules

Strong-field photoelectron momentum imaging of the prototypical biomolecule indole was disentangled in a combined experimental and computational approach. Experimentally, strong control over the molecules enabled the acquisition of photoelectron momentum distributions in the molecular frame for a well-defined, narrow range of incident intensities. A novel, highly efficient semiclassical simulation setup based on the adiabatic tunneling theory quantitatively reproduced these results. Jointly, experiment and computations revealed holographic structures in the asymptotic momentum distributions, which were found to sensitively depend on the alignment of the molecular frame. We identified the essential molecular properties that shape the photoelectron wavepacket in the first step of the ionization process and employ a quantum-chemically exact description of the cation during the subsequent continuum dynamics. The detailed modeling of the molecular ion, which accounts for its polarization by the laser-electric field, enables the simulation of laser-induced electron diffraction off large and complex molecules and provides full insight into the photoelectron's dynamics in terms of semiclassical trajectories. This provides the computational means to unravel strong-field diffractive imaging of biomolecular systems on femtosecond time scales.

Laser-induced electron diffraction of the ultrafast umbrella motion in ammonia.

Visualizing molecular transformations in real-time requires a structural retrieval method with Ångström spatial and femtosecond temporal atomic resolution. Imaging of hydrogen-containing molecules additionally requires an imaging method sensitive to the atomic positions of hydrogen nuclei, with most methods possessing relatively low sensitivity to hydrogen scattering. Laser-induced electron diffraction (LIED) is a table-top technique that can image ultrafast structural changes of gas-phase polyatomic molecules with sub-Ångström and femtosecond spatiotemporal resolution together with relatively high sensitivity to hydrogen scattering. Here, we image the umbrella motion of an isolated ammonia molecule (NH3) following its strong-field ionization. Upon ionization of a neutral ammonia molecule, the ammonia cation (NH3+) undergoes an ultrafast geometrical transformation from a pyramidal () to planar () structure in approximately 8 femtoseconds. Using LIED, we retrieve a near-planar () field-dressed NH3+ molecular structure femtoseconds after ionization. Our measured field-dressed NH3+ structure is in excellent agreement with our calculated equilibrium field-dressed structure using quantum chemical ab initio calculations.

Attosecond streaking using a rescattered electron in an intense laser field

When an atom or molecule is exposed to a strong laser field, an electron can tunnel out from the parent ion and moves along a specific trajectory. This ultrafast electron motion is sensitive to a variation of the laser field. Thus, it can be used as a fast temporal gate for the temporal characterization of the laser field. Here, we demonstrate a new type of attosecond streaking wherein a rescattered electron trajectory is manipulated by an ultrashort laser pulse. The vector potential of the laser pulse is directly recorded in the photoelectron spectra of the rescattered electron. In contrast to high harmonic generation methods, our approach has no directional ambiguity in space, leading to complete in situ temporal characterization. In addition, it provides timing information on ionization and re-scattering events. Therefore, our approach can be a useful tool for the investigation of strong-field processes triggered by rescattering, such as non-sequential double ionization and laser-induced electron diffraction.

Effect of Coulomb field on laser-induced ultrafast imaging methods

By performing a joint theoretical and experimental investigation on the high-order above-threshold ionization (HATI) spectrum, the dominant role of the 3rd-return-recollision trajectories in the region near the cutoff due to the ionic Coulomb field is identified. This invalidates the key assumption adopted in the conventional laser-induced electron diffraction (LIED) approach that the 1st-returnrecollision trajectories dominate the spectrum according to strong field approximation (SFA). Our results show that the incident (return) electron beams produced by the 1st and 3rd returns possess distinct characteristics of beam energy, beam diameter and temporal evolution law due to the influence of Coulomb field, and therefore the extracted results in the LIED will be altered if the significance of the 3rd-return-recollision trajectories is properly considered in the analysis. Such Coulomb field effect should be taken into account in all kinds of laser-induced imaging schemes based on recollision.

Double-slit effect on laser induced electron diffraction of dimers

We theoretically study strong-field ionization of dimers with large internuclear distance in linearly and circularly polarized light fields. By numerically solving the time-dependent Schrödinger equation (TDSE), we show that the double-slit interference effect plays a significant role in the laser-induced electron diffraction of dimers. And the prominent double-slit interference structures are sensitive to the symmetry and orientation of the orbitals of dimers. We then develop a semi-classical trajectory model including the double-slit effect by coherently summing up the contributions of two separated atoms. This model explains the interference fringes of TDSE simulations. And the effect of long-range potential on the double-slit interference is discussed. This work provides intuitive physical insights into how dimers being ionized in strong laser fields and has implications to extract ultrafast dynamics of polyatomic molecules from strong-field photoelectron spectroscopy.

Sensitivity of gas-phase electron diffraction images to the molecular potential parameters

The gas-phase electron diffraction (GED) is a conventional method to extract the geometrical structure and the vibration parameters of molecules. In practice, the mean vibration amplitude is retrieved successfully, while the anharmonicity parameter is usually fixed by a relation with the former. To explicit the reason, we examine the sensitivity of the molecular scattering curve (sM(s)) of N2 molecule to the vibration parameters. The results show that the sM(s) curve is sensitive to the mean vibration amplitude but considerably stable with the changing of the anharmonic parameter even at a high temperature. Besides, many recent studies also focus on the investigation of the laser-induced electron diffraction (LIED) since its high temporal and spatial resolution. However, it is hard to extract the vibration parameters from the LIED data because of the shortage of the analytical form of sM(s) caused by the complicated physical process. So we propose to directly reconstruct the molecular potential instead of extracting the vibration parameters from the LIED. The preliminary purpose is to test the sensitivity of the sM(s) curve to the potential parameters of the Morse potential of N2 considering the nuclear vibration for GED. We demonstrate that the sM(s) curve is sensitive to the change of the potential parameters; thus, the molecular potential can be reconstructed from the GED. This statement is an essential precondition for further investigation of not only the influence of the vibrational effect on the probing of the molecular dissociation but also the reconstruction of the molecular potential from the LIED data.

Multiple scattering model considering the vibration effect

The independent atomic (IAM) and the multiple scattering (MS) models are recently adopted to extract the molecular geometrical structures from the electron diffraction images, especially, in the laser-induced electron diffraction. In this study, firstly, we clarify the working range of the MS and the IAM models by comparing its diffraction images at various collision energies. We claim that the MS model is effective at low energy of incident electron while both MS and IAM models give similar results at high collision energy. Secondly, we successfully develop the MS model by numerically including the molecular vibration. By comparing with the diffraction patterns calculated within the IAM model at considerably high collision energy, we verify the accuracy of the developed MS model. We show that the diffraction curves simulated by the MS and IAM methods considering the vibration effect are consistent with each other. Moreover, the extracted interatomic distance from diffraction images well agrees with the initial input. This evidence proves that the MS model with the vibration effect is reliable.

Control of electron recollision and molecular nonsequential double ionization

Intense laser pulses lasting a few optical cycles, are able to ionize molecules via different mechanisms. One such mechanism involves a process whereby within one optical period an electron tunnels away from the molecule, and is then accelerated and driven back as the laser field reverses its direction, colliding with the parent molecule and causing correlated non-sequential double ionization (NSDI). Here we report control over NSDI via spectral-phase pulse shaping of femtosecond laser pulses. The measurements are carried out on ethane molecules using shaped pulses. We find that the shaped pulses can enhance or suppress the yield of dications resulting from electron recollision by factors of 3 to 6. This type of shaped pulses is likely to impact all phenomena stemming from electron recollision processes induced by strong laser fields such as above threshold ionization, high harmonic generation, attosecond pulse generation, and laser-induced electron diffraction.