Laser-induced Electron Diffraction Research Articles

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.

Imaging an isolated water molecule with an attosecond electron wave packet

SynopsisWe use laser-induced electron diffraction (LIED) to self-image the molecular structure of an isolated water molecular ion using its own retuning attosecond electron wave packet (EWP). Using LIED’s sub-femtosecond and picometre spatio-temporal resolution imaging capabilities, we observe the symmetric stretching of the O-H and H-H internuclear distances with increasing laser field strength.

Ultrafast imaging of the Renner-Teller effect in a field-dressed molecule

SynopsisWe present experimental results of linear-to-bent transition of field-dressed molecules, mediated by Renner-Teller effect. Using the state-of-the-art laser-induced electron diffraction (LIED) technique, we image a bent and symmetrically stretched carbon disulfide (CS2) molecule populating an excited electronic state under the influence of strong laser field. Our findings are well-supported by ab initio quantum mechanical calculations.

Imaging an isolated water molecule using a single electron wave packet.

Observing changes in molecular structure requires atomic-scale Ångstrom and femtosecond spatio-temporal resolution. We use the Fourier transform (FT) variant of laser-induced electron diffraction (LIED), FT-LIED, to directly retrieve the molecular structure of H2O+ with picometer and femtosecond resolution without a priori knowledge of the molecular structure nor the use of retrieval algorithms or ab initio calculations. We identify a symmetrically stretched H2O+ field-dressed structure that is most likely in the ground electronic state. We subsequently study the nuclear response of an isolated water molecule to an external laser field at four different field strengths. We show that upon increasing the laser field strength from 2.5 to 3.8 V/Å, the O-H bond is further stretched and the molecule slightly bends. The observed ultrafast structural changes lead to an increase in the dipole moment of water and, in turn, a stronger dipole interaction between the nuclear framework of the molecule and the intense laser field. Our results provide important insights into the coupling of the nuclear framework to a laser field as the molecular geometry of H2O+ is altered in the presence of an external field.

Atomic-resolution imaging of carbonyl sulfide by laser-induced electron diffraction.

Measurements on the strong-field ionization of carbonyl sulfide molecules by short, intense, 2 µm wavelength laser pulses are presented from experiments where angle-resolved photoelectron distributions were recorded with a high-energy velocity map imaging spectrometer, designed to reach a maximum kinetic energy of 500 eV. The laser-field-free elastic-scattering cross section of carbonyl sulfide was extracted from the measurements and is found in good agreement with previous experiments, performed using conventional electron diffraction. By comparing our measurements to the results of calculations, based on the quantitative rescattering theory, the bond lengths and molecular geometry were extracted from the experimental differential cross sections to a precision better than ±5 pm and in agreement with the known values.

Tomographic Extraction of the Internuclear Separation Based on Two-Center Interference with Aligned Diatomic Molecules.

We experimentally investigate the two-dimensional photoelectron momentum spectra of aligned diatomic molecules in an intense laser field. Our results reveal a novel prominent valley structure in the molecular alignment dependence of the high-energy photoelectron spectra along the laser polarization. Resorting to the molecular strong-field approximation and a simple semiclassical analysis, we show that this valley structure stems from the destructive two-center interference of the laser-driven rescattered electrons in diatomic molecules. Based on this two-center interference with aligned diatomic molecules, we demonstrate for the first time a tomographic method to extract the molecular internuclear separation, providing a more straightforward approach of molecular imaging, in comparison with, e.g., laser-induced electron diffraction and fixed-angle broadband laser-driven electron scattering.

Imaging the Renner–Teller effect using laser-induced electron diffraction

Structural information on electronically excited neutral molecules can be indirectly retrieved, largely through pump-probe and rotational spectroscopy measurements with the aid of calculations. Here, we demonstrate the direct structural retrieval of neutral carbonyl disulfide (CS2) in the [Formula: see text] excited electronic state using laser-induced electron diffraction (LIED). We unambiguously identify the ultrafast symmetric stretching and bending of the field-dressed neutral CS2 molecule with combined picometer and attosecond resolution using intrapulse pump-probe excitation and measurement. We invoke the Renner-Teller effect to populate the [Formula: see text] excited state in neutral CS2, leading to bending and stretching of the molecule. Our results demonstrate the sensitivity of LIED in retrieving the geometric structure of CS2, which is known to appear as a two-center scatterer.

Multiple-orbital effects in laser-induced electron diffraction of aligned molecules

Photoelectron Angular Distributions (PADs) resulting from 800 nm and 1300 nm strong field ionization of impulsively aligned CF$_3$I molecules were analyzed using time-dependent density functional theory (TDDFT). The normalized difference between the PADs for aligned and anti-aligned molecules displays large modulations in the high-energy re-collision plateau that are assigned to the diffraction of back-scattered photoelectrons. The TDDFT calculations reveal that, in spite of their 2.6 eV energy difference, ionization from the HOMO-1 orbital contributes to the diffraction pattern on the same footing as ionization from the doubly degenerate HOMO orbital.

Photoelectron-momentum distribution of H2+ molecules at different internuclear distances in an elliptically polarized laser field

We investigate molecular photoelectron-momentum distribution (MPMD) and molecular photoelectron angular distribution (MPAD) of oriented ${\mathrm{H}}_{2}{}^{+}$ under frozen-nuclei approximation driven by elliptically polarized laser pulse by numerically solving a two-dimensional time-dependent $\mathrm{Schr}\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{o}}\mathrm{dinger}$ equation. The results show that the MPMDs and MPADs are sensitive to the internuclear distance, which is illustrated by the initial MPMDs and the evolution of MPMDs. In addition, they are also dependent on laser ellipticity and wavelength. When the laser wavelength is $5\phantom{\rule{4pt}{0ex}}\mathrm{nm}$, the phenomenon of laser-induced electron diffraction can be observed in both MPMD and MPAD.

Attosecond time-resolved photoelectron holography

Ultrafast strong-field physics provides insight into quantum phenomena that evolve on an attosecond time scale, the most fundamental of which is quantum tunneling. The tunneling process initiates a range of strong field phenomena such as high harmonic generation (HHG), laser-induced electron diffraction, double ionization and photoelectron holography—all evolving during a fraction of the optical cycle. Here we apply attosecond photoelectron holography as a method to resolve the temporal properties of the tunneling process. Adding a weak second harmonic (SH) field to a strong fundamental laser field enables us to reconstruct the ionization times of photoelectrons that play a role in the formation of a photoelectron hologram with attosecond precision. We decouple the contributions of the two arms of the hologram and resolve the subtle differences in their ionization times, separated by only a few tens of attoseconds.

Polarization and exchange effects in elastic scattering of electron with atoms and ions**Project supported by the National Natural Science Foundation of China (Grant No. 11274219) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China.

Laser-induced electron diffraction (LIED), in which elastic scattering of the returning electron with the parent ion takes place, has been used to extract atomic potential and image molecular structures with sub-Å precision and exposure time of a few femtoseconds. So far, the polarization and exchange effects have not been taken into account in the theoretical calculation of differential cross section (DCS) for the laser-induced rescattering processes. However, the validity of this theoretical treatment has never been verified. In this work, we investigate the polarization and exchange effects on electron impact elastic scattering with rare gas atoms and ions. It is found that, while the exchange effect generally plays a more important role than the polarization effect in the elastic scattering process, the exchange effect is less important on electron–ion collisions than on electron–atom collisions, especially for scattering in backward direction. In addition, our calculations show that, for electron–atom collisions at incident energies above 50 eV, both the polarization and exchange effects can be safely neglected, while for electron–ion collisions, both the polarization and exchange potentials do not make substantial contributions to the DCS at incident energies above 20 eV and scattering angles larger than 90°. Our investigation confirms the validity of the current LIED method.

Dynamic molecular structure retrieval from low-energy laser-induced electron diffraction spectra

A recently developed quantitative rescattering theory showed that a laser-free elastic cross section can be separated from laser-induced electron diffraction (LIED) spectra. Based upon this idea, Blaga et al investigated the possibility of reconstructing molecular structure from LIED spectra (2012 Nature 483 7388). In the above study, an independent atoms model (IAM) was used to interpret high-energy electron–molecule collisions induced by a mid-infrared laser. Our research aims to extend the application range of this structural retrieval method to low-energy spectra induced by more common near-infrared laser sources. The IAM is insufficient in this case, so we switch to a more comprehensive model—the multiple scattering (MS) theory. From the original version concerning only neutral targets, we upgrade the model so that it is compatible with electron–ion collisions at low energy. With available LIED experiment data of CO2 and O2, the upgraded MS is shown to be greatly effective as a tool for molecular imaging from spectra induced by a near-infrared laser. The captured image is at about 2 fs after the ionization, shorter than the period 4–6 fs by using the mid-infrared laser in Blaga’s experiment.

Extraction of geometrical structure of ethylene molecules by laser-induced electron diffraction combined with ab initio scattering calculations

Author(s): Ito, Y; Carranza, R; Okunishi, M; Lucchese, RR; Ueda, K | Abstract: We measured angle-resolved high-energy electron spectra emitted from C2H4 in an intense laser field, extracted field-free electron-ion elastic scattering differential cross sections (DCSs) according to quantitative rescattering theory, and obtained molecular contrast factors (MCFs) subtracting the incoherent sum of DCSs of all the atoms in the molecule. Comparing the results with ab initio scattering calculations and employing least-squares fitting, we have extracted the C-C and C-H bond lengths of the molecule with ∼5% uncertainty. This approach opens the way to retrieve the structure of hydrocarbon molecules, potentially at high temporal resolution, employing low collision energies where electron scattering is sensitive to the hydrogen atoms; and where the independent atom model calculations may fail to reproduce the experimentally extracted MCF.

Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering

Strong-field photoelectron holography and laser-induced electron diffraction (LIED) are two powerful emerging methods for probing the ultrafast dynamics of molecules. However, both of them have remained restricted to static systems and to nuclear dynamics induced by strong-field ionization. Here we extend these promising methods to image purely electronic valence-shell dynamics in molecules using photoelectron holography. In the same experiment, we use LIED and photoelectron holography simultaneously, to observe coupled electronic-rotational dynamics taking place on similar timescales. These results offer perspectives for imaging ultrafast dynamics of molecules on femtosecond to attosecond timescales.

Laser-induced electron diffraction: alignment defects and symmetry breaking

ABSTRACTThe fringe pattern that allows geometrical and orbital structure information to be extracted from LIED (laser-induced electron diffraction) spectra of symmetric molecules is shown to reflect a symmetry conservation principle. We show that under a field polarisation which preserves certain symmetry elements of the molecule, the symmetry character of the initial wave function is conserved during its time-evolution. We present a symmetry analysis of a deviation from a perfect alignment by decomposing the field into a major, symmetry-determining part, and a minor, symmetry-breaking part. This decomposition leads to a corresponding factorisation of the time-evolution operator. The formalism is applied to the analysis of the robustness of LIED readings and inversions with respect to deviations from a perfect perpendicular and parallel alignment of a symmetric ABA triatomic molecule. The results indicate a particularly strong stability of the type of LIED spectra associated with the perpendicular alignment situation.

Laser-induced electron diffraction: inversion of photo-electron spectra for molecular orbital imaging

ABSTRACTIn this paper, we discuss the possibility of imaging molecular orbitals from photoelectron spectra obtained via laser -induced electron diffraction in linear molecules. This is an extension of our recent work to the case of the HOMO-1 orbital of the carbon dioxide molecule. We show that such an imaging technique has the potential to image molecular orbitals at different internuclear distances in a sub-femtosecond time scale and with a resolution of a fraction of an Angström.

Above-threshold ionization and laser-induced electron diffraction in diatomic molecules

Strong field photoemission and electron recollision provide a viable route to extract electronic and nuclear dynamics from molecular targets with attosecond temporal resolution. However, since an {\em ab-initio} treatment of even the simplest diatomic systems is beyond today's capabilities approximate qualitative descriptions are warranted. In this paper, we develop such a theoretical approach to model the photoelectrons resulting from intense laser-molecule interaction. We present a general theory for symmetric diatomic molecules in the single active electron approximation that, amongst other capabilities, allows adjusting both the internuclear separation and molecular potential in a direct and simple way. More importantly we derive an analytic approximate solution of the time dependent Schr\"odinger equation (TDSE), based on a generalized strong field approximation (SFA) version. Using that approach we obtain expressions for electrons emitted transition amplitudes from two different molecular centres, and accelerated then in the strong laser field. One innovative aspect of our theory is the fact that the dipole matrix elements are free from non-physical gauge and coordinate system dependent terms -- this is achieved by adapting the coordinate system, in which SFA is performed, to the centre from which the corresponding part of the time dependent wave function originates. Our analytic results agree very well with the numerical solution of the full three-dimensional TDSE for the H$_2^+$ molecule. Moreover, the theoretical model was applied to describe laser-induced electron diffraction (LIED) measurements of O$_2^+$ molecules, obtained at ICFO, and reproduces the main features of the experiment very well. Our approach can be extended in a natural way to more complex molecules and multi-electron systems.

Ultrafast electron diffraction imaging of bond breaking in di-ionized acetylene.

Visualizing chemical reactions as they occur requires atomic spatial and femtosecond temporal resolution. Here, we report imaging of the molecular structure of acetylene (C2H2) 9 femtoseconds after ionization. Using mid-infrared laser-induced electron diffraction (LIED), we obtained snapshots as a proton departs the [C2H2]2+ ion. By introducing an additional laser field, we also demonstrate control over the ultrafast dissociation process and resolve different bond dynamics for molecules oriented parallel versus perpendicular to the LIED field. These measurements are in excellent agreement with a quantum chemical description of field-dressed molecular dynamics.

Carrier-envelope phase mapping in laser-induced electron diffraction

We present laser-induced electron diffraction measurements of elastic differential scattering cross sections (DCSs) of a photoelectron on the parent ion for argon, krypton, and xenon, using waveform-controlled few-cycle pulses. Considering only cutoff electrons and employing the adiabatic theory for the analysis enables us to eliminate ambiguities in extracting the DCSs from experimental spectra. Contrary to previous works, which mainly focused on the angular dependence of the DCS, our method allows us to extract also its dependence on the scattering momentum. In the case of xenon, we demonstrate how this method can be used to obtain the complete angular and momentum dependence of the DCS in a range of these variables determined by the pulse. The obtained results are compared to theoretical calculations based on the single-active-electron approximation, which shows a high level of agreement. Further investigations may provide opportunities to study multielectron effects when more advanced theoretical models become available.