4D attosecond imaging with free electrons: Diffraction methods and potential applications

Monochromatization of Electron Beams with Spatially and Temporally Modulated Optical Fields

Inelastic interaction between coherent light with constant frequency and free electrons enables periodic phase modulation of electron wave packets leading to periodic sidebands in the electron energy spectra. In this Letter, we propose a generalization of the interaction by considering linearly chirped electron wave packets interacting with chirped optical fields. We theoretically demonstrate that when matching the chirp parameters of the electron and light waves, the interaction leads to partial monochromatization of the electron spectra in one of the energy sidebands. Depending on the coherence time of the electrons, the electron spectrum may be narrowed down by a factor of 5 times with 26% of the electron distribution in the monochromatized energy band. This approach will improve the spectral resolution and reduce color aberrations in ultrafast imaging experiments with free electrons.

Generation of Isolated Subfemtosecond Electron Bunches by the Diffraction of a Polarization-Tailored Intense Laser Beam

We propose utilizing a polarization-tailored high-power laser pulse to extract and accelerate electrons from the edge of a solid foil target to produce isolated subfemtosecond electron bunches. The laser pulse consists of two orthogonally polarized components with a time delay comparable to the pulse duration, such that the polarization in the middle of the pulse rapidly rotates over 90° within few optical cycles. Three-dimensional particle-in-cell simulations show that when such a light pulse diffracts at the edge of a plasma foil, a series of isolated relativistic electron bunches are emitted into separated azimuthal angles determined by the varying polarization. In comparison with most other methods that require an ultrashort drive laser, we show the proposed scheme works well with typical multicycle (∼30  fs) pulses from high-power laser facilities. The generated electron bunches have typical durations of a few hundred attoseconds and charges of tens of picocoulombs.

Electromagnetic-Thermal Coupling Study for RF Compression Cavity Applied to Ultrafast Electron Diffraction

Ultrafast electron diffraction (UED) is a powerful tool for observing the evolution of transient structures at the atomic level. However, temporal resolution is a huge challenge for UEDs, mainly depending on the pulse duration. Unfortunately, the Coulomb force between electrons causes the pulse duration to increase continually when propagating, reducing the temporal resolution. In this paper, we theoretically design a radio frequency (RF) compression cavity using the finite-element method of electromagnetic-thermal coupling to overcome this limitation and obtain a high-brightness, short-pulse-duration, and stable electron beam. In addition, the cavity's size parameters are optimized, and a water-cooling system is designed to ensure stable operation. To the best of our knowledge, this is the first time that the electromagnetic-thermal coupling method has been used to study the RF cavity applied to UED. The results show that the RF cavity operates in TM010 mode with a resonant frequency of 2970 MHz and generates a resonant electric field. This mode of operation generates an electric field that varies periodically and transiently, compressing the electronic pulse duration. The electromagnetic-thermal coupling method proposed in this study effectively improves the temporal resolution of UED.

Inelastic electron scattering at a single-beam structured light wave

In free space, electrons undergo inelastic scattering in the presence of ponderomotive potentials generated by light pulses and standing light waves. The resulting modulated electron energy spectrum can exhibit the formation of discrete energy sidebands when multiple light beams are employed. Here, we demonstrate the inelastic scattering of slow-electron wavepackets at a propagating Hermite-Gaussian light beam. The pulsed Hermite-Gaussian beam thus forms a ponderomotive potential for the electron with sufficient momentum components, leading to the inelastic scattering and subsequent formation of discrete energy sidebands. We show that the resulting energy-gain spectra after the interaction are strongly influenced by the self-interference of the electrons in this ponderomotive potential. This effect is observable across various wavelengths, and the energy modulation can be controlled by varying the electron velocity and light intensity. By utilizing the vast landscape of structured electromagnetic fields, this effect introduces an additional platform for manipulating electron wavepackets.

Monitoring molecular nonadiabatic dynamics with femtosecond X-ray diffraction

Ultrafast time-resolved X-ray scattering, made possible by free-electron laser sources, provides a wealth of information about electronic and nuclear dynamical processes in molecules. The technique provides stroboscopic snapshots of the time-dependent electronic charge density traditionally used in structure determination and reflects the interplay of elastic and inelastic processes, nonadiabatic dynamics, and electronic populations and coherences. The various contributions to ultrafast off-resonant diffraction from populations and coherences of molecules in crystals, in the gas phase, or from single molecules are surveyed for core-resonant and off-resonant diffraction. Single-molecule [Formula: see text] scaling and two-molecule [Formula: see text] scaling contributions, where N is the number of active molecules, are compared. Simulations are presented for the excited-state nonadiabatic dynamics of the electron harpooning at the avoided crossing in NaF. We show how a class of multiple diffraction signals from a single molecule can reveal charge-density fluctuations through multidimensional correlation functions of the charge density.

X-Ray Sum Frequency Diffraction for Direct Imaging of Ultrafast Electron Dynamics

X-ray diffraction from molecules in the ground state produces an image of their charge density, and time-resolved x-ray diffraction can thus monitor the motion of the nuclei. However, the density change of excited valence electrons upon optical excitation can barely be monitored with regular diffraction techniques due to the overwhelming background contribution of the core electrons. We present a nonlinear x-ray technique made possible by novel free electron laser sources, which provides a spatial electron density image of valence electron excitations. The technique, sum frequency generation carried out with a visible pump and a broadband x-ray diffraction pulse, yields snapshots of the transition charge densities, which represent the electron density variations upon optical excitation. The technique is illustrated by ab initio simulations of transition charge density imaging for the optically induced electronic dynamics in a donor or acceptor substituted stilbene.

Ponderomotive Generation and Detection of Attosecond Free-Electron Pulse Trains

Atomic motion dynamics during structural changes or chemical reactions have been visualized by pico- and femtosecond pulsed electron beams via ultrafast electron diffraction and microscopy. Imaging the even faster dynamics of electrons in atoms, molecules, and solids requires electron pulses with subfemtosecond durations. We demonstrate here the all-optical generation of trains of attosecond free-electron pulses. The concept is based on the periodic energy modulation of a pulsed electron beam via an inelastic interaction, with the ponderomotive potential of an optical traveling wave generated by two femtosecond laser pulses at different frequencies in vacuum. The subsequent dispersive propagation leads to a compression of the electrons and the formation of ultrashort pulses. The longitudinal phase space evolution of the electrons after compression is mapped by a second phase-locked interaction. The comparison of measured and calculated spectrograms reveals the attosecond temporal structure of the compressed electron pulse trains with individual pulse durations of less than 300 as. This technique can be utilized for tailoring and initial characterization of suboptical-cycle free-electron pulses at high repetition rates for stroboscopic time-resolved experiments with subfemtosecond time resolution.

Acceleration of sub-relativistic electrons with an evanescent optical wave at a planar interface

We report on a theoretical and experimental study of the energy transfer between an optical evanescent wave, propagating in vacuum along the planar boundary of a dielectric material, and a beam of sub-relativistic electrons. The evanescent wave is excited via total internal reflection in the dielectric by an infrared (λ = 2 μm) femtosecond laser pulse. By matching the electron propagation velocity to the phase velocity of the evanescent wave, energy modulation of the electron beam is achieved. A maximum energy gain of 800 eV is observed, corresponding to the absorption of more than 1000 photons by one electron. The maximum observed acceleration gradient is 19 ± 2 MeV/m. The striking advantage of this scheme is that a structuring of the acceleration element's surface is not required, enabling the use of materials with high laser damage thresholds that are difficult to nano-structure, such as SiC, Al₂O₃ or CaF₂.

Optical gating and streaking of free electrons with sub-optical cycle precision

The temporal resolution of ultrafast electron diffraction and microscopy experiments is currently limited by the available experimental techniques for the generation and characterization of electron bunches with single femtosecond or attosecond durations. Here, we present proof of principle experiments of an optical gating concept for free electrons via direct time-domain visualization of the sub-optical cycle energy and transverse momentum structure imprinted on the electron beam. We demonstrate a temporal resolution of 1.2±0.3 fs. The scheme is based on the synchronous interaction between electrons and the near-field mode of a dielectric nano-grating excited by a femtosecond laser pulse with an optical period duration of 6.5 fs. The sub-optical cycle resolution demonstrated here is promising for use in laser-driven streak cameras for attosecond temporal characterization of bunched particle beams as well as time-resolved experiments with free-electron beams.

Perspective: 4D ultrafast electron microscopy--Evolutions and revolutions

In this Perspective, the evolutionary and revolutionary developments of ultrafast electron imaging are overviewed with focus on the "single-electron concept" for probing methodology. From the first electron microscope of Knoll and Ruska [Z. Phys. 78, 318 (1932)], constructed in the 1930s, to aberration-corrected instruments and on, to four-dimensional ultrafast electron microscopy (4D UEM), the developments over eight decades have transformed humans' scope of visualization. The changes in the length and time scales involved are unimaginable, beginning with the micrometer and second domains, and now reaching the space and time dimensions of atoms in matter. With these advances, it has become possible to follow the elementary structural dynamics as it unfolds in real time and to provide the means for visualizing materials behavior and biological functions. The aim is to understand emergent phenomena in complex systems, and 4D UEM is now central for the visualization of elementary processes involved, as illustrated here with examples from past achievements and future outlook.

Ultrafast electron diffraction optimized for studying structural dynamics in thin films and monolayers

A compact electron source specifically designed for time-resolved diffraction studies of free-standing thin films and monolayers is presented here. The sensitivity to thin samples is achieved by extending the established technique of ultrafast electron diffraction to the "medium" energy regime (1-10 kV). An extremely compact design, in combination with low bunch charges, allows for high quality diffraction in a lensless geometry. The measured and simulated characteristics of the experimental system reveal sub-picosecond temporal resolution, while demonstrating the ability to produce high quality diffraction patterns from atomically thin samples.

Sub-phonon-period compression of electron pulses for atomic diffraction

Visualizing the rearrangement of atoms in a wide range of molecular and condensed-matter systems requires resolving picometre displacements on a 10-fs timescale, which is achievable using pump–probe diffraction, given short enough pulses. Here we demonstrate the compression of single-electron pulses with a de Broglie wavelength of 0.08 ångström to a full-width at half-maximum duration of 28 fs or equivalently 12-fs root-mean square, substantially shorter than most phonon periods and molecular normal modes. Atomic resolution diffraction from a complex organic molecule is obtained with good signal-to-noise ratio within a data acquisition period of minutes. The electron-laser timing is found to be stable within 5 fs (s.d.) over several hours, allowing pump–probe diffraction at repetitive excitation. These measurements show the feasibility of laser-pump/electron-probe scans that can resolve the fastest atomic motions relevant in reversible condensed-matter transformations and organic chemistry.

High spatial and temporal resolutions are required in order to follow chemical and condensed matter transformations in real time. Here, the authors compress single-electron pulses in time, with low jitter and high repetition rates, and demonstrate atomic resolution via diffraction from organic molecules.

Femtosecond single-electron diffraction

Ultrafast electron diffraction allows the tracking of atomic motion in real time, but space charge effects within dense electron packets are a problem for temporal resolution. Here, we report on time-resolved pump-probe diffraction using femtosecond single-electron pulses that are free from intra-pulse Coulomb interactions over the entire trajectory from the source to the detector. Sufficient average electron current is achieved at repetition rates of hundreds of kHz. Thermal load on the sample is avoided by minimizing the pump-probe area and by maximizing heat diffusion. Time-resolved diffraction from fibrous graphite polycrystals reveals coherent acoustic phonons in a nanometer-thick grain ensemble with a signal-to-noise level comparable to conventional multi-electron experiments. These results demonstrate the feasibility of pump-probe diffraction in the single-electron regime, where simulations indicate compressibility of the pulses down to few-femtosecond and attosecond duration.

Site-specific recoil diffraction of backscattered electrons in crystals

A novel diffraction effect in high-energy electron backscattering is demonstrated: the formation of element-specific diffraction patterns via nuclear recoil. For sapphire (Al(2)O(3)), the difference in recoil energy allows us to determine if an electron scattered from aluminum or from oxygen. The angular electron distribution obtained in such measurements is a strong function of the recoiling lattice site. These element-specific recoil diffraction features are explained using the dynamical theory of electron diffraction. Our observations open up new possibilities for local, element-resolved crystallographic analysis using quasielastically backscattered electrons in scanning electron microscopy.

Single-electron pulses for ultrafast diffraction

Visualization of atomic-scale structural motion by ultrafast electron diffraction and microscopy requires electron packets of shortest duration and highest coherence. We report on the generation and application of single-electron pulses for this purpose. Photoelectric emission from metal surfaces is studied with tunable ultraviolet pulses in the femtosecond regime. The bandwidth, efficiency, coherence, and electron pulse duration are investigated in dependence on excitation wavelength, intensity, and laser bandwidth. At photon energies close to the cathode's work function, the electron pulse duration shortens significantly and approaches a threshold that is determined by interplay of the optical pulse width and the acceleration field. An optimized choice of laser wavelength and bandwidth results in sub-100-fs electron pulses. We demonstrate single-electron diffraction from polycrystalline diamond films and reveal the favorable influences of matched photon energies on the coherence volume of single-electron wave packets. We discuss the consequences of our findings for the physics of the photoelectric effect and for applications of single-electron pulses in ultrafast 4D imaging of structural dynamics.