Time-dependent Diffraction Research Articles

Unusual photoinduced crystal structure dynamics in TaTe2 with double zigzag chain superstructure

Transition metal dichalcogenides with superperiodic lattice distortions have been widely investigated as the platform of ultrafast structural phase manipulations. Here we performed ultrafast electron diffraction on RT TaTe2, which exhibits a peculiar double zigzag chain pattern of Ta atoms. From the time-dependent electron diffraction pattern, we revealed a photoinduced change in the crystal structure occurring within <0.5 ps, although there is no corresponding high-temperature equilibrium phase. We further clarified the slower response (∼1.5 ps) reflecting the lattice thermalization. Our result suggests the unusual ultrafast crystal structure dynamics specific to the non-equilibrium transient process in TaTe2.

Ultrafast Kapitza-Dirac effect.

Similar to the optical diffraction of light passing through a material grating, the Kapitza-Dirac effect occurs when an electron is diffracted by a standing light wave. In its original description, the effect is time independent. Here, we extended the Kapitza-Dirac effect to the time domain. By tracking the spatiotemporal evolution of a pulsed electron wave packet diffracted by a 60-femtosecond (where one femtosecond = 10-15 seconds) standing wave pulse in a pump-probe scheme, we observed time-dependent diffraction patterns. The fringe spacing in the observed pattern differs from that generated by the conventional Kapitza-Dirac effect. By exploiting this time-resolved diffraction scheme, we can access the time evolution of the phase properties of a free electron and potentially image ionic potentials and electronic decoherences.

Femtosecond Electronic and Hydrogen Structural Dynamics in Ammonia Imaged with Ultrafast Electron Diffraction.

Directly imaging structural dynamics involving hydrogen atoms by ultrafast diffraction methods is complicated by their low scattering cross sections. Here we demonstrate that megaelectronvolt ultrafast electron diffraction is sufficiently sensitive to follow hydrogen dynamics in isolated molecules. In a study of the photodissociation of gas phase ammonia, we simultaneously observe signatures of the nuclear and corresponding electronic structure changes resulting from the dissociation dynamics in the time-dependent diffraction. Both assignments are confirmed by abinitio simulations of the photochemical dynamics and the resulting diffraction observable. While the temporal resolution of the experiment is insufficient to resolve the dissociation in time, our results represent an important step towards the observation of proton dynamics in real space and time.

Time-Varying Optical Spin-Orbit Interactions in Tight Focusing of Self-Torqued Beams

Self-torque has recently been observed as a novel property of light that features time-varying orbital angular momentum (OAM) along a light pulse. This property offers an additional degree of freedom for manipulating light fields and light-matter interactions on ultrafast time scales. In this work, we theoretically study the self-torque's role in modulating tightly focused fields and reveal spin-orbit interactions (SOIs) in the focused fields using time-dependent vectorial diffraction theory. It is found that time-varying SOIs occur between the spin angular momentum (SAM), intrinsic OAM and extrinsic OAM. Specifically, the spin-to-orbit conversion, orbit-to-local-spin conversion, and optical spin-Hall effect are observed in the focused self-torqued beams. In particular, when the incident beams are circularly polarized, the time-dependent transverse SAM distributions will appear in the focal plane. Moreover, the self-torque of the focused light fields can be controlled via spin-to-orbit conversion. These observations could benefit potential applications in ultrafast light field modulation, microscopy, and optical manipulation.

Method for extracting the equivalent admittance from time-varying metasurfaces and its application to self-tuned spatiotemporal wave manipulation

With their self-tuned time-varying responses, waveform-selective metasurfaces embedded with nonlinear electronics have shown fascinating applications, including distinguishing different electromagnetic waves depending on the pulse width (PW). However, thus far they have only been realized with a spatially homogeneous scattering profile. Here, by modeling a metasurface as time-varying admittance sheets, we provide an analytical calculation method to predict the metasurface time-domain responses. This allows derivation of design specifications in the form of equivalent sheet admittance, which is useful in synthesizing a metasurface with spatiotemporal control, such as to realize a metasurface with prescribed time-dependent diffraction characteristics. As an example, based on the proposed equivalent admittance sheet modeling, we synthesize a waveform-selective Fresnel zone plate with variable focal length depending on the incoming PW. The proposed synthesis method for PW-dependent metasurfaces may be extended to designing metasurfaces with more complex spatiotemporal wave manipulation, benefiting applications such as sensing, wireless communications and signal processing.

Temporal effect on tight focusing, optical force and spin torque of high-order vector-vortex beams

We theoretically study the dependence of the light field distributions, optical force and spin torque of high-order vector-vortex (HOVV) beams focused by a high numerical aperture objective on ultrafast variable time (0–400 fs). It is accomplished by the fast Fourier transform, time-dependent vectorial diffraction theory and Rayleigh scattering model. Firstly, it is shown that the light field patterns of tightly focused HOVV beams can be quasi-periodically reshaped by adjusting the intrinsic fleeting time. We further examine the three-dimensional (3D) distributions of optical force on a Rayleigh particle (with a size much smaller than the light wavelength) in the focal volume induced from tightly focused HOVV beams, which reveals that the distinct vector-vortex light fields as a function of ultrafast time endow the capability of the selective trapping for particles. Beyond that, we proceed to the 3D spin torque on the given particle, which makes the conversions between transverse and longitudinal spin torques possible, resulting in the 3D spatial rotation within an ultrafast timescale. Additionally, it is found that the vortex order plays a pivotal role in steering the focused light fields and related optical forces and spin torques. The proposed pathway and acquired results not only provide a novel degree of freedom for the ultrafast control of light fields, but also have potential applications in integrated spectroscopic analysis, ultrafast optical tweezers and spanners, and high-speed optical measurements.

Ultrafast multi-target control of tightly focused light fields

The control of ultrafast optical field is of great interest in developing ultrafast optics as well as the investigation on various light-matter interactions with ultrashort pulses. However, conventional spatial encoding approaches have only limited steerable targets usually neglecting the temporal effect, thus hindering their broad applications. Here we present a new concept for realizing ultrafast modulation of multi-target focal fields based on the facile combination of time-dependent vectorial diffraction theory with fast Fourier transform. This is achieved by focusing femtosecond pulsed light carrying vectorial-vortex by a single objective lens under tight focusing condition. It is uncovered that the ultrafast temporal degree of freedom within a configurable temporal duration (~400 fs) plays a pivotal role in determining the rich and exotic features of the focused optical field at one time, namely, bright-dark alternation, periodic rotation, and longitudinal/transverse polarization conversion. The underlying control mechanisms have been unveiled. Besides being of academic interest in diverse ultrafast spectral regimes, these peculiar behaviors of the space-time evolutionary beams may underpin prolific ultrafast-related applications such as multifunctional integrated optical chip, high-efficiency laser trapping, microstructure rotation, super-resolution optical microscopy, precise optical measurement, and liveness tracking.

Imaging charge migration in chiral molecules using time-resolved x-ray diffraction

Four-dimensional imaging of charge migration is crucial to the understanding of several ubiquitous processes in nature. The present work focuses on imaging of charge migration in an oriented epoxypropane: a chiral molecule. A linearly polarized pulse is used to induce the charge migration, which is imaged by time-resolved x-ray diffraction. It is found that the total time-resolved diffraction signals are significantly different for both enantiomers. Furthermore, a connection between time-resolved x-ray diffraction and the electronic continuity equation is discussed by analyzing the time-dependent diffraction signal and the time derivative of the total electron density in the momentum space.

Ultrafast Valence-Electron Dynamics in Oxazole Monitored by X-ray Diffraction Following a Stimulated X-ray Raman Excitation.

Direct imaging of the ultrafast quantum motion of valence electrons in molecules is essential for understanding many elementary chemical and physical processes. We present a simulation study of valence-electron dynamics of oxazole. A valence-state electronic wavepacket is prepared with an attosecond soft X-ray pulse through a stimulated resonant X-ray Raman process and then probed with time-resolved off-resonant single-molecule X-ray diffraction. We find that the time dependent diffraction signal originates solely from the electronic coherences and can be detected by existing experimental techniques. We thus provide a feasible way of imaging electron dynamics in molecules. Moreover, the created electronic coherences and subsequent electron dynamics can be manipulated by the resonant X-ray Raman excitation tuned to different core-excited states.

Ultrafast laser-induced strain waves in thin ruthenium layers

We report on the time-dependent optical diffraction from ultra-high frequency laser-induced acoustic waves in thin layers of ruthenium deposited on glass substrates. We show that the thermo-optic and strain-optic effects dominate the optical response of Ru layers to a traveling longitudinal strain wave. In addition, we show the generation and detection of acoustic waves with a central frequency ranging from 130 GHz to 750 GHz on ultra-thin layers with thicknesses in the range of 1.2 - 20 nm. For these ultra-thin layers we measure a strong dependency of the speed of sound on the layer thickness and, thus, the frequency. This frequency-dependent speed of sound results in a frequency-dependent acoustic impedance mismatch between the ruthenium and the glass substrate, leading to a faster decay of the measured signals for increasing frequency. Furthermore, for these extremely high-frequency oscillations, we find that the frequency and phase remain constant for times longer than about 2 ps after optical excitation. Back extrapolation of the acquired acoustic signals to t = 0 gives a starting phase of -π/2. As this seems unlikely, we interpret this as an indication of possible dynamic changes in the phase/frequency of the acoustic wave in the first 2 ps after excitation.

Laser-induced ultrasonics for detection of low-amplitude grating through metal layers with finite roughness.

We report on the use of laser-induced ultrasonics for the detection of gratings with amplitudes as small as 0.5 nm, buried underneath an optically opaque nickel layer. In our experiments, we use gratings fabricated on top of a nickel layer on glass, and we optically pump and probe the sample from the glass side. The diffraction of the probe pulse from the acoustic echo from the buried grating is measured as a function of time. We use a numerical model to show how the various physical phenomena such as interface displacement, strain-optic effects, thermo-optic effects, and surface roughness influence the shape and strength of the time-dependent diffraction signal. More importantly, we use a Rayleigh-Rice scattering theory to quantify the amount of light scattering, which is then used as in input parameter in our numerical model to predict the time-dependent diffracted signal.

Detection of Hidden Gratings through Multilayer Nanostructures Using Light and Sound

We report on the detection of diffraction gratings buried below a stack of tens of 18 nm thick $\mathrm{SiO_2}$ and $\mathrm{Si_3N_4}$ layers and an optically opaque metal layer, using laser-induced, extremely-high frequency ultrasound. In our experiments, the shape and amplitude of a buried metal grating is encoded on the spatial phase of the reflected acoustic wave. This grating-shaped acoustic echo from the buried grating is detected by diffraction of a delayed probe pulse. The shape and strength of the time-dependent diffraction signal can be accurately predicted using a 2D numerical model. Surprisingly, our numerical calculations show that the diffracted signal strength is not strongly influenced by the number of dielectric layers through which the acoustic wave has to propagate. Replacing the $\mathrm{SiO_2}$/$\mathrm{Si_3N_4}$ layer stack with a single layer having an equivalent time-averaged sound velocity and average density, has only a small effect on the shape and amplitude of the diffracted signal as a function of time. Our results show that laser-induced ultrasound is a promising technique for sub-surface nano-metrology applications.

Exploring the configuration spaces of surface materials using time-dependent diffraction patterns and unsupervised learning

Computational methods for exploring the atomic configuration spaces of surface materials will lead to breakthroughs in nanotechnology and beyond. In order to develop such methods, especially ones utilizing machine learning approaches, descriptors which encode the structural features of the candidate configurations are required. In this paper, we propose the use of time-dependent electron diffraction simulations to create descriptors for the configurations of surface materials. Our proposal utilizes the fact that the sub-femtosecond time-dependence of electron diffraction patterns are highly sensitive to the arrangement of atoms in the surface region of the material, allowing one to distinguish configurations which possess identical symmetry but differ in the locations of the atoms in the unit cell. We demonstrate the effectiveness of this approach by considering the simple cases of copper(111) and an organic self-assembled monolayer system, and use it to search for metastable configurations of these materials.

Nondestructive Measurements of the Mechanical and Structural Properties of Nanostructured Metalattices.

Metalattices are artificial 3D solids, periodic on sub-100 nm length scales, that enable the functional properties of materials to be tuned. However, because of their complex structure, predicting and characterizing their properties is challenging. Here we demonstrate the first nondestructive measurements of the mechanical and structural properties of metalattices with feature sizes down to 14 nm. By monitoring the time-dependent diffraction of short wavelength light from laser-excited acoustic waves in the metalattices, we extract their acoustic dispersion, Young's modulus, filling fraction, and thicknesses. Our measurements are in excellent agreement with macroscopic predictions and potentially destructive techniques such as nanoindentation and scanning electron microscopy, with increased accuracy over larger areas. This is interesting because the transport properties of these metalattices do not obey bulk predictions. Finally, this approach is the only way to validate the filling fraction of metalattices over macroscopic areas. These combined capabilities can enable accurate synthesis of nanoenhanced materials.

Hierarchically Porous Co-MOF-74 Hollow Nanorods for Enhanced Dynamic CO2 Separation.

Metal-organic frameworks (MOFs) with coordinatively unsaturated (open) metal sites have been intensively investigated in gas separations because their active sites can selectively interact with targeted molecules such as CO2. Although such MOFs have shown to exhibit exceptional CO2 uptake capacity at equilibrium, the dynamic separation behavior is often not satisfactory to be considered in practical applications. Herein, we report a facile and efficient self-sacrifice template strategy based on the nanoscale Kirkendall effect to form novel Co-MOF-74 hollow nanorods enabling adsorption/desorption of gas molecules in a facilitated manner. The time-dependent microscopic and diffraction examinations were performed to elucidate the formation mechanism of Co-MOF-74 hollow nanorods and to obtain insights into the factors critical to maintaining the rodlike morphology. Such nanostructured MOF exhibited much sharper CO2 molecular separation behavior than conventional MOF bulk crystals under a dynamic flow condition, because of its enhanced adsorption kinetics through the shortened diffusion distance. Such enhanced dynamic molecular separation behavior was further confirmed by chromatographic separations where a significant peak narrowing was demonstrated.

Energy-resolved coherent diffraction from laser-driven electronic motion in atoms

We investigate theoretically the use of energy-resolved ultrafast electron diffraction to image laser-driven electronic motion in atoms. A chirped laser pulse is used to transfer the valence electron of the lithium atom from the ground state to the first excited state. During this process, the electronic motion is imaged by 100-fs and 1-fs electron pulses in energy-resolved diffraction measurements. Simulations show that the angle-resolved spectra reveal the time evolution of the energy content and symmetry of the electronic state. The time-dependent diffraction patterns are further interpreted in terms of the momentum transfer. For the case of incident 1-fs electron pulses, the rapid $2s\ensuremath{-}2p$ quantum beat motion of the target electron is imaged as a time-dependent asymmetric oscillation of the diffraction pattern.

Robust reconstruction of time-resolved diffraction from ultrafast streak cameras

In conjunction with ultrafast diffraction, streak cameras offer an unprecedented opportunity for recording an entire molecular movie with a single probe pulse. This is an attractive alternative to conventional pump-probe experiments and opens the door to studying irreversible dynamics. However, due to the “smearing” of the diffraction pattern across the detector, the streaking technique has thus far been limited to simple mono-crystalline samples and extreme care has been taken to avoid overlapping diffraction spots. In this article, this limitation is addressed by developing a general theory of streaking of time-dependent diffraction patterns. Understanding the underlying physics of this process leads to the development of an algorithm based on Bayesian analysis to reconstruct the time evolution of the two-dimensional diffraction pattern from a single streaked image. It is demonstrated that this approach works on diffraction peaks that overlap when streaked, which not only removes the necessity of carefully choosing the streaking direction but also extends the streaking technique to be able to study polycrystalline samples and materials with complex crystalline structures. Furthermore, it is shown that the conventional analysis of streaked diffraction can lead to erroneous interpretations of the data.

Numerical simulation of THz-wave-assisted electron diffraction for ultrafast molecular imaging

A scheme for achieving high temporal resolution in gas electron diffraction is proposed, in which time-dependent electron diffraction patterns can be obtained from energy-resolved angular distributions of electrons scattered by molecules in dynamical processes under the presence of a single-cycle THz-wave pulse. Derived formulae of the differential cross section and numerical simulations of electron signals scattered by Ar atoms and $\mathrm{C}{\mathrm{l}}_{2}$ molecules show that the temporal resolution of the proposed method can be $&lt;10\phantom{\rule{0.16em}{0ex}}\mathrm{fs}$ in the pump-probe measurement without scanning the time delay.

Monitoring coherent electron wave packet excitation dynamics by two-color attosecond laser pulses.

We propose a method to monitor coherent electron wave packet (CEWP) excitation dynamics with two-color attosecond laser pulses. Simulations are performed on aligned H2+ by numerically solving the three-dimensional time-dependent Schrödinger equation with combinations of a resonant linearly polarized λl= 100/70 nm pump pulse and a circularly polarized λc=5 nm attosecond probe pulse. It is found that time dependent diffraction patterns in molecular frame photoelectron angular distributions (MFPADs) produced by the circular probe pulse exhibit sensitivity to the molecular alignments and time-dependent geometry of the CEWPs during and after the coherent excitation between the ground and excited states induced by the linear pump pulse. The time dependent MFPADs are described by an ultrafast diffraction model for the ionization of the bound CEWPs.

Capturing Structural Dynamics in Crystalline Silicon Using Chirped Electrons from a Laser Wakefield Accelerator.

Recent progress in laser wakefield acceleration has led to the emergence of a new generation of electron and X-ray sources that may have enormous benefits for ultrafast science. These novel sources promise to become indispensable tools for the investigation of structural dynamics on the femtosecond time scale, with spatial resolution on the atomic scale. Here, we demonstrate the use of laser-wakefield-accelerated electron bunches for time-resolved electron diffraction measurements of the structural dynamics of single-crystal silicon nano-membranes pumped by an ultrafast laser pulse. In our proof-of-concept study, we resolve the silicon lattice dynamics on a picosecond time scale by deflecting the momentum-time correlated electrons in the diffraction peaks with a static magnetic field to obtain the time-dependent diffraction efficiency. Further improvements may lead to femtosecond temporal resolution, with negligible pump-probe jitter being possible with future laser-wakefield-accelerator ultrafast-electron-diffraction schemes.