Attosecond X-ray sources, methods, and applications at present and future free-electron lasers: tutorial

A semi-analytical theory of the interaction between a relativistic laser pulse and the overdense plasma to generate an attosecond X-ray source is presented.The physical parameters such as plasma oscillation trajectory,surface electric field and magnetic field can be given by this model,and the high-order harmonic spectrum is also calculated accurately from the solution of the plasma surface oscillations,the obtained result is consistent with the result from the PIC simulation program.This model can be valid for arbitrary laser duration,solid densities,and a large set of laser peak intensities (1018-1021 W/cm2).In addition,the model is not applicable for the small laser focal spots (less than ten times the laser wavelength),although two-dimensional effects such as the pulse finite size may significantly change the movement progress of the electrons,the laser spot can be larger than ten times the laser wavelength under the general laboratory conditions. In this model,the laser energy absorption is small,and the electron kinetic pressure is also small.Due to the radiation pressure of the laser pulse,the electrons are pushed into the solid,forming a very steep density profile.As a result,the relevant forces makes the electrons ponderomotive and the longitudinal electric field is caused by the strong electric charge separation effect.This semi-analytical self-consistent theory can give us a reasonable physical description, and the momentum equation and the continuity equation of the electric and magnetic field at the boundary allow us to determine the plasma surface oscillations.The spatiotemporal characteristics of the reflected magnetic and electric field at the boundary can allow us to determine the emitting characteristics of the high order harmonic. Our results show that the radiation of the attosecond X-ray source is dependent on the plasma surface oscillation. The plasma surface oscillates with a duration about twice the laser optical cycle,and the high-order harmonics also emit twice the laser optical cycle,thus an attosecond pulse train driven by the multi-cycle laser pulse can be formed.By using a few-cycle laser field,the smooth high-order harmonics can be obtained,which leads to a single attosecond pulse with high signal-to-noise ratio.In a word,our calculation results show that the time evolution progress of plasma surface can be controlled by changing the carrier envelope phase of the few-cycle laser pulse,and then the radiation progress of the high-order harmonics can be influenced as result of a single attosecond X-ray pulse.

The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.

Obtaining two attosecond pulses for X-ray stimulated Raman spectroscopy

An attosecond x-ray pulse with known spectrotemporal information is an essential tool for the investigation of ultrafast electron dynamics in quantum systems. Ultrafast free-electron lasers (FELs) have the unique advantage on unprecedented high intensity at x-ray wavelengths. However, no suitable method has been established so far for the spectrotemporal characterization of these ultrashort x-ray pulses. In this Letter, a simple method has been proposed based on self-referenced spectral interferometry for reconstructing the temporal profile and phase of ultrashort FEL pulses. We have demonstrated that the proposed method is reliable to completely characterize the attosecond x-ray FEL pulses with an error at the level of a few percent. Moreover, the first proof-of-principle experiment has been performed to achieve the single-shot spectrotemporal characterization of ultrashort pulses from a high-gain FEL. The precision of the proposed method will be enhanced with the decrease of the pulse duration, paving a new way for complete attosecond pulse characterization at x-ray FELs.

We present measurements made with attosecond soft x-ray pulses and pulse pairs from an x-ray free-electron laser. This source offers the possibility to create and probe coherent electron dynamics with elemental specificity on its natural attosecond timescale.

In this paper, several schemes of soft X-ray and hard X-ray free electron lasers (XFEL) and their progress are reviewed. Self-amplified spontaneous emission (SASE) schemes, the high gain harmonic generation (HGHG) scheme and various enhancement schemes through seeding and beam manipulations are discussed, especially in view of the generation of attosecond X-ray pulses. Our recent work on the generation of attosecond hard X-ray pulses is also discussed. In our study, the enhanced SASE scheme is utilized, using electron beam parameters of an XFEL under construction at Pohang Accelerator Laboratory (PAL). Laser, chicane and electron beam parameters are optimized to generate an isolated attosecond hard X-ray pulse at 0.1 nm (12.4 keV). The simulations show that the manipulation of electron energy beam profile may lead to the generation of an isolated attosecond hard X-ray of 150 attosecond pulse at 0.1 nm.

Time-resolved investigation of electron dynamics relies on the generation of isolated attosecond pulses in the (soft) X-ray regime. Thomson scattering is a source of high energy radiation of increasing prevalence in modern labs, complementing large scale facilities like undulators and X-ray free electron lasers. We propose a scheme to generate isolated attosecond X-ray pulses based on Thomson scattering by colliding microbunched electrons on a chirped laser pulse. The electrons collectively act as a relativistic chirped mirror, which superradiantly reflects the laser pulse into a single localized beat. As such, this technique extends chirped pulse compression, developed for radar and applied in optics, to the X-ray regime. In this paper we theoretically show that, by using this approach, attosecond soft X-ray pulses with GW peak power can be generated from pC electron bunches at tens of MeV electron beam energy. While we propose the generation of few cycle X-ray pulses on a table-top system, the theory is universally scalable over the electromagnetic spectrum.

High-gain Free Electron Laser amplifiers are a potential source of single X-ray attosecond pulses and Attosecond Pulse Trains. Single-pulse output from short electron bunches is prone to significant power and arrival-time fluctuations. A Mode Locked Optical Klystron configuration of the FEL amplifier predicts generation of a frequency comb that may be locked to give APT output. In this paper it is shown using numerical simulations that a low feedback (so-called Regenerative Amplifier) FEL cavity resonator configuration can significantly improve output stability for single-pulse operation. The MLOK configuration may also be used in a cavity resonator to generate a frequency comb with spacing much greater than those of the axial cavity modes. As with the MLOK amplifier case, these modes can lock to generate a stable pulse train, each of a few optical cycles.

Ångstrom and attosecond are the fundamental spatiotemporal scales for electron dynamics in various materials. Although attosecond pulses with wavelengths comparable to the atomic scales are expected to be a key tool in advancing attosecond science, producing high-power hard X-ray attosecond pulses at ångstrom wavelengths remains a formidable challenge. Here, we report the generation of terawatt-scale attosecond hard X-ray pulses using a free-electron laser in a special operation mode. We achieved 9 keV single-spike X-ray pulses with a mean pulse energy of around 180 μJ, exceeding previous reports by more than an order of magnitude, and an estimated average pulse duration of 200 as at full-width at half-maximum. Exploiting the unique capability of the European XFEL, which can deliver ten pulse trains per second with each containing hundreds of pulses at megahertz repetition rates, this study demonstrates the generation of attosecond X-ray pulses at a 2.25 MHz repetition rate. These intense high-repetition-rate attosecond X-ray pulses present transformative prospects for structural and electronic damage-free X-ray measurements and attosecond time-resolved X-ray methodologies, heralding a new era in ultrafast X-ray science.

In quantum systems, coherent superpositions of electronic states evolve on ultrafast time scales (few femtoseconds to attoseconds; 1 attosecond = 0.001 femtoseconds = 10-18 seconds), leading to a time-dependent charge density. Here we performed time-resolved measurements using attosecond soft x-ray pulses produced by a free-electron laser, to track the evolution of a coherent core-hole excitation in nitric oxide. Using an additional circularly polarized infrared laser pulse, we created a clock to time-resolve the electron dynamics and demonstrated control of the coherent electron motion by tuning the photon energy of the x-ray pulse. Core-excited states offer a fundamental test bed for studying coherent electron dynamics in highly excited and strongly correlated matter.

Accelerator-based x-ray free-electron lasers (XFELs) are the latest addition to the revolutionary tools of discovery for the 21st century. The two major components of an XFEL are an accelerator-produced electron beam and a magnetic undulator, which tend to be kilometer-scale long and expensive. A proof-of-principle demonstration of free-electron lasing at 27 nm using beams from compact laser wakefield accelerators was shown recently by using a magnetic undulator. However, scaling these concepts to x-ray wavelengths is far from straightforward as the requirements on the beam quality and jitters become much more stringent. Here, we present an ultracompact scheme to produce tens of attosecond x-ray pulses with several GW peak power utilizing a novel aspect of the FEL instability using a highly chirped, prebunched, and ultrabright tens of MeV electron beam from a plasma-based accelerator interacting with an optical undulator. The FEL resonant relation between the prebunched period and the energy selects resonant electrons automatically from the highly chirped beam which leads to a stable generation of attosecond x-ray pulses. Furthermore, two-color attosecond pulses with subfemtosecond separation can be produced by adjusting the energy distribution of the electron beam so that multiple FEL resonances occur at different locations within the beam. Such a tunable coherent attosecond x-ray sources may open up a new area of attosecond science enabled by x-ray attosecond pump/probe techniques. Published by the American Physical Society 2024

Attosecond pulses at photon energies that cover the principal absorption edges of the building blocks of materials are a prerequisite for time-resolved probing of the triggering events leading to electronic dynamics such as exciton formation and annihilation. We demonstrate experimentally the isolation of individual attosecond pulses at the carbon K-shell edge (284 eV) in the soft X-ray water window with pulse duration below 400 as and with a bandwidth supporting a 30-as pulse duration. Our approach is based on spatiotemporal isolation of long-wavelength-driven harmonics and validates a straightforward and scalable approach for robust and reproducible attosecond pulse isolation.

The compact linear accelerator for research and applications (CLARA) is an ultrabright electron beam test facility being developed at STFC Daresbury Laboratory. The ultimate aim of CLARA is to test advanced free electron laser (FEL) schemes that can later be implemented on existing and future short-wavelength FELs. In addition, CLARA is a unique facility to provide a high-quality electron beam to test novel concepts and ideas in a wide range of disciplines and to function as a technology demonstrator for a future United Kingdom x-ray FEL facility. CLARA is being built in three phases; the first phase, or front end (FE), comprises an S-band rf photoinjector, a linac, and an S-bend merging with the existing versatile electron linear accelerator beam line; the second phase will complete the acceleration to full beam energy of 250 MeV and also incorporate a separate beam line for use of electrons at 250 MeV; and the third phase will include the FEL section. The CLARA FE was commissioned during 2018, and the facility was later made available for user experiments. Significant advancements have been made in developing high-level software and a simulation framework for start-to-end simulations. The high-level software has been successfully used for unmanned rf conditioning and for characterization of the electron beam. This paper describes the design of the CLARA FE, performance of technical systems, high-level software developments, preliminary results of measured beam parameters, and plans for improvements and upgrades. © 2020 authors. Published by the American Physical Society.

<sec>In 2005, the FLASH soft X-ray free-electron laser (FEL) in Hamburg, Germany, achieved its first lasing, which began an intensive phase of global FEL construction. Subsequently, the United States, Japan, South Korea, China, Italy, and Switzerland all began building such photon facilities. Recently, the new generation of FEL has started to utilize superconducting acceleration technology to achieve high-repetition-rate pulse output, thereby improving experimental efficiency. Currently completed facility is the European XFEL, ongoing constructions are the LCLS-II in the United States and the SHINE facility in Shanghai, and the facility in preparation is the Shenzhen superconducting soft X-ray free-electron laser (S<sup>3</sup>FEL).</sec><sec>These FEL facilities generate coherent and tunable ultrashort pulses ranging from the extreme ultraviolet to hard X-ray spectrum, which advances the FEL-based scattering techniques such as ultrafast X-ray scattering, spectroscopy, and X-ray nonlinear optics, thereby transforming the way we study correlated quantum materials on an ultrafast timescale.</sec><sec>The self-amplified spontaneous emission (SASE) process in FEL leads to timing jitter between FEL pulses and the synchronized pump laser, influencing the accuracy of ultrafast time-resolved measurements. To address this issue, timing tools have been developed to measure these jitters and reindexed each pump-probe signal after measurement. This success enables ultrafast X-ray diffraction (UXRD) to be first realized, and a systematic study of Peierls distorted materials is demonstrated. In addition, the high flux of FEL pulses enables Fourier transform inelastic X-ray scattering (FT-IXS) method, which can extract the phonon dispersion curve of the entire Brillouin zone by performing the Fourier transform on the measured momentum dependent coherent phonon scattering signals, even when the system is in a non-equilibrium state.</sec><sec>The UXRD is typically used to study ultrafast lattice dynamics, which requires hard X-ray wavelengths. In contrast, time resolved resonant elastic X-ray scattering (tr-REXS) in the soft X-ray regime has become a standard method of investigating nano-sized charge and spin orders in correlated quantum materials on an ultrafast time scale.</sec><sec>In correlated quantum materials, the interplay between electron dynamics and lattice dynamics represents another important research direction. In addition to Zhi-Xun Shen's successful demonstration of the combined tr-ARPES and UXRD method at SLAC, this paper also reports the attempts to integrate UXRD with resonant X-ray emission spectroscopy (RXES) for the simultaneous measurement of electronic and lattice dynamics.</sec><sec>Resonant inelastic X-ray scattering (RIXS) is a powerful tool for studying elementary and collective excitations in correlated quantum materials. However, in FEL-based soft X-ray spectroscopy, the wavefront tilt introduced by the widely used grating monochromators inevitably stretches the FEL pulses, which degrades the time resolution. Therefore, the new design at FEL beamlines adopts low line density gratings with long exit arms to reduce pulse stretch and achieve relatively high energy resolution. For example, the Heisenberg-RIXS instrument at the European XFEL achieves an energy resolution of 92 meV at the Cu <i>L</i><sub>3</sub> edge and approximately 150 fs time resolution.</sec><sec>In recent years, scientists at SwissFEL’s Furka station have drawn inspiration from femtosecond optical covariance spectroscopy to propose a new method of generating two-dimensional time-resolved resonant inelastic X-ray scattering (2D tr-RIXS) spectra. This method involves real-time detection of single-shot FEL incident and scattered spectra, followed by deconvolution calculation to avoid photon waste and wavefront tilt caused by monochromator slits. The SQS experimental station at European XFEL, built in 2023, features a 1D-XUV spectrometer that utilizes subtle variations in photon energy absorption across the sample to induce spatial energy dispersion. Using Wolter mirrors, it directly images spatially resolved fluorescence emission from the sample onto the detector to generate 2D tr-RIXS spectra without the need for deconvolution. However, this design is limited to specific samples. Currently, the S<sup>3</sup>FEL under designing has a novel 2D tr-RIXS instrument that uses an upstream low line density grating monochromator to generate spatial dispersion of the beam spot, allowing the full bandwidth of SASE to project spatially dispersed photon energy onto the sample. Subsequently, an optical design similar to the 1D-XUV spectrometer will be employed to achieve 2D tr-RIXS spectra, thereby expanding the applicability beyond specific liquid samples. These new instruments are designed to minimize pulse elongation by fully utilizing SASE’s full bandwidth, approaching Fourier-transform-limited RIXS spectra in both time and energy resolution.</sec><sec>Nonlinear X-ray optical techniques, such as sum-frequency generation (SFG) and second-harmonic generation, are adapting to X-ray wavelengths and opening up new avenues for detecting elementary excitations. The X-ray transient grating spectroscopy extends its capabilities to studying charge transport and spin dynamics on an ultrafast timescale. The future development of these scattering methods provides unique opportunities for detecting dynamical events in various systems, including surface and interface processes, chirality, nanoscale transport, and so-called multidimensional core-level spectroscopy.</sec>

Ultrafast electron dynamics determines how physical and chemical changes occur at a fundamental level. The investigation of such processes requires (isolated) attosecond pulses [1]. On all time scales down to the attosecond regime, there are a number of physical processes that depend on the electric field, rather than just the intensity envelope of a driving pulse. There have been numerous proposals to produce ultrashort pulses in free-electron lasers (FELs) [2]. However, the temporal coherence of the output radiation is limited. In order to solve this problem, we proposed a robust method for producing waveform-controlled CEP-stable attosecond pulses in the EUV spectral range in a FEL [3]. Here, we investigate the feasibility of our setup when a laser-plasma accelerator (LPA) is used as the electron source, rather than a LINAC.