Coherent X-ray Laser Research Articles

On the self-assembly of polarization domain observed in the relaxor ferroelectric Pb[(Mg1/3Nb2/3)0.722Ti0.278]O3

Self-assembly of polarization domain in relaxor-ferroelectrics Pb[(Mg1/3Nb2/3)0.722Ti0.278]O3 is discussed based on the observation of the coherent soft X-ray laser reflection. We investigate the autocorrelation of the polarization domain at the early stage of evolution. Local order of the polarization domain become in phase and periodic over 600 μm as the temperature of the crystal cool down to 383 K keeping with almost thermal equilibrium condition. Minimum domain formation free energy is discussed qualitatively.

Seeded stimulated X-ray emission at 5.9 keV.

X-ray free-electron lasers (XFELs) provide intense pulses that can generate stimulated X-ray emission, a phenomenon that has been observed and studied in materials ranging from neon to copper. Two schemes have been employed: amplified spontaneous emission (ASE) and seeded stimulated emission (SSE), where a second color XFEL pulse provides the seed. Both phenomena are currently explored for coherent X-ray laser sources and spectroscopy. Here, we report measurements of ASE and SSE of the 5.9 keV Mn Kα1 fluorescence line from a 3.9 molar NaMnO4 solution, pumped with 7 femtosecond FWHM XFEL pulses at 6.6 keV. We observed ASE at a pump pulse intensity of 1.7 × 1019 W/cm2, consistent with earlier findings. We observed SSE at dramatically reduced pump pulse intensities down to 1.1 × 1017 W/cm2. These intensities are well within the range of many existing XFEL instruments, which supports the experimental feasibility of SSE as a tool to generate coherent X-ray pulses, spectroscopic studies of transition metal complexes, and other applications.

Coherent and ultrashort soft x-ray pulses from echo-enabled harmonic cascade free-electron lasers

It is a long-standing challenge for laser technologies to generate intense fully coherent pulses in the x-ray regime. Here, we demonstrate an external seeding mechanism, termed echo-enabled harmonic cascade (EEHC) for generating coherent and ultrashort soft x-ray pulses. The mechanism uses echo-enabled harmonic generation as the first stage, producing intense extreme ultraviolet pulses that seed the second stage x-ray free-electron laser (FEL) with the high-gain harmonic generation setup. Benefiting from the low sensitivity to electron-beam imperfections of EEHC, we generated high-power nearly transform-limited soft x-ray pulses. We have also demonstrated a unique feature of EEHC in generating isolated few-femtosecond-long x-ray pulses. The supreme up-frequency conversion efficiency and flexible pulse length control of this EEHC mechanism allow us to exceed the current limitations of seeded FELs while preserving the coherence of the seed. Our results are a step towards fully coherent and ultrashort x-ray lasers and could enable the extension of nonlinear optical techniques to shorter wavelengths.

Online single-shot characterization of ultrafast pulses from high-gain free-electron lasers

X-ray free-electron lasers (FELs) provide cutting-edge tools for fundamental researches to study nature down to the atomic level at a time-scale that fits this resolution. A precise knowledge of temporal information of FEL pulses is the central issue for its applications. Here we proposed and demonstrated a novel method to determine the FEL temporal profiles online. This robust method, designed for ultrafast FELs, allows researchers to acquire real-time longitudinal profiles of FEL pulses as well as their arrive times with respect to the external optical laser with a resolution better than 6 fs. Based on this method, we can also directly measure various properties of FEL pulses and correlations between them online. This helps us to further understand the FEL lasing processes and realize the generation of stable, nearly fully coherent soft X-ray laser pulses at the Shanghai Soft X-ray FEL facility. This method will enhance the experimental opportunities for ultrafast science in various areas.

High field X-ray laser physics

High field X-ray laser physics

Narrow-band hard-x-ray lasing with highly charged ions

A scheme is put forward to generate fully coherent x-ray lasers based on population inversion in highly charged ions, created by fast inner-shell photoionization using broadband x-ray free-electron-laser (XFEL) pulses in a laser-produced plasma. Numerical simulations based on the Maxwell–Bloch theory show that one can obtain high-intensity, femtosecond x-ray pulses of relative bandwidths Δω/ω = 10−5–10−7, by orders of magnitude narrower than in x-ray free-electron-laser pulses for discrete wavelengths down to the sub-ångström regime. Such x-ray lasers can be applicable in the study of x-ray quantum optics and metrology, investigating nonlinear interactions between x-rays and matter, or in high-precision spectroscopy studies in laboratory astrophysics.

Two-Color Soft X-Ray Lasing in a High-Density Nickel-like Krypton Plasma.

We report evidence of strong lasing on the 4p-4s transition at 62.7nm in nickel-like krypton occurring simultaneously with the usual 4d-4p lasing at 32.8nm. The gain dynamics of both transitions were experimentally and numerically investigated and found comparable. The two-color amplifier was seeded by the same harmonic pulse, therefore producing a short-duration coherent two-color soft x-ray laser pulse. Both transitions offer similar prospects of pulse energy and duration and could lead to the delivery of intense and ultrashort two-color coherent soft x-ray pulses with a controllable delay.

Pulse duration of a partially coherent soft X-ray laser estimated from far-field speckle statistics.

A novel method for estimating the pulse duration of partially coherent soft X-ray pulses from a far-field intensity pattern is presented. The method is based on intensity statistics at a single point in space and time, which allows the number of coherent longitudinal modes to be measured. Utilizing the knowledge of the coherence time of the radiation, either from the measurement of the spectral bandwidth or from numerical simulations, the duration of each individual pulse can be evaluated. This method was used to estimate the pulse duration of the laser-driven nickel-like molybdenum soft X-ray laser that is based on amplified spontaneous emission from a narrow plasma column and emits at a wavelength of 18.9nm. By varying the length of the gain medium, a clear dependence of the number of modes caused mainly by the spectral line narrowing was observed. Supported by simulations of radiative transfer and pulse propagation, the pulse duration at the end of a 3mm long gain medium was estimated to be 3.5ps. The experimental data from far-field intensity patterns were also analyzed by applying the generalized van Cittert-Zernike theorem, providing a lower bound of effective source size.

Assessing uncertainties in x-ray single-particle three-dimensional reconstruction.

Modern technology for producing extremely bright and coherent x-ray laser pulses provides the possibility to acquire a large number of diffraction patterns from individual biological nanoparticles, including proteins, viruses, and DNA. These two-dimensional diffraction patterns can be practically reconstructed and retrieved down to a resolution of a few angstroms. In principle, a sufficiently large collection of diffraction patterns will contain the required information for a full three-dimensional reconstruction of the biomolecule. The computational methodology for this reconstruction task is still under development and highly resolved reconstructions have not yet been produced. We analyze the expansion-maximization-compression scheme, the current state of the art approach for this very challenging application, by isolating different sources of resolution-limiting factors. Through numerical experiments on synthetic data we evaluate their respective impact. We reach conclusions of relevance for handling actual experimental data, and we also point out certain improvements to the underlying estimation algorithm. We also introduce a practically applicable computational methodology in the form of bootstrap procedures for assessing reconstruction uncertainty in the real data case. We evaluate the sharpness of this approach and argue that this type of procedure will be critical in the near future when handling the increasing amount of data.

High brightness fully coherent x-ray amplifier seeded by a free-electron laser oscillator

X-ray free-electron laser oscillator (XFELO) is expected to be a cutting-edge tool for fully coherent x-ray laser generation, and undulator taper technique is well-known for considerably increasing the efficiency of free-electron lasers (FELs). In order to combine the advantages of these two schemes, FEL amplifier seeded by XFELO is proposed by simply using a chirped electron beam. With the right choice of the beam parameters, the bunch tail is within the gain bandwidth of XFELO, and lase to saturation, which will be served as a seeding for further amplification. Meanwhile, the bunch head which is outside the gain bandwidth of XFELO, is preserved and used in the following FEL amplifier. It is found that the natural ``double-horn'' beam current, as well as residual energy chirp from chicane compressor, are quite suitable for the new scheme. Inheriting the advantages from XFELO seeding and undulator tapering, it is feasible to generate nearly terawatt level, fully coherent x-ray pulses with unprecedented shot-to-shot stability, which might open up new scientific opportunities in various research fields.

Auger decay rates of core hole states using equation of motion coupled cluster method

The recent development of Linac coherent light source high intense X-ray laser makes it possible to create double core ionization in the molecule. The generation of double core hole state and its decay is identified by Auger spectroscopy. The decay of this double core hole (DCH) states can be used as a powerful spectroscopic tool in chemical analysis. In the present work, we have implemented a promising approach, known as CAP-EOMCC method, which is a combination of complex absorbing potential (CAP) and equation-of-motion coupled cluster (EOMCC) approach to calculate the lifetime of single and double core hole states. We have applied this method to calculate the lifetime of the single core hole (K-LL) and double core hole (KK-KLL) states of CH4, NH3 and HF molecules. The predicted lifetime is found to be extremely short.

Generation of phase - matched coherent point source in plasma media by propagated X-ray laser seeded beam

There is a significant interest in developing the coherent table-top X-ray lasers. Advent of plasma-based transient collisional excitation x-ray laser and particular, injection of coherent seeded beam, especially high-order harmonics, has tremendously improved the spatial coherence of such lasers, what allowed them to be the same widely used as synchrotron sources. Here we report experimental founding of unknown interference structure in a spatial profile of the output beam of the two-stage plasma X-ray laser. That allowed us experimental and theoretical discovering a new phenomenon consisted in a generation of phase-matched coherent point source in a laser plasma media by propagated X-ray laser seeded beam. This phenomenon could extend the applications of such x-ray lasers. For explanation of the observed phenomenon a new method of solving the standard system of Maxwell-Bloch equations has been developed. It was found that the interference pattern in the output laser beam was formed due to an emergence of phase-matched coherent virtual point source in the XRL amplifier and could be treated as the first observation of mirage phenomenon, analogous to the optical mirage, but in X-rays. The obtained results bring new comprehension into the physical nature of amplification of X-ray radiation in laser-induced plasma amplifiers and opening new opportunities for X-ray interferometry, holography and other applications, which requiring multiple rigidly phased sources of coherent radiation.

Modeling the gain of inner-shell X-ray laser transitions in neon, argon, and copper driven by X-ray free electron laser radiation using photo-ionization and photo-excitation processes

Using an X-ray free electron laser (XFEL) at 960 eV to photo-ionize the 1s electron in neutral neon followed by lasing on the 2p-1s transition in singly-ionized neon, an inner-shell X-ray laser was demonstrated at 849 eV in singly-ionized neon gas several years ago. It took decades to demonstrate this scheme, because it required a very strong X-ray source that could photo-ionize the 1s (K shell) electron in neon on a timescale comparable to the intrinsic Auger lifetime in neon of 2 fs. In this paper, we model the neon inner shell X-ray laser under similar conditions to those used in the XFEL experiments at the SLAC Linac Coherent Light Source (LCLS), and show how we can improve the efficiency of the neon laser and reduce the drive requirements by tuning the XFEL to the 1s-3p transition in neutral neon in order to create gain on the 2p-1s line in neutral neon. We also show how the XFEL could be used to photo-ionize L-shell electrons to drive gain on n = 3–2 transitions in singly-ionized Ar and Cu plasmas. These bright, coherent, and monochromatic X-ray lasers may prove very useful for doing high-resolution spectroscopy and for studying non-linear process in the X-ray regime.

Resonant Auger decay of the 4d → 6p excitation in Xe driven by short intense coherent soft x-ray pulses

The dynamics of the resonant Auger decay of the Xe excited state induced by a short coherent and intense soft x-ray laser pulse is investigated theoretically. The present approach includes (i) the non-Hermitian coupling between the ground state and the resonance caused by the driving pulse, (ii) the interference between the coherent populations of the final ionic states by the decay of the resonance and by the direct photoionization of the ground state, and (iii) the direct ionization of the resonance itself. The individual influence of the different competing physical processes on the total ion yield and on the electron spectrum of the most intense Xe spectator Auger decay line is examined. The present numerical spectra are interpreted analytically in terms of the dynamic interference of the electron waves emitted on the rising and falling sides of the driving pulse. Our results provide a theoretical basis for experiments on the verification of the dynamic interference at currently available sources of intense high-frequency laser pulses.

Investigation of femtosecond collisional ionization rates in a solid-density aluminium plasma.

The rate at which atoms and ions within a plasma are further ionized by collisions with the free electrons is a fundamental parameter that dictates the dynamics of plasma systems at intermediate and high densities. While collision rates are well known experimentally in a few dilute systems, similar measurements for nonideal plasmas at densities approaching or exceeding those of solids remain elusive. Here we describe a spectroscopic method to study collision rates in solid-density aluminium plasmas created and diagnosed using the Linac Coherent light Source free-electron X-ray laser, tuned to specific interaction pathways around the absorption edges of ionic charge states. We estimate the rate of collisional ionization in solid-density aluminium plasmas at temperatures ~30 eV to be several times higher than that predicted by standard semiempirical models.

Machine learning for ultrafast X-ray diffraction patterns on large-scale GPU clusters

The classical method of determining the atomic structure of complex molecules by analyzing diffraction patterns is currently undergoing drastic developments. Modern techniques for producing extremely bright and coherent X-ray lasers allow a beam of streaming particles to be intercepted and hit by an ultrashort high-energy X-ray beam. Through machine learning methods the data thus collected can be transformed into a three-dimensional volumetric intensity map of the particle itself. The computational complexity associated with this problem is very high such that clusters of data parallel accelerators are required. We have implemented a distributed and highly efficient algorithm for the inversion of large collections of diffraction patterns targeting clusters of hundreds of GPUs. With the expected enormous amount of diffraction data to be produced in the foreseeable future, this is the required scale to approach real-time processing of data at the beam site. Using both real and synthetic data we look at the scaling properties of the application and discuss the overall computational viability of this exciting and novel imaging technique.

Research at the NSF STC for Biology with X-ray lasers

"The NSF BioXFEL Science and Technology Center (STC) is a new consortium of six research campuses devoted to the application of x-ray free-electron lasers (XFELs) to structural biology. Over the last four years a variety of approaches have been made to the observation of protein structure and dynamics for various classes of proteins. The Linac Coherent Light source at SLAC, the first hard-Xray EXFEL, provides intense coherent hard X-ray pulses at 120 Hz which vaporize protein when focussed to a sub-micron beam. Atomic-resolution Bragg diffraction patterns are nevertheless obtained using 50 fs pulses prior to the onset of significant damage, in this ""diffract-then-destroy"" mode, which outruns radiation damage. This use of short pulses instead of freezing samples to reduce radiation damage therefore opens the way to the study of protein dynamics at room temperature in a native environment. I'll review the work of several groups using a range of approaches to different types of sample, including the following: 1. Differences between the frozen sychrotron structure of GPCR proteins and the RT XFEL structure [1]. 2. Pump-probe dynamic structures in Photosynthesis [2]. 3. XFEL study of 2D protein crystals [3]. 4. Prospects for improved resolution in XFEL imaging from single particles such as viruses, where patterns can be obtained from a single virus. 5. New ideas - the Lipid Cubic Phase injector (which allows protein nanocrystals to be studied also at sychrotrons) [4], prospects for fast Laue diffraction using coherent attosecond X-ray lasers, ab-initio phasing [5], the use of angular correlation functions for analysis of fast solution scattering, and two-color opportunites for serial femtosecond crystallography (SFX). See [6] for a recent review of the field. 1. W.Liu et al Science 342, 1521 (2013) 2. A.Aquila et al Optics Express 20, 2706 (2012) 3. M.Frank et al IUCrJ (2014) In press. 4. U.Weierstall et al Nature Comms. (2014) In press. 5. J. Spence et al Optics Express 19, 2866 (2011). 6. J. Spence et al Rep. Prog. Phys. 75, 102601 (2012)."

Coherent convergent-beam time-resolved X-ray diffraction.

The use of coherent X-ray lasers for structural biology allows the use of nanometre diameter X-ray beams with large beam divergence. Their application to the structure analysis of protein nanocrystals and single particles raises new challenges and opportunities. We discuss the form of these coherent convergent-beam (CCB) hard X-ray diffraction patterns and their potential use for time-resolved crystallography, normally achieved by Laue (polychromatic) diffraction, for which the monochromatic laser radiation of a free-electron X-ray laser is unsuitable. We discuss the possibility of obtaining single-shot, angle-integrated rocking curves from CCB patterns, and the dependence of the resulting patterns on the focused beam coordinate when the beam diameter is larger or smaller than a nanocrystal, or smaller than one unit cell. We show how structure factor phase information is provided at overlapping interfering orders and how a common phase origin between different shots may be obtained. Their use in refinement of the phase-sensitive intensity between overlapping orders is suggested.

A proposal for multi-tens of GW fully coherent femtosecond soft X-ray lasers

X-ray free-electron lasers1,2 delivering up to 1 × 1013 coherent photons in femtosecond pulses are bringing about a revolution in X-ray science3,4,5. However, some plasma-based soft X-ray lasers6 are attractive because they spontaneously emit an even higher number of photons (1 × 1015), but these are emitted in incoherent and long (hundreds of picoseconds) pulses7 as a consequence of the amplification of stochastic incoherent self-emission. Previous experimental attempts to seed such amplifiers with coherent femtosecond soft X-rays resulted in as yet unexplained weak amplification of the seed and strong amplification of incoherent spontaneous emission8. Using a time-dependent Maxwell–Bloch model describing the amplification of both coherent and incoherent soft X-rays in plasma, we explain the observed inefficiency and propose a new amplification scheme based on the seeding of stretched high harmonics using a transposition of chirped pulse amplification to soft X-rays. This scheme is able to deliver 5 × 1014 fully coherent soft X-ray photons in 200 fs pulses and with a peak power of 20 GW. Researchers describe a path towards 5 × 1014 fully coherent soft X-ray photons in 200 fs pulses reaching 20 GW peak power. The proposed amplification scheme is based on seeding stretched high harmonics using a transposition of Chirped Pulse Amplification to soft x-rays.

Enhanced nonlinear response of Ne8+to intense ultrafast x rays

We investigate the possible reasons for the discrepancy between the theoretical two-photon ionization cross section, $\sim 10^{-56}$ $\text{cm}^4 \text{s}$, of Ne$^{8+}$ obtained within the perturbative nonrelativistic framework for monochromatic light [J. Phys. B {\bf 34}, 4857 (2001)] and the experimental value, $7 \times 10^{-54}$ $\text{cm}^4 \text{s}$, reported in [Phys. Rev. Lett. {\bf 106}, 083002 (2011)] at a photon energy of 1110 eV. To this end, we consider Ne$^{8+}$ exposed to deterministic and chaotic ensembles of intense x-ray pulses. The time-dependent configuration-interaction singles (TDCIS) method is used to quantitatively describe nonlinear ionization of Ne$^{8+}$ induced by coherent intense ultrashort x-ray laser pulses. The impact of the bandwidth of a chaotic ensemble of x-ray pulses on the effective two-photon ionization cross section is studied within the lowest nonvanishing order of perturbation theory. We find that, at a bandwidth of 11 eV, the effective two-photon ionization cross section of Ne$^{8+}$ at a photon energy of 1110 eV amounts to $5 \times 10^{-57}$ and $1.6 \times 10^{-55}$ $\text{cm}^4 \text{s}$ for a deterministic ensemble and a chaotic ensemble, respectively. We show that the enhancement obtained for a chaotic ensemble of pulses originates from the presence of the one-photon 1$s^2$--1$s4p$ resonance located at 1127 eV. Using the TDCIS approach, we also show that, for currently available radiation intensities, two-photon ionization of a 1$s$ electron in neutral neon remains less probable than one-photon ionization of a valence electron.