Four-wave mixing experiments with extreme ultraviolet transient gratings.

Four-wave mixing (FWM) processes, based on third-order nonlinear light-matter interactions, can combine ultrafast time resolution with energy and wavevector selectivity, and enable the exploration of dynamics inaccessible by linear methods. The coherent and multi-wave nature of the FWM approach has been crucial in the development of advanced technologies, such as silicon photonics, subwavelength imaging and quantum communications. All these technologies operate at optical wavelengths, which limits the spatial resolution and does not allow the probing of excitations with energy in the electronvolt range. Extension to shorter wavelengths--that is, the extreme ultraviolet and soft-X-ray ranges--would allow the spatial resolution to be improved and the excitation energy range to be expanded, as well as enabling elemental selectivity to be achieved by exploiting core resonances. So far, FWM applications at such wavelengths have been prevented by the absence of coherent sources of sufficient brightness and of suitable experimental set-ups. Here we show how transient gratings, generated by the interference of coherent extreme-ultraviolet pulses delivered by the FERMI free-electron laser, can be used to stimulate FWM processes at suboptical wavelengths. Furthermore, we have demonstrated the possibility of observing the time evolution of the FWM signal, which shows the dynamics of coherent excitations as molecular vibrations. This result opens the way to FWM with nanometre spatial resolution and elemental selectivity, which, for example, would enable the investigation of charge-transfer dynamics. The theoretical possibility of realizing these applications has already stimulated ongoing developments of free-electron lasers: our results show that FWM at suboptical wavelengths is feasible, and we hope that they will enable advances in present and future photon sources.

Ultrafast Plasmon Dynamics in Crystalline LiF Triggered by Intense Extreme UV Pulses.

An extreme ultraviolet pump and visible-light probe transmission experiment in crystalline LiF, carried out at the Free Electron Laser facility FERMI, revealed an oscillating time dependence of the plasmon mode excited in the high-density high-temperature electron plasma. The effect is interpreted as a fingerprint of the electron-ion interaction: the ion motion, shaped by the electron dynamic screening, induces, in turn, electron density fluctuations that cause the oscillation of the plasmon frequency at the timescale of the ion dynamics. Fitting the high resolution transmission data with an RPA model for the temperature-dependent dielectric function, which includes electron self-energy and electron-ion coupling, confirms the interpretation of the time modulation of the plasmon mode.

Atomic and Electronic Structure of Solid-Density Liquid Carbon.

A liquid carbon (l-C) sample is generated through constant volume heating exposing an amorphous carbon foil to an intense ultrashort laser pulse. Time-resolved x-ray absorption spectroscopy at the C K edge is used to monitor the dynamics of the melting process revealing a subpicosecond rearrangement of the electronic structure associated with a sudden change of the C bonding hybridization. The obtained l-C sample, resulting from a nonthermal melting mechanism, reaches a transient equilibrium condition with a temperature of about 14 200 K and pressure in the order of 0.5 Mbar in about 0.3 ps, prior to hydrodynamic expansion. A detailed analysis of the atomic and electronic structure in solid-density l-C based on time-resolved x-ray absorption spectroscopy and theoretical simulations is presented. The method can be fruitfully used for extending the experimental investigation of the C phase diagram in a vast unexplored region covering the 10^{3}-10^{4} K temperature range with pressures up to 1 Mbar.

Characterization of ultrafast free-electron laser pulses using extreme-ultraviolet transient gratings.

The characterization of the time structure of ultrafast photon pulses in the extreme-ultraviolet (EUV) and soft X-ray spectral ranges is of high relevance for a number of scientific applications and photon diagnostics. Such measurements can be performed following different strategies and often require large setups and rather high pulse energies. Here, high-quality measurements carried out by exploiting the transient grating process, i.e. a third-order non-linear process sensitive to the time-overlap between two crossed EUV pulses, is reported. From such measurements it is possible to obtain information on both the second-order intensity autocorrelation function and on the coherence length of the pulses. It was found that the pulse energy density needed to carry out such measurements on solid state samples can be as low as a few mJ cm-2. Furthermore, the possibility to control the arrival time of the crossed pulses independently might permit the development of a number of coherent spectroscopies in the EUV and soft X-ray regime, such as, for example, photon echo and two-dimensional spectroscopy.

Optical constants modelling in silicon nitride membrane transiently excited by EUV radiation.

We hereby report on a set of transient optical reflectivity and transmissivity measurements performed on silicon nitride thin membranes excited by extreme ultraviolet (EUV) radiation from a free electron laser (FEL). Experimental data were acquired as a function of the membrane thickness, FEL fluence and probe polarization. The time dependence of the refractive index, retrieved using Jones matrix formalism, encodes the dynamics of electron and lattice excitation following the FEL interaction. The observed dynamics are interpreted in the framework of a two temperature model, which permits to extract the relevant time scales and magnitudes of the processes. We also found that in order to explain the experimental data thermo-optical effects and inter-band filling must be phenomenologically added to the model.

First Evidence of Purely Extreme-Ultraviolet Four-Wave Mixing.

The extension of nonlinear optical techniques to the extreme-ultraviolet (EUV), soft and hard x-ray regime represents one of the open challenges of modern science since it would combine chemical specificity with background-free detection and ultrafast time resolution. We report on the first observation of a four-wave-mixing (FWM) response from solid-state samples stimulated exclusively by EUV pulses. The all-EUV FWM signal was generated by the diffraction of high-order harmonics of the FERMI free-electron laser (FEL) from the standing wave resulting from the interference of two crossed FEL pulses at the fundamental wavelength. From the intensity of the FWM signal, we are able to extract the first-ever estimate of an effective value of ∼6×10^{-24} m^{2} V^{-2} for the third-order nonlinear susceptibility in the EUV regime. This proof of principle experiment represents a significant advance in the field of nonlinear optics and sets the starting point for a manifold of techniques, including frequency and phase-resolved FWM methods, that are unprecedented in this photon-energy regime.

Four-wave-mixing experiments with seeded free electron lasers.

The development of free electron laser (FEL) sources has provided an unprecedented bridge between the scientific communities working with ultrafast lasers and extreme ultraviolet (XUV) and X-ray radiation. Indeed, in recent years an increasing number of FEL-based applications have exploited methods and concepts typical of advanced optical approaches. In this context, we recently used a seeded FEL to demonstrate a four-wave-mixing (FWM) process stimulated by coherent XUV radiation, namely the XUV transient grating (X-TG). We hereby report on X-TG measurements carried out on a sample of silicon nitride (Si3N4). The recorded data bears evidence for two distinct signal decay mechanisms: one occurring on a sub-ps timescale and one following slower dynamics extending throughout and beyond the probed timescale range (100 ps). The latter is compatible with a slower relaxation (time decay > ns), that may be interpreted as the signature of thermal diffusion modes. From the peak intensity of the X-TG signal we could estimate a value of the effective third-order susceptibility which is substantially larger than that found in SiO2, so far the only sample with available X-TG data. Furthermore, the intensity of the time-coincidence peak shows a linear dependence on the intensity of the three input beams, indicating that the measurements were performed in the weak field regime. However, the timescale of the ultrafast relaxation exhibits a dependence on the intensity of the XUV radiation. We interpreted the observed behaviour as the generation of a population grating of free-electrons and holes that, on the sub-ps timescale, relaxes to generate lattice excitations. The background free detection inherent to the X-TG approach allowed the determination of FEL-induced electron dynamics with a sensitivity largely exceeding that of transient reflectivity and transmissivity measurements, usually employed for this purpose.

Spatial correlation between chemical and topological defects in vitreous silica: UV-resonance Raman study.

A spatial correlation between chemical and topological defects in the tetrahedron network in vitreous silica produced by a fusion process of natural quartz crystals was found by synchrotron-based UV resonance Raman experiments. Furthermore, a quantitative correlation between these defects was obtained by comparing visible Raman and UV absorption spectra. These results indicate that in vitreous silica produced by the fusion process the topological defects disturb the surrounding tetrahedral silica network and induce further disorder regions with sub nanometric sizes.

Element- and enantiomer-selective visualization of molecular motion in real-time.

Ultrafast optical-domain spectroscopies allow to monitor in real time the motion of nuclei in molecules. Achieving element-selectivity had to await the advent of time resolved X-ray spectroscopy, which is now commonly carried at X-ray free electron lasers. However, detecting light element that are commonly encountered in organic molecules, remained elusive due to the need to work under vacuum. Here, we present an impulsive stimulated Raman scattering (ISRS) pump/carbon K-edge absorption probe investigation, which allowed observation of the low-frequency vibrational modes involving specific selected carbon atoms in the Ibuprofen RS dimer. Remarkably, by controlling the probe light polarization we can preferentially access the enantiomer of the dimer to which the carbon atoms belong.

Extreme ultraviolet transient gratings: A tool for nanoscale photoacoustics.

Collective lattice dynamics determine essential aspects of condensed matter, such as elastic and thermal properties. These exhibit strong dependence on the length-scale, reflecting the marked wavevector dependence of lattice excitations. The extreme ultraviolet transient grating (EUV TG) approach has demonstrated the potential of accessing a wavevector range corresponding to the 10s of nm length-scale, representing a spatial scale of the highest relevance for fundamental physics and forefront technology, previously inaccessible by optical TG and other inelastic scattering methods. In this manuscript we report on the capabilities of this technique in the context of probing thermoelastic properties of matter, both in the bulk and at the surface, as well as discussing future developments and practical considerations.

Determination of the ion temperature in a stainless steel slab exposed to intense ultrashort laser pulses.

We present an effective approach to determine the amount of energy absorbed by solid samples exposed to ultrashort laser pulses, thus, retrieving the maximum temperature attained by the ion lattice in the picosecond time scale. The method is based on the pyrometric detection of a slow temperature fluctuation on the rear side of a sample slab associated with absorption of the laser pulse on the front side. This approach, successfully corroborated by theoretical calculations, can provide a robust and practical diagnostic tool for characterization of laser-generated warm dense matter.

The dispersive behavior of collective excitations in fluids: an experimental test for the generalized collective modes theory.

The predictions of the generalized collective modes (GCM) theory on the non-hydrodynamic dispersion of collective excitations of liquids and supercritical fluids have been tested against previous inelastic x-ray scattering measurements on samples of increasing complexity. We observed a good agreement between experimental results and theoretical predictions within the hypothesis that sound propagation is adiabatic. Overall, the performed comparison provides an experimental validation of GCM predictions and shows that, even in the transition region between the hydrodynamic and the mesoscopic regimes, thermal fluctuations have a minor influence on the dispersion, whose non-hydrodynamic effects are mostly driven by viscoelastic phenomena.

All-reflective femtosecond optical pump-probe setup for transient grating spectroscopy.

We developed a pump-probe setup that can be used for free electron lasers based four-wave mixing experiments in the extreme ultraviolet/soft x-ray spectral range. The main feature of the proposed optical layout is the absence of transmission optics. Test measurements on liquid and solid samples carried out using the transient grating technique in both transmission and reflection geometry demonstrate the reliability of the setup.

The single particle dynamics of iodine in the Sachs-Teller regime: an inelastic x-ray scattering study.

The high frequency dynamics of liquid iodine has been investigated by deep inelastic x-ray scattering at exchanged wave-vectors (q) ranging from 2.5 to 15 Å(-1). The experimental data have been analyzed in the frame of the Sachs-Teller theory of the molecular spectrum while accounting for final state corrections to the lineshape. The performed data analysis carries insights on physical quantities as relevant as the mean rototranslational kinetic energy and the mean square Laplacian of the intermolecular potential. In both cases the measured values are consistent with corresponding theoretical expectations.

Pressure dependence of the large-scale structure of water.

We report on small-angle x-ray scattering measurements on liquid water aimed at characterizing the pressure evolution of its large-scale structure. Diffraction profiles have been fitted assuming a Lorentzian dependence on the exchanged momentum. As a result, we observe an anomalous behavior of the diffracted intensity that tends to disappear, increasing either the pressure or the temperature. This effect is discussed in detail and imputed to the ability of hydrostatic pressure to weaken hydrogen bonds.

Temperature and density dependence of the structural relaxation time in water by inelastic ultraviolet scattering.

The density and temperature dependence of the structural relaxation time (tau) in water was determined by inelastic ultraviolet scattering spectroscopy in the thermodynamic range (P=1-4000 bars, T=253-323 K), where several water anomalies take place. We observed an activation (Arrhenius) temperature dependence of tau at constant density and a monotonic density decrease at constant temperature. The latter trend was accounted for by introducing a density-dependent activation entropy associated to water local structure. The combined temperature and density behavior of tau indicates that differently from previous results, in the probed thermodynamic range, the relaxation process is ruled by a density-dependent activation Helmholtz free energy rather than a simple activation energy. Finally, the extrapolation of the observed phenomenology at lower temperature suggests a substantial agreement with the liquid-liquid phase transition hypothesis.

High frequency dynamics in liquids and supercritical fluids: A comparative inelastic x-ray scattering study.

The microscopic dynamics of four prototype systems (water, ammonia, nitrogen, and neon) across the critical temperature has been investigated by means of high-resolution inelastic x-ray scattering. The experimental line shape has been described using a model based on the memory function formalism. Two main relaxations, the thermal and the structural one, were observed in all the investigated systems. We found that the microscopic mechanism driving the structural relaxation clearly changes, being mainly governed by intermolecular bond rearrangements below the critical temperature and by binary collisions above it. Moreover, we observed that the relative weight of the thermal relaxation systematically increases on approaching the critical temperature, thus allowing for the observation of a transition from an adiabatic to an isothermal regime of sound propagation. Finally, we found the presence of an additional instantaneous relaxation, likely related to the coupling between collective vibrational modes and intramolecular degrees of freedom.

Exploring the multiparameter nature of EUV-visible wave mixing at the FERMI FEL.

The rapid development of extreme ultraviolet (EUV) and x-ray ultrafast coherent light sources such as free electron lasers (FELs) has triggered the extension of wave-mixing techniques to short wavelengths. This class of experiments, based on the interaction of matter with multiple light pulses through the Nth order susceptibility, holds the promise of combining intrinsic ultrafast time resolution and background-free signal detection with nanometer spatial resolution and chemical specificity. A successful approach in this direction has been the combination of the unique characteristics of the seeded FEL FERMI with dedicated four-wave-mixing (FWM) setups, which leads to the demonstration of EUV-based transient grating (TG) spectroscopy. In this perspective paper, we discuss how the TG approach can be extended toward more general FWM spectroscopies by exploring the intrinsic multiparameter nature of nonlinear processes, which derives from the ability of controlling the properties of each field independently.

Nanoscale transient gratings excited and probed by extreme ultraviolet femtosecond pulses.

Advances in developing ultrafast coherent sources operating at extreme ultraviolet (EUV) and x-ray wavelengths allow the extension of nonlinear optical techniques to shorter wavelengths. Here, we describe EUV transient grating spectroscopy, in which two crossed femtosecond EUV pulses produce spatially periodic nanoscale excitations in the sample and their dynamics is probed via diffraction of a third time-delayed EUV pulse. The use of radiation with wavelengths down to 13.3 nm allowed us to produce transient gratings with periods as short as 28 nm and observe thermal and coherent phonon dynamics in crystalline silicon and amorphous silicon nitride. This approach allows measurements of thermal transport on the ~10-nm scale, where the two samples show different heat transport regimes, and can be applied to study other phenomena showing nontrivial behaviors at the nanoscale, such as structural relaxations in complex liquids and ultrafast magnetic dynamics.

High-frequency dynamics of liquid and supercritical water.

The dynamic structure factor S(Q,omega) of water has been determined by high-resolution inelastic x-ray scattering (IXS) in a momentum (Q) and energy (E) transfer range extending from 2 to 4 nm{-1} and from +/-40meV . IXS spectra have been recorded along an isobaric path (400bar) in a temperature (T) interval ranging from ambient up to supercritical (T>647K) conditions. The experimental data have been described in the frame of the generalized hydrodynamic theory, utilizing a model based on the memory function approach. This model allows identifying the active relaxation processes which affect the time decay of density fluctuations, as well as a direct determination of the Q , T , and density (rho) dependencies of the involved transport parameters. The experimental spectra are well described by considering three different relaxation processes: the thermal, the structural, and the instantaneous one. On approaching supercritical conditions, we observe that the microscopic mechanism responsible for the structural relaxation is no longer related to the making and breaking of intermolecular bonds, but to binary intermolecular collisions.