Four-wave mixing experiments with extreme ultraviolet transient gratings

Nanoscale polarization transient gratings

Light manipulation at the nanoscale is essential both for fundamental science and modern technology. The quest to shorter lengthscales, however, requires the use of light wavelengths beyond the visible. In particular, in the extreme ultraviolet regime these manipulation capabilities are hampered by the lack of efficient optics, especially for polarization control. Here, we present a method to create periodic, polarization modulations at the nanoscale using a tailored configuration of the FERMI free electron laser and demonstrate its capabilities by comparing the dynamics induced by this polarization transient grating with those driven by a conventional intensity grating on a thin ferrimagnetic alloy. While the intensity grating signal is dominated by the thermoelastic response, the polarization grating excitation minimizes it, uncovering helicity-dependent responses previously undetected. We anticipate nanoscale polarization transient gratings to become useful for the study of physical, chemical and biological systems possessing chiral symmetry.

Excitation and detection of coherent nanoscale spin waves via extreme ultraviolet transient gratings

The advent of free electron lasers has opened the opportunity to explore interactions between extreme ultraviolet (EUV) photons and collective excitations in solids. While EUV transient grating spectroscopy, a noncollinear four-wave mixing technique, has already been applied to probe coherent phonons, the potential of EUV radiation for studying nanoscale spin waves has not been harnessed. Here we report EUV transient grating experiments with coherent magnons in Fe/Gd ferrimagnetic multilayers. Magnons with tens of nanometers wavelengths are excited by a pair of femtosecond EUV pulses and detected via diffraction of a probe pulse tuned to an absorption edge of Gd. The results unlock the potential of nonlinear EUV spectroscopy for studying magnons and provide a tool for exploring spin waves in a wave vector range not accessible by established inelastic scattering techniques.

Impact of MoS2 Monolayers on the Thermoelastic Response of Silicon Heterostructures

Understanding the thermoelastic response of a nanostructure is crucial for the choice of materials and interfaces in electronic devices with improved and tailored transport properties at the nanoscale. Here, we show how the deposition of a MoS2 monolayer can strongly modify the nanoscale thermoelastic dynamics of silicon substrates close to their interface. We demonstrate this by creating a transient grating with extreme ultraviolet light, using ultrashort free-electron laser pulses, whose ≈84 nm period is comparable to the size of elements typically used in nanodevices, such as electric contacts and nanowires. The thermoelastic response, featuring coherent acoustic waves and incoherent relaxation, is tangibly modified by the presence of monolayer MoS2. Namely, we observed a major reduction of the amplitude of the surface mode, which is almost suppressed, while the longitudinal mode is basically unperturbed, aside from a faster decay of the acoustic modulations. We interpret this behavior as a selective modification of the surface elasticity, and we discuss the conditions to observe such effect, which may be of immediate relevance for the design of Si-based nanoscale devices.

Core-Hole Coherent Spectroscopy in Molecules

We study the ultrafast dynamics initiated by a coherent superposition of core-excited states of nitrous oxide molecule. Using high-level ab initio methods, we show that the decoherence caused by the electronic decay and the nuclear dynamics is substantially slower than the induced ultrafast quantum beatings, allowing the system to undergo several oscillations before it dephases. We propose a proof-of-concept experiment using the harmonic up-conversion scheme available at x-ray free-electron laser facilities to trace the evolution of the created core-excited-state coherence through a time-resolved x-ray photoelectron spectroscopy.

Exploring the Fundamental Spatial Limits of Magnetic All-Optical Switching

All-optical switching (AOS) results in ultrafast and deterministic magnetization reversal upon single laser pulse excitation, potentially supporting faster and more energy-efficient data storage. To explore the fundamental limits of achievable bit densities in AOS, we have used soft X-ray transient grating spectroscopy to study the ultrafast magnetic response of a GdFe alloy after a spatially structured excitation with a periodicity of 17 nm. The ultrafast spatial evolution of the magnetization in combination with atomistic spin dynamics and microscopic temperature model calculations allows us to derive a detailed phase diagram of AOS as a function of both the absorbed energy density and the nanoscale excitation period. Our results suggest that the minimum size for AOS in GdFe alloys, induced by a nanoscale periodic excitation, is around 25 nm and that this limit is governed by ultrafast lateral electron diffusion and by the threshold for optical damage.

Transient grating spectroscopy on a DyCo5 thin film with femtosecond extreme ultraviolet pulses

Surface acoustic waves (SAWs) are excited by femtosecond extreme ultraviolet (EUV) transient gratings (TGs) in a room-temperature ferrimagnetic DyCo5 alloy. TGs are generated by crossing a pair of EUV pulses from a free electron laser with the wavelength of 20.8 nm matching the Co M-edge, resulting in a SAW wavelength of Λ = 44 nm. Using the pump-probe transient grating scheme in reflection geometry, the excited SAWs could be followed in the time range of -10 to 100 ps in the thin film. Coherent generation of TGs by ultrafast EUV pulses allows to excite SAW in any material and to investigate their couplings to other dynamics, such as spin waves and orbital dynamics. In contrast, we encountered challenges in detecting electronic and magnetic signals, potentially due to the dominance of the larger SAW signal and the weakened reflection signal from underlying layers. A potential solution for the latter challenge involves employing soft x-ray probes, albeit introducing additional complexities associated with the required grazing incidence geometry.

Transient responses of double core-holes generation in all-attosecond pump-probe spectroscopy

Double core-holes (DCHs) show remarkable and sensitive effects for understanding electron correlations and coherence. With advanced modulation of x-ray free-electron laser (XFEL) facility, we propose the forthcoming all-attosecond XFEL pump-probe spectroscopy can decipher the hidden photon-initiated dynamics of DCHs. The benchmark case of neon is investigated, and norm-nonconserving Monte-Carlo wavefunction method simulates non-Hermitian dynamics among vast states, which shows superiority in efficiency and reliability. In our scheme, population transfer to DCHs is sequentially irradiated by pump and probe laser. By varying time delay, Stark shifts and quantum path interference of resonant lines sensitively emerge at specific interval of two pulses. These ubiquitous multi-channel effects are also observed in phase-fluctuating pulses, derived from extra phases of impulsive Raman processes by pump laser. Non-perturbation absorption/emission verifies the uniquely interchangeable role of two pules in higher intensity. Our results reveal sensitive and robust responses on pulse parameters, which show potential capacity for XFEL attosecond pulse diagnosis and further attosecond-timescale chemical analysis.

Millijoule Femtosecond X-Ray Pulses from an Efficient Fresh-Slice Multistage Free-Electron Laser

We present the generation of x-ray pulses with average pulse energies up to one millijoule and rms pulse durations down to the femtosecond level. We have produced these intense and short pulses by employing the fresh-slice multistage amplification scheme with a transversely tilted electron beam in a free-electron laser. In this scheme, a short pulse is produced in the first stage and later amplified by fresh parts of the electron bunch in up to a total of four stages of amplification. Our implementation is efficient, since practically the full electron beam contributes to produce the x-ray pulse. Our implementation is also compact, utilizing only 32 m of undulator. The demonstration was done at Athos, the soft x-ray beamline of SwissFEL, which was designed with high flexibility to take full advantage of the multistage amplification scheme. It opens the door for scientific opportunities following ultrafast dynamics using nonlinear x-ray spectroscopy techniques or avoiding electronic damage when capturing structures with a single intense pulse via single-particle imaging.

Stimulated Brillouin Scattering in the Time Domain at 1 nm^{-1} Wave Vector

We used extreme ultraviolet (EUV) pulses to create transient gratings (TGs) with sub-100 nm spatial periodicity in a β-Ga_{2}O_{3} single crystal. The EUV TG launches acoustic modes parallel to the sample surface, whose dynamics were revealed via backward diffraction of a third, time-delayed, EUV pulse. In addition, the sharp penetration depth of EUV light launches acoustic modes along the surface normal with a broad wave vector spectrum. The dynamics of selected modes at a wave vector tangibly larger (≈1  nm^{-1}) than the TG one is detected in the time domain via the interference between the backward diffracted TG signal and the stimulated Brillouin backscattering of the EUV probe. While stimulated Brillouin backscattering of an optical probe was reported in previous EUV TG experiments, its extension to shorter wavelengths can be used as a contactless experimental tool for filling the gap between the wave vector range accessible by inelastic hard x-ray and thermal neutron scattering techniques, and the one accessible through Brillouin scattering of visible and UV light.

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.

Elettra-Sincrotrone Trieste: present and future

We present an overview of the Elettra-Sincrotrone Trieste research center, which hosts synchrotron and free-electron laser light sources. We review the current status, provide examples of recent achievements in basic and applied research and discuss the upgrade programs of the facility.

Molecular Chirality and Its Monitoring by Ultrafast X-ray Pulses

Major advances in X-ray sources including the development of circularly polarized and orbital angular momentum pulses make it possible to probe matter chirality at unprecedented energy regimes and with Ångström and femtosecond spatiotemporal resolutions. We survey the theory of stationary and time-resolved nonlinear chiral measurements that can be carried out in the X-ray regime using tabletop X-ray sources or large scale (XFEL, synchrotron) facilities. A variety of possible signals and their information content are discussed.

Pump-guided nonlinear film for phase conjugation

It is known that phase conjugation technique is achieved by the nonlinearity of materials, and widely adopted in various applications, such as high-resolution imaging, signal amplification, and target detecting. Here, we have proposed a field-enhancement method for the degenerate four wave mixing (FWM) for phase conjugation purpose. In this method, a thin film waveguide with nonlinear property is utilized to confine and guide the pumps, achieving the enhanced FWM within a flexible structure. Compared to existing degenerate FWM methods, three merits are introduced by the proposed pump-guided nonlinear film. First, the pump is confined and guided in the nonlinear waveguide, and the pump energy is concentrated to achieve high power level of the phase-conjugated signals. Second, less pump energy leaks out from the thin film, with less interference to the phase-conjugated signals. The last one is that pump-guided film can be engineered into flexible shapes for different practical applications. Based on these advantages, the phase conjugation property is numerically verified for high-resolution image reconstruction, even with damping of waveguide or in the presence of the metallic particles and the dielectric blocks.

Extreme Ultraviolet Wave Packet Interferometry of the Autoionizing HeNe Dimer

Femtosecond extreme ultraviolet wave packet interferometry (XUV-WPI) was applied to study resonant interatomic Coulombic decay (ICD) in the HeNe dimer. The high demands on phase stability and sensitivity for vibronic XUV-WPI of molecular-beam targets are met using an XUV phase-cycling scheme. The detected quantum interferences exhibit vibronic dephasing and rephasing signatures along with an ultrafast decoherence assigned to the ICD process. A Fourier analysis reveals the molecular absorption spectrum with high resolution. The demonstrated experiment shows a promising route for the real-time analysis of ultrafast ICD processes with both high temporal and high spectral resolution.

Probing electron and hole colocalization by resonant four-wave mixing spectroscopy in the extreme ultraviolet

Extending nonlinear spectroscopic techniques into the x-ray domain promises unique insight into photoexcited charge dynamics, which are of fundamental and applied interest. We report on the observation of a third-order nonlinear process in lithium fluoride (LiF) at a free-electron laser. Exploring the yield of four-wave mixing (FWM) in resonance with transitions to strongly localized core exciton states versus delocalized Bloch states, we find resonant FWM to be a sensitive probe for the degree of charge localization: Substantial sum- and difference-frequency generation is observed exclusively when in a one- or three-photon resonance with a LiF core exciton, with a dipole forbidden transition affecting details of the nonlinear response. Our reflective geometry-based approach to detect FWM signals enables the study of a wide variety of condensed matter sample systems, provides atomic selectivity via resonant transitions, and can be easily scaled to shorter wavelengths at free-electron x-ray lasers.

Ultra-strong optical four-wave mixing signal induced by strong exciton-phonon and exciton-plasmon couplings

We propose a scheme to generate ultra-strong four-wave mixing (FWM) signal based on a suspended monolayer graphene nanoribbon nanomechanical resonator (NR) coupled to an Au nanoparticle (NP). It is shown that, the FWM spectrum can switch among two-peaked, three-peaked, four-peaked or five-peaked via the modulation of exciton-phonon and exciton-plasmon couplings. This is mainly attributed to the vibrational properties of NR related to the exciton-phonon coupling, and the energy-level splitting of the localized exciton correlated to three classes of resonances consisting of three-photon resonance, Rayleigh Resonance, and AC-Stark atomic resonance. Especially, in a dual-strong coupling regime, the gains for these peaks can be as high as nine orders of magnitude (∼ 10⁹) around the lower bistable threshold due to a combined effect of two couplings. Our findings not only offer an efficient way to measure the vibrational frequency of NR and the exciton-phonon coupling strength but also provide a possibility to fabricate high-performance optoelectronic nanodevices.

SU(2)-in-SU(1,1) Nested Interferometer for High Sensitivity, Loss-Tolerant Quantum Metrology

We present experimental and theoretical results on a new interferometer topology that nests a SU(2) interferometer, e.g., a Mach-Zehnder or Michelson interferometer, inside a SU(1,1) interferometer, i.e., a Mach-Zehnder interferometer with parametric amplifiers in place of beam splitters. This SU(2)-in-SU(1,1) nested interferometer (SISNI) simultaneously achieves a high signal-to-noise ratio (SNR), sensitivity beyond the standard quantum limit (SQL) and tolerance to photon losses external to the interferometer, e.g., in detectors. We implement a SISNI using parametric amplification by four-wave mixing (FWM) in Rb vapor and a laser-fed Mach-Zehnder SU(2) interferometer. We observe path-length sensitivity with SNR 2.2 dB beyond the SQL at power levels (and thus SNR) 2 orders of magnitude beyond those of previous loss-tolerant interferometers. We find experimentally the optimal FWM gains and find agreement with a minimal quantum noise model for the FWM process. The results suggest ways to boost the in-practice sensitivity of high-power interferometers, e.g., gravitational wave interferometers, and may enable high-sensitivity, quantum-enhanced interferometry at wavelengths for which efficient detectors are not available.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

Ultrafast dynamics in (TaSe4)2I triggered by valence and core-level excitation

Dimensionality plays a key role for the emergence of ordered phases such as charge-density-waves (CDW), which can couple to, and modulate, the topological properties of matter. In this work, we...

Resonantly Enhanced Difference-Frequency Generation in the Core X-ray Absorption of Molecules

We use real-time time-dependent density functional theory simulations to numerically demonstrate that resonantly enhanced difference-frequency generation (re-DFG) involving intense ultrashort coherent X-ray pulses can selectively excite core states of atoms in molecules. As a model case, we evaluate the spectral selectivity of re-DFG excitation of the oxygen K-edge by illumination of a single gas-phase water molecule with two-color X-ray pulses of different photon energies and durations. The re-DFG excitation is further probed by a small delayed pulse with central photon energy resonant with the oxygen K-edge peak absorption line. Based on these results, we anticipate that highly selective excitation by re-DFG X-ray nonlinear processes might be achieved in more complex molecular systems and bulk materials by using highly penetrating two-color hard X-ray pulses, with extensive applications.

Exciton delocalization length in chlorosomes investigated by lineshape dynamics of two-dimensional electronic spectra

A chlorosome, a photosynthetic light-harvesting complex found in green sulfur bacteria, is an aggregate of self-assembled pigments and is optimized for efficient light harvesting and energy transfer under dim-light conditions. In this highly-disordered aggregate, the absorption and transfer of photoexcitation energy are governed by the degree of disorder. To describe the disorder, the number of molecules forming excitons, which is termed exciton delocalization length (EDL), is a relevant parameter because the EDL sensitively changes with the disorder of the constituent molecules. In this work, we determined the EDL in chlorosomes using two-dimensional electronic spectroscopy (2D-ES). Since spectral features correlated with EDL are spread out in the two-dimensional (2D) electronic spectra, we were able to determine the EDL accurately without the effects of homogeneous and inhomogeneous line broadening. In particular, by taking advantage of the multi-dimensionality and the time evolution of 2D spectra, we not only determined the excitation frequency dependence of EDL but also monitored the temporal change of EDL. We found that the EDL is ∼7 at 77 K and ∼6 at 298 K and increases with the excitation frequency, with the maximum located well above the maximum of the absorption spectrum of chlorosomes. The spectral profile of EDL changes rapidly within 100 fs and becomes flat over time due to dephasing of initial exciton coherence. From the coherent oscillations superimposed on the decay of EDL, it was learned that high-frequency phonons are more activated at 298 K than at 77 K.

Supermagnonic Propagation in Two-Dimensional Antiferromagnets

We investigate the propagation of magnons after ultrashort perturbations of the exchange interaction in the prototype two-dimensional Heisenberg antiferromagnet. Using the recently proposed neural quantum states, we predict highly anisotropic spreading in space constrained by the symmetry of the perturbation. Interestingly, the propagation speed at the shortest length scale and timescale is up to 40% higher than the highest magnon velocity. We argue that the enhancement stems from extraordinary strong magnon-magnon interactions, suggesting new avenues for manipulating information transfer on ultrashort length scales and timescales.

Gigahertz Optomechanical Photon-Phonon Transduction between Nanostructure Lines

High-frequency surface phonons have a myriad of applications in telecommunications and sensing, but their generation and detection have often been limited to transducers occupying micron-scale regions because of the use of two-dimensional transducer arrays. Here, by means of transient reflection spectroscopy we experimentally demonstrate optically coupled nanolocalized gigahertz surface phonon transduction based on a gold nanowire emitter arranged parallel to linear gold nanorod receiver arrays, that is, quasi-one-dimensional emitter-receivers. We investigate the response up to 10 GHz of these individual optoacoustic and acousto-optic transducers, respectively, by exploiting plasmon-polariton longitudinal resonances of the nanorods. We also demonstrate how the surface phonon detection efficiency is highly dependent on the nanorod orientation with respect to the phonon wave vector, which constrains the symmetry of the detectable modes, and on the nanorod acoustic resonance spectrum. Applications include nanosensing.

XUV pump-XUV probe transient absorption spectroscopy at FELs

The emergence of ultra-intense extreme-ultraviolet (XUV) and X-ray free-electron lasers (FELs) has opened the door for the experimental realization of non-linear XUV and X-ray spectroscopy techniques. Here we demonstrate an experimental setup for an all-XUV transient absorption spectroscopy method for gas-phase targets at the FEL. The setup combines a high spectral resolving power of E/ΔE ≈ 1500 with sub-femtosecond interferometric resolution, and covers a broad XUV photon-energy range between approximately 20 and 110 eV. We demonstrate the feasibility of this setup firstly on a neon target. Here, we intensity- and time-resolve key aspects of non-linear XUV-FEL light-matter interactions, namely the non-resonant ionization dynamics and resonant coupling dynamics of bound states, including XUV-induced Stark shifts of energy levels. Secondly, we show that this setup is capable of tracking the XUV-initiated dissociation dynamics of small molecular targets (oxygen and diiodomethane) with site-specific resolution, by measuring the XUV transient absorption spectrum. In general, benefitting from a single-shot detection capability, we show that the setup and method provides single-shot phase-locked XUV pulse pairs. This lays the foundation to perform, in the future, experiments as a function of the XUV interferometric time delay and the relative phase, which enables advanced coherent non-linear spectroscopy schemes in the XUV and X-ray spectral range.

Femtosecond laser driven precessing magnetic gratings

Manipulation and detection of spins at the nanoscale is of considerable contemporary interest as it may not only facilitate a description of fundamental physical processes but also plays a critical role in the development of spintronic devices. Here, we describe the application of a novel combination of transient grating excitation with Lorentz ultrafast electron microscopy to control and detect magnetization dynamics with combined nanometer and picosecond resolutions. Excitation of Ni80Fe20 thin film samples results in the formation of transient coherently precessing magnetic gratings. From the time-resolved results, we extract detailed real space information of the magnetic precession, including local magnetization, precession frequency, and relevant decay factors. The Lorentz contrast of the dynamics is sensitive to the alignment of the in-plane components of the applied field. The experimental results are rationalized by a model considering local demagnetization and the phase of the precessing magnetic moments. We envision that this technique can be extended to the study of spin waves and dynamic behavior in ferrimagnetic and antiferromagnetic systems.

Multi-wave mixing in the high harmonic regime: monitoring electronic dynamics

It has been demonstrated that electronic coherences across many eV can be detected in pump-probe experiments involving high harmonic sources. An additional degree of control over the phase matching can be employed by investigating a more general class of multi-wave mixing. Non-collinear multi-wave mixing of high harmonics with energy (q₁ω₁ + q₂ω₂) can be selectively detected along the direction of (q₁k₁ + q₂k₂). Simulations based on a recently developed semi-perturbative approach show that only the specific harmonic signals with q₁ω₁ close to the energy difference between ground state and excited states are observable when the two input pulses are well separated in time. The coherent dynamics between different states can be selectively tracked by detecting the time-delay dependent signals with different q₁k₁, which can overcome the potential spectral congestion in real experiments. Additionally, such non-collinear geometry can be used to separate the dephasing induced decay and collision induced recovery behaviors of pump-probe high harmonic signal typically observed in the time-resolved high harmonic pump-probe signals.

Localized Core Four-Wave Mixing Buildup in the X-ray Spectrum of Chemical Species

Using the Kohn-Sham density functional theory, we numerically study the four-wave mixing response of a carbon atom model system exposed to a train of femtosecond two color ω-3ω random phase coherent X-ray pulses near the K-edge. The phase-sensitivity cancellation of the 5ω anti-Stokes component previously described in two- and three-level systems in the infrared and optical regions is extended into the X-ray. Resonances with the absorption lines in the XANES and EXAFS regions produce 5ω peak intensities that increase near the phase-sensitivity cancellation frequencies. Based on this effect, we predict that highly selective intense X-ray 5ω photon energies can be achieved in real systems. The high localization of the ω-3ω four-wave mixing nonlinear technique that we address entails a new valuable tool in X-ray spectroscopies of chemical species as it can readily be extended to different photon energies in other atomic absorption edges, with broad applications.

Probing Delocalized Current Densities in Selenophene by Resonant X-ray Sum-Frequency Generation

Time-resolved, resonant X-ray sum-frequency generation in aligned selenophene molecules is calculated. A wave packet of valence-excited states, prepared by an extreme-ultraviolet pump pulse, is probed by two 12-keV X-ray probe pulses resonant with the Se core-excited states for variable time delays. At these hard-X-ray frequencies, the angström wavelength of the X-ray probe is comparable to the molecular size. We thus employ a nonlocal description of the light-matter interaction based on the minimal-coupling Hamiltonian. The wavevector-resolved resonant stimulated sum-frequency-generation signal, obtained by varying the propagation direction of hard-X-ray pulses, can thus directly monitor the transition current densities between core and ground/valence states. This is in contrast to off-resonant diffraction, which detects the transition charge densities.

High-gain harmonic generation with temporally overlapping seed pulses and application to ultrafast spectroscopy

Collinear double-pulse seeding of the High-Gain Harmonic Generation (HGHG) process in a free-electron laser (FEL) is a promising approach to facilitate various coherent nonlinear spectroscopy schemes in the extreme ultraviolet (XUV) spectral range. However, in collinear arrangements using a single nonlinear medium, temporally overlapping seed pulses may introduce nonlinear mixing signals that compromise the experiment at short time delays. Here, we investigate these effects in detail by extending the analysis described in a recent publication (Wituschek et al., Nat. Commun., 11, 883, 2020). High-order fringe-resolved autocorrelation and wave packet interferometry experiments at photon energies > 23 eV are performed, accompanied by numerical simulations. It turns out that both the autocorrelation and the wave-packet interferometry data are very sensitive to saturation effects and can thus be used to characterize saturation in the HGHG process. Our results further imply that time-resolved spectroscopy experiments are feasible even for time delays smaller than the seed pulse duration.

Ultrafast Demagnetization Dominates Fluence Dependence of Magnetic Scattering at Co M Edges

We systematically study the fluence dependence of the resonant scattering cross-section from magnetic domains in Co/Pd-based multilayers. Samples are probed with single extreme ultraviolet (XUV) pulses of femtosecond duration tuned to the Co M_{3,2} absorption resonances using the FERMI@Elettra free-electron laser. We report quantitative data over 3 orders of magnitude in fluence, covering 16  mJ/cm^{2}/pulse to 10 000  mJ/cm^{2}/pulse with pulse lengths of 70 fs and 120 fs. A progressive quenching of the diffraction cross-section with fluence is observed. Compression of the same pulse energy into a shorter pulse-implying an increased XUV peak electric field-results in a reduced quenching of the resonant diffraction at the Co M_{3,2} edge. We conclude that the quenching effect observed for resonant scattering involving the short-lived Co 3p core vacancies is noncoherent in nature. This finding is in contrast to previous reports investigating resonant scattering involving the longer-lived Co 2p states, where stimulated emission has been found to be important. A phenomenological model based on XUV-induced ultrafast demagnetization is able to reproduce our entire set of experimental data and is found to be consistent with independent magneto-optical measurements of the demagnetization dynamics on the same samples.

Simultaneous two-color snapshot view on ultrafast charge and spin dynamics in a Fe-Cu-Ni tri-layer

Ultrafast phenomena on a femtosecond timescale are commonly examined by pump-probe experiments. This implies multiple measurements, where the sample under investigation is pumped with a short light pulse and then probed with a second pulse at various time delays to follow its dynamics. Recently, the principle of streaking extreme ultraviolet (XUV) pulses in the temporal domain has enabled recording the dynamics of a system within a single pulse. However, separate pump-probe experiments at different absorption edges still lack a unified timing, when comparing the dynamics in complex systems. Here, we report on an experiment using a dedicated optical element and the two-color emission of the FERMI XUV free-electron laser to follow the charge and spin dynamics in composite materials at two distinct absorption edges, simultaneously. The sample, consisting of ferromagnetic Fe and Ni layers, separated by a Cu layer, is pumped by an infrared laser and probed by a two-color XUV pulse with photon energies tuned to the M-shell resonances of these two transition metals. The experimental geometry intrinsically avoids any timing uncertainty between the two elements and unambiguously reveals an approximately 100 fs delay of the magnetic response with respect to the electronic excitation for both Fe and Ni. This delay shows that the electronic and spin degrees of freedom are decoupled during the demagnetization process. We furthermore observe that the electronic dynamics of Ni and Fe show pronounced differences when probed at their resonance, while the demagnetization dynamics are similar. These observations underline the importance of simultaneous investigation of the temporal response of both charge and spin in multi-component materials. In a more general scenario, the experimental approach can be extended to continuous energy ranges, promising the development of jitter-free transient absorption spectroscopy in the XUV and soft X-ray regimes.

Characterization of soft X-ray FEL pulse duration with two-color photoelectron spectroscopy

The pulse duration of soft X-ray free-electron laser (FEL) pulses of SACLA BL1 (0.2-0.3 nC per bunch, 0.5-0.8 MeV) were characterized by photoelectron sideband measurements. The intensity of the He 1 s^-1 photoelectron sidebands generated by a near-infrared femtosecond laser was measured as a function of the time delay between the two pulses using an arrival time monitor. From the width of the cross-correlation trace thus derived, the FEL pulse duration was evaluated to be 28 ± 5 fs full width at half-maximum in the photon energy range between 40 eV and 120 eV.

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.

Time-resolved ultrafast transient polarization spectroscopy to investigate nonlinear processes and dynamics in electronically excited molecules on the femtosecond time scale

We report a novel experimental technique to investigate ultrafast dynamics in photoexcited molecules by probing the 3rd-order nonlinear optical susceptibility. A non-collinear 3-pulse scheme is developed to probe the ultrafast dynamics of excited electronic states using the optical Kerr effect. Optical homodyne and optical heterodyne detections are demonstrated to measure the 3rd-order nonlinear optical response for the S₁ excited state of liquid nitrobenzene, which is populated by 2-photon absorption of a 780 nm 40 fs excitation pulse.

Molecular Structure and Modeling of Water-Air and Ice-Air Interfaces Monitored by Sum-Frequency Generation

From a glass of water to glaciers in Antarctica, water-air and ice-air interfaces are abundant on Earth. Molecular-level structure and dynamics at these interfaces are key for understanding many chemical/physical/atmospheric processes including the slipperiness of ice surfaces, the surface tension of water, and evaporation/sublimation of water. Sum-frequency generation (SFG) spectroscopy is a powerful tool to probe the molecular-level structure of these interfaces because SFG can specifically probe the topmost interfacial water molecules separately from the bulk and is sensitive to molecular conformation. Nevertheless, experimental SFG has several limitations. For example, SFG cannot provide information on the depth of the interface and how the orientation of the molecules varies with distance from the surface. By combining the SFG spectroscopy with simulation techniques, one can directly compare the experimental data with the simulated SFG spectra, allowing us to unveil the molecular-level structure of water-air and ice-air interfaces. Here, we present an overview of the different simulation protocols available for SFG spectra calculations. We systematically compare the SFG spectra computed with different approaches, revealing the advantages and disadvantages of the different methods. Furthermore, we account for the findings through combined SFG experiments and simulations and provide future challenges for SFG experiments and simulations at different aqueous interfaces.

Topological photonic crystals: a review

The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008. Photonic band structures embraced topological phases of matter, have spawned a novel platform for studying topological phase transitions and designing topological optical devices. Here, we present a brief review of topological photonic crystals based on different material platforms, including all-dielectric systems, metallic materials, optical resonators, coupled waveguide systems, and other platforms. Furthermore, this review summarizes recent progress on topological photonic crystals, such as higherorder topological photonic crystals, non-Hermitian photonic crystals, and nonlinear photonic crystals. These studies indicate that topological photonic crystals as versatile platforms have enormous potential applications in maneuvering the flow of light.

Generating three-color pulses in high-gain harmonic-generation free-electron lasers with a tilted electron bunch

A multi-color light source is a significant tool for nonlinear optics experiments, pump-dump/repump-probe experiments and in other fields. Here, a novel method is proposed to create three-color pulses based on a high-gain harmonic-generation (HGHG) free-electron laser with a tilted electron bunch. In this method, the initial bunch tilt is created by transverse wakefields after the bunch passes through a corrugated structure with an off-axis orbit, and is further enlarged in a following drift section. Then the tilted bunch experiences the off-axis field of a quadrupole magnet to cool down the large transverse velocity induced before. After that, it enters an HGHG configuration adopting a transverse gradient undulator (TGU) as the radiator, where only three separated fractions of the tilted bunch will resonate at three adjacent harmonics of the seed wavelength and are enabled to emit three-color pulses simultaneously. In addition, the use of the natural transverse gradient of a normal planar undulator instead of the TGU radiator to emit three-color pulses is also studied in detail. Numerical simulations including the generation of the tilted bunch and the free-electron laser radiation confirm the validity and feasibility of this scheme both for the TGU radiator and the natural gradient in the extreme-ultraviolet waveband.

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.

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.

Shaping femtosecond laser pulses at short wavelength with grazing-incidence optics

We present the design of an extreme ultraviolet (XUV) pulse shaper relying on reflective optics. The instrument will allow tailoring of the time-frequency spectrum of femtosecond pulses generated by seeded free-electron lasers (FEL) and high-harmonic generation (HHG) sources down to a central wavelength of ~15 nm. The device is based on the geometry of a 4f grating compressor that is a standard concept in ultrafast laser science and technology. We apply it to shorter wavelengths using grazing-incidence optics operated under ultra-high vacuum conditions. The design blaze angle and the line density of the gratings allow the manipulation of all different harmonics typical for seeded FEL and HHG photon sources without the need of realignment of the instrument and even simultaneously in multi-color experiments. A proof-of-principle pulse shaping experiment using 266 nm laser light has been performed, demonstrating relative phase-control of femtosecond UV pulses.

Nonlinear XUV signal generation probed by transient grating spectroscopy with attosecond pulses

Nonlinear spectroscopies are utilized extensively for selective measurements of chemical dynamics in the optical, infrared, and radio-frequency regimes. The development of these techniques for extreme ultraviolet (XUV) light sources facilitates measurements of electronic dynamics on attosecond timescales. Here, we elucidate the temporal dynamics of nonlinear signal generation by utilizing a transient grating scheme with a subfemtosecond XUV pulse train and two few-cycle near-infrared pulses in atomic helium. Simultaneous detection of multiple diffraction orders reveals delays of ≥1.5 fs in higher-order XUV signal generation, which are reproduced theoretically by solving the coupled Maxwell–Schrödinger equations and with a phase grating model. The delays result in measurable order-dependent differences in the energies of transient light induced states. As nonlinear methods are extended into the attosecond regime, the observed higher-order signal generation delays will significantly impact and aid temporal and spectral measurements of dynamic processes.

Ultrafast dynamics following light-matter interaction are governed by nonlinear processes. Here the authors show that initial nonlinear signal time-evolution is a consequence of phase grating accumulation using transient grating measurements with attosecond and near-infrared pulses.

Stable interferometric platform for phase modulation of seeded free-electron lasers

We present a compact phase modulation setup designed for high laser intensities sufficient to drive highly nonlinear processes, such as high-gain harmonic generation in seeded free-electron lasers. This paves the way for all-extreme-ultravioloet coherent nonlinear spectroscopy. The high linearity, phase stability, and sensitivity of the setup are demonstrated by probing the quantum interference of electronic wave packets in the deep ultraviolet region (268 nm) combined with photoion time-of-flight mass spectrometry.

Towards X-ray transient grating spectroscopy

The extension of transient grating spectroscopy to the x-ray regime will create numerous opportunities, ranging from the study of thermal transport in the ballistic regime to charge, spin, and energy transfer processes with atomic spatial and femtosecond temporal resolution. Studies involving complicated split-and-delay lines have not yet been successful in achieving this goal. Here we propose a novel, simple method based on the Talbot effect for converging beams, which can easily be implemented at current x-ray free electron lasers. We validate our proposal by analyzing printed interference patterns on polymethyl methacrylate and gold samples using ∼3  keV X-ray pulses.

Non-linear soft x-ray methods on solids with MUSIX-the multi-dimensional spectroscopy and inelastic x-ray scattering endstation

With the intense and coherent x-ray pulses available from free-electron lasers, the possibility to transfer non-linear spectroscopic methods from the laser lab to the x-ray world arises. Advantages especially regarding selectivity and thus information content as well as an improvement of signal levels are expected. The use of coherences is especially fruitful and the example of coherent x-ray/optical sum-frequency generation is discussed. However, many non-linear x-ray methods still await discovery, partially due to the necessity for extremely adaptable and versatile instrumentation that can be brought to free-electron lasers for the analysis of the spectral content emitted from the sample into a continuous range of emission angles. Such an instrument (called MUSIX) is being developed and employed at FLASH, the free-electron laser in Hamburg and is described in this contribution together with first results.

Two-dimensional UV spectroscopy: a new insight into the structure and dynamics of biomolecules

Two-dimensional ultraviolet spectroscopy has the potential to deliver rich structural and dynamical information on biomolecules such as DNA and proteins.

Impulsive UV-pump/X-ray probe study of vibrational dynamics in glycine

We report an ab-initio study of a pump-probe experiment on the amino-acid glycine. We consider an UV pump followed by an X-ray probe tuned to carbon K-edge and study the vibronic structure of the core transition. The simulated experiment is feasible using existing free electron laser or high harmonic generation sources and thanks to the localization of the core orbitals posseses chemical selectivity. The present theory applies to other experimental schemes, including the use of a THz probe, available with present soft X-ray free electron lasers and/or high harmonic generation sources.

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.

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.