The advent of extreme ultraviolet (EUV) and soft x-ray free electron lasers (FELs) has enabled nonlinear optical experiments at wavelengths shorter than the visible-UV range. An important class of experiments is those based on the four-wave-mixing (FWM) approach, which are often based on interactions between pulses at different wavelengths. The exploitation of multiple EUV/soft x-ray wavelengths is not straightforward, but it can significantly expand the range of applications. In this manuscript we report on an experimental approach, based on the concomitant use of a non-collinear split-delay-and-recombination unit ("mini-Timer") and on a two-color seeded FEL emission scheme ("twin-seed mode"). We used a diamond sample for demonstrating the capability of this setup of generating and detecting a FWM signal stimulated by two-color EUV FEL pulses. This approach can be further exploited for developing experimental methods based on non-linear EUV/x-ray optics.

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.

Among the fourth-generation light sources, the Italian free-electron laser (FEL) FERMI is the only one operating in the high-gain harmonic generation (HGHG) seeding mode. FERMI delivers pulses characterized by a quasi transform limited temporal structure, photon energies lying in the extreme ultra-violet (EUV) region, supreme transversal and longitudinal coherences, high peak brilliance, and full control of the polarization. Such state of the art performances recently opened the doors to a new class of time-resolved spectroscopies, difficult or even impossible to be performed using self-amplified spontaneous sources (SASE) light sources. FERMI is currently equipped with three operating beamlines opened to external users (DiProl, LDM and EIS), while two more are under commissioning (MagneDYN and TeraFERMI). Here, we present the recent highlights of the EIS (Elastic and Inelastic Scattering) beamline, which has been purposely designed to take full advantage from the coherence, the intensity, the harmonics content, and the temporal duration of the pulses. EIS is a flexible experimental facility for time-resolved EUV scattering experiments on condensed matter systems, consisting of two independent end-stations. The first one (EIS-TIMEX) aims to study materials in metastable and warm dense matter (WDM) conditions, while the second end-station (EIS-TIMER) is fully oriented to the extension of four-wave mixing (FWM) spectroscopies towards the EUV spectral regions, trying to reveal the behavior of matter in portions of the mesoscopic regime of exchanged momentum impossible to be probed using conventional light sources.

The full comprehension of magnetic phenomena at the femtosecond (fs) time scale is of high demand for current material science and technology. Here we report the observation of coherent collective modes in the antiferromagnetic insulator nickel oxide (NiO) identified by a frequency of 0.86 THz, which matches the expected out-of-plane single-mode magnon resonance. Such collective excitations are inelastically stimulated by extreme ultraviolet (EUV) pulses delivered by a seeded free-electron laser (FEL) and subsequently revealed probing the transient optical activity of NiO looking at the Faraday effect. Moreover, the unique capability of the employed FEL source to deliver circularly polarized pulses allows us to demonstrate optomagnetic control of such collective modes at EUV photon energies. These results may set a starting point for future investigations of magnetic materials at time scales comparable or faster than those typical of exchange interactions.

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.