Four wave mixing (FWM) processes, based on third-order non-linear light-matter interactions, can combine ultrafast time resolution with energy and wavevector selectivity, and enables to explore dynamics inaccessible by linear methods. [1][2][3][4][5][6][7] The coherent and multi-wave nature of FWM approach has been crucial in the development of cutting edge technologies, such as silicon photonics, 8 sub-wavelength imaging 9 and quantum communications. 10 All these technologies operate with optical wavelengths, which limit the spatial resolution and do not allow probing excitations with energy in the eV range. The extension to shorter wavelengths, that is the extreme ultraviolet (EUV) and soft-x-ray (SXR) range, will allow to improve the spatial resolution and to expand the excitation energy range, as well as to achieve elemental selectivity by exploiting core resonances. [5][6][7][11][12][13][14] So far FWM applications at these wavelengths have been prevented by the absence of coherent sources of sufficient brightness and suitable experimental setups. Our results show how transient gratings, generated by the interference of coherent EUV pulses delivered by the FERMI free electron laser (FEL), 15 can be used to stimulate FWM processes at sub-optical wavelengths. Furthermore, we have demonstrated the possibility to read the time evolution of the FWM signal, which embodies the dynamics of coherent excitations as molecular vibrations. This result opens the perspective for FWM with nanometer spatial resolution and elemental selectivity,

The pulse duration, and, more generally, the temporal intensity profile of free-electron laser (FEL)\ud pulses, is of utmost importance for exploring the new perspectives offered by FELs; it is a nontrivial\ud experimental parameter that needs to be characterized. We measured the pulse shape of an extreme\ud ultraviolet externally seeded FEL operating in high-gain harmonic generation mode. Two different methods\ud based on the cross-correlation of the FEL pulses with an external optical laser were used. The two methods,\ud one capable of single-shot performance, may both be implemented as online diagnostics in FEL facilities.\ud The measurements were carried out at the seeded FEL facility FERMI. The FEL temporal pulse\ud characteristics were measured and studied in a range of FEL wavelengths and machine settings, and they\ud were compared to the predictions of a theoretical model. The measurements allowed a direct observation of\ud the pulse lengthening and splitting at saturation, in agreement with the proposed theory

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.

X-ray free electron lasers (FEL) coupled with optical lasers have opened unprecedented opportunities for studying ultrafast dynamics in matter. The major challenge in pump-probe experiments using FEL and optical lasers is synchronizing the arrival time of the two pulses. Here we report a technique that benefits from the seeded-FEL scheme and uses the optical seed laser for nearly jitter-free pump-probe experiments. Timing jitter as small as 6 fs has been achieved and confirmed by measurements of FEL-induced transient reflectivity changes of Si3N4 using both collinear and non-collinear geometries. Planned improvements of the experimental set-up are expected to further reduce the timing jitter between the two pulses down to fs level.

We present a novel method to map the two-dimensional transverse coherence of an x-ray beam using the dynamical near-field speckles formed by scattering from colloidal particles. Owing to the statistical nature of the method, the coherence properties of synchrotron radiation from an undulator source is obtained with high accuracy. The two-dimensional complex coherence function is determined at the sample position and the imaging optical scheme further allowed us to evaluate the coherence factor at the undulator output despite the aberrations introduced by the focusing optics.