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

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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.