Advances in instrumentation for FEL-based four-wave-mixing experiments

Experimental approaches based on nonlinear optical processes (wave-mixing) have allowed major breakthroughs in diverse fields of science and technology. Nevertheless, these concepts were restricted to the optical regime due to the lack of coherent photon sources of sufficient peak brightness at sub-optical wavelengths. Nowadays, while the development of free electron lasers (FELs) potentially allows extreme ultraviolet (EUV) and X-ray wave-mixing, their full exploitation still requires efforts in instrumentation developments. The need to control (both in the spatial and temporal coordinates) multiple FEL input pulses, which may have different photon frequencies and polarizations, calls for the developments of instruments with a higher degree of complexity with respect to those typically used at synchrotron and FEL beamlines. Here we report on the progresses in the development of such kind of instrumentation at the FERMI FEL facility. Our FEL-based wave-mixing setups rely upon the transient grating (TG) approach, which represents a relevant benchmark for the development of advanced EUV/soft x-ray four-wave-mixing (FWM) experiments, as for instance coherent Raman scattering and multi-dimensional spectroscopy.