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.