Four-wave mixing experiments with extreme ultraviolet transient gratings

Four-wave mixing processes are achieved at suboptical wavelengths by using a free-electron laser as a source to generate extreme ultraviolet pulses that produce transient gratings. The phenomenon of four-wave mixing (FWM) occurs when two wavelengths of light interact to produce two extra wavelengths in the signal. It has been exploited in many optics technologies, from optical fibre communication to spectroscopy. Until now FWM has been limited to optical wavelengths. Here Filippo Bencivenga et al. show how to stimulate four-wave mixing processes at suboptical wavelengths using the FERMI free-electron laser as a source to generate extreme ultraviolet pulses that produce transient gratings. The extension of FWM to shorter wavelengths — combined with new developments in free-electron lasers — promises higher resolution for many techniques and the possibility of probe excitations to higher energies. Four-wave mixing (FWM) processes, based on third-order nonlinear light–matter interactions, can combine ultrafast time resolution with energy and wavevector selectivity, and enable the exploration of dynamics inaccessible by linear methods1,2,3,4,5,6,7. The coherent and multi-wave nature of the FWM approach has been crucial in the development of advanced technologies, such as silicon photonics8, subwavelength imaging9 and quantum communications10. All these technologies operate at optical wavelengths, which limits the spatial resolution and does not allow the probing of excitations with energy in the electronvolt range. Extension to shorter wavelengths—that is, the extreme ultraviolet and soft-X-ray ranges—would allow the spatial resolution to be improved and the excitation energy range to be expanded, as well as enabling elemental selectivity to be achieved by exploiting core resonances5,6,7,11,12,13,14. So far, FWM applications at such wavelengths have been prevented by the absence of coherent sources of sufficient brightness and of suitable experimental set-ups. Here we show how transient gratings, generated by the interference of coherent extreme-ultraviolet pulses delivered by the FERMI free-electron laser15, can be used to stimulate FWM processes at suboptical wavelengths. Furthermore, we have demonstrated the possibility of observing the time evolution of the FWM signal, which shows the dynamics of coherent excitations as molecular vibrations. This result opens the way to FWM with nanometre spatial resolution and elemental selectivity, which, for example, would enable the investigation of charge-transfer dynamics5,6,7. The theoretical possibility of realizing these applications has already stimulated ongoing developments of free-electron lasers16,17,18,19,20: our results show that FWM at suboptical wavelengths is feasible, and we hope that they will enable advances in present and future photon sources.