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.

Spatially patterned extreme ultraviolet light pulses can be used for probing multiple dynamical processes at the nanoscale.

We investigate the excitation of coherent acoustic and optical phonons by ultrashort extreme ultraviolet (EUV) pulses produced by a free electron laser. Two crossed femtosecond EUV (wavelength 12.7 nm) pulses are used to excite coherent phonons at a wavelength of 280 nm, which are detected via diffraction of an optical probe beam. Longitudinal and surface acoustic waves are measured in BK-7 glass, diamond, and Bi₄Ge₃O₁₂; in the latter material, the excitation of a coherent optical phonon mode is also observed. We discuss probing different acoustic modes in reflection and transmission geometries and frequency mixing of surface and bulk acoustic waves in the signal. The use of extreme ultraviolet radiation will allow the creation of tunable GHz to THz acoustic sources in any material without the need to fabricate transducer structures.

We use femtosecond extreme ultraviolet pulses derived from a free electron laser to excite and probe surface acoustic waves (SAWs) on the (001) surface of single crystal SrTiO₃. SAWs are generated by a pair of 39.9 nm pulses crossed at the sample with the crossing angle defining the SAW wavelength at 84 nm. Detection of SAWs is performed via diffraction of a time-delayed 13.3 nm probe pulse by SAW-induced surface ripples. Despite the low reflectivity of the sample in the extreme ultraviolet range, the reflection mode detection is found to be efficient because of an increase in the diffraction efficiency for shorter wavelengths. We describe a methodology for extracting the SAW attenuation in the presence of a thermal grating, which is based on measuring the decay of oscillations at twice the SAW frequency. The proposed approach can be used to study ultrahigh frequency SAWs in a broad range of materials and will bridge the wave vector gap in surface phonon spectroscopy between Brillouin scattering and He atom scattering.

We report on new opportunities for ultrafast science thanks to the use of two-colour extreme ultraviolet (XUV) pulses at the FERMI free electron laser (FEL) facility. The two pulses have been employed to carry out a pioneering FEL-pump/FEL-probe diffraction experiment using a Ti target and tuning the FEL pulses to the M_2/3-edge in order to explore the dependence of the dielectric constant on the excitation fluence. The future impact that the use of such a two-colour FEL emission will have on the development of ultrafast wave-mixing methods in the XUV/soft X-ray range is addressed and discussed.