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Results and Perspectives for Short-Wavelength, Four-Wave-Mixing Experiments with Fully Coherent Free Electron Lasers

The discovery of the nonlinear optical response [1] has triggered the development of new theoretical and experimental approaches. These are based on the perspective that light-matter interactions are not necessarily cast in the picture of “one photon at a time,” typical of linear processes, but more photons can “work together” in order to coherently stimulate and probe (via nonlinear interactions) different kinds of dynamics in a sample. Nowadays, such a “multi-wave” concept is extensively used in a large array of methods, also termed wave-mixing, that have found numerous applications in almost all fields of physics, chemistry, and biology [2, 3]. Such methods are often based on third-order processes, referred to as four-wave-mixing (FWM), in which a threefold light-matter interaction results in the generation of a (fourth) signal photon, whose photon parameters (frequency, wave vector, polarization, etc.) may differ from those of the input fields. The possibility to control the latter parameters turns into the capability to selectively probe different FWM processes, which can contain distinct and complementary information. In addition to this high degree of selectivity, FWM is often featured in ultrafast time resolution and can be used to study dynamics hardly accessible by linear methods [3], such as spin waves and relaxations [4, 5] or Raman transitions between unoccupied electronic states [6, 7].