Kramers-Kronig relations in FWM spectroscopy

The Kramers-Kronig (K-K) relations are verified for the third-order non-linear optical susceptibilities which are described by known expressions, obtained by the density matrix formalism. Possible applications of the K-K relations in non-linear Raman spectroscopy techniques are also discussed. Coupling of the real and imaginary parts of CARS excitation and probe profiles, as well as a relation between the spectra of two variants of OHD-RIKE are demonstrated. Some cases are shown when the susceptibility does not obey the K-K relations. This result is not a consequence of a break of the causality principle.