## 4 Discussion  
The experimental ISRS results reported in Figure 2b show that when the sample is in the pre-focal maximum signal position (\(z\)...), the signal on the photodiode has a sharp drop for pump-probe coincidence, followed by an increase for positive delays. This corresponds to an initial defocusing and a subsequent focusing behavior of the nonlinear Kerr lens. Recalling that, for a pre-focal Kerr lens defocusing behavior, the associated nonlinear refractive index is positive [20], we deduced from Figure 2b that the Kerr nonlinearity created by the pump pulse has a positive instantaneous value (due to the cross-phase modulation originated by the non-resonant electronic nonlinearity) followed by an opposite behavior. The same conclusions can obviously be drawn from the analysis of the post-focal (\(z_{+}\)) signal. The behavior at positive delays is due to the superposition of the intermolecular modes, such as diffusive re-orientational motions and libration, and of intramolecular modes due to the impulsively excited Raman vibrations [15].  
As far as the single-beam Z-scan measurement shown in Figure 5 is concerned, our result is consistent with the data reported in Figure 2b, where the ultrafast instantaneous nonlinearity is positive. We underline that this result is the first determination of the electronic non-resonant nonlinearity in dibromomethane and is completely unaffected by thermo-optical effects, differently from the results [21] reported using a high-repetition rate laser, where the strong thermo-optical effects produce a peak-valley Z-scan trace. Noticeably, single-beam Z-scan measurements on transparent solvents, when not affected by thermo-optical effects, unavoidably show a positive Kerr lens (i.e., valley-peak Z-scan trace), due to the strong ultrafast non-resonant electronic nonlinearity [30]. The small negative contribution due to molecular modes can only be sorted out by differential pump on/off measurements, as shown in Figure 6. Analogously to what was conducted to obtain the instantaneous electronic non-resonant Kerr nonlinearity using single-beam measurements, the easy calibration procedure of Z-scan measurements can be used to quantify the Raman and intermolecular contributions to the Kerr nonlinearity from the pump-probe data shown in Figures 5 and 6.  
Therefore, we demonstrated what we believe to be the first unambiguous \"true\" Z-scan measurements of the stimulated Raman scattering phenomenon. Our proposed technique allows, in principle, the quantitative evaluation of the contribution of the internal (Raman) and external molecular modes to the nonlinear refractive index [31], a task which will be the subject of a future paper, as it is beyond the scope of the present work.  
Conceptualization, M.F.; methodology, M.F.; software, M.F.; validation, M.F., S.G. and M.M.; formal analysis, M.F.; investigation, M.F., S.G., F.R. and M.M.; resources, M.F., S.G. and F.R.; data curation, M.F. and W.D.K.; writing--original draft preparation, M.F.; writing--review and editing, S.G., F.R., M.M. and W.D.K.; visualization, S.G., F.R., M.M. and W.D.K.; supervision, M.F.; project administration, M.F.; funding acquisition, M.F. All authors have read and agreed to the published version of the manuscript.  
This research was co-funded by the Italian Ministry of Foreign Affairs and International Cooperation (MAECI), under the Italy-USA Great Relevance Project \"Spectrometro Raman coerenate al femtosecondo a bassi numeri d'onda\".  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.