## 3 Results  
The typical ISRS signals obtained on the CH\({}_{2}\)Br\({}_{2}\) sample from both the spectral and the Kerr lens detection arms are shown in Figure 2a,b, for the sample positions corresponding to the maximum signal intensity for each method, together with the corresponding Fourier transform (Figure 2c), showing the sample spectrum. The observed peak is due to the well-known scissoring mode of the CH\({}_{2}\)Br\({}_{2}\) molecule. The phase of the Raman oscillations in Figure 2a,b shows the expected sine and cosine dependence on the delay for the spectral and refractive nonlinearities, respectively, as predicted by ISRS models [13; 29]. While the Raman signal intensity obtained from spectral shift detection showed a single maximum when the sample was placed in the L1 lens focus, in the case of refractive detection (see Figure 2b), we observed two signal maxima at pre-focal and post-focal positions (\(z_{-}\) and \(z_{+}\), respectively) equidistant from the L1 lens focus, with opposite focusing behavior. The two signal maxima observed for refractive detection correspond to the positions where the effect of the nonlinear Kerr lens on the beam propagation is maximized, i.e., to the positions of the peak and valley in Z-scan signals. The dependence of the Raman signal intensity on the sample position for the two detection methods is shown in Figure 4, together with a reference Z-scan trace evidencing the correspondence of the two signal maxima observed using the Kerr lens detection method with the valley and peak in Z-scan measurements. Having demonstrated and characterized the operation of the experimental apparatus as an ISRS interferometer and as a femtosecond Z-scan system on reference samples, we now show the Z-scan traces obtained from the CH\({}_{2}\)Br\({}_{2}\) sample in the single-beam (probe alone) configuration, and in the presence of a pump pulse preceding the probe pulse by 1.5 ps, in Figure 5. The precise value of the pump-probe delay was selected by first finding the position corresponding to coincidence, with the help of the strong cross-phase modulation signal produced in this case. The single-beam trace shows a valley-peak configuration corresponding to a positive Kerr lens phase shift, as expected for a non-resonant nonlinearity, with \(\Delta T_{pp}^{p}\) = 4.7%, and, using Equation (1), we can infer a nonlinear refractive index \(\gamma_{p}\) = 7.2 \(\times\) 10\({}^{-7}\) cm\({}^{2}\)/GW. Figure 4: Dependence of the normalized intensity of the ISRS Raman mode at 173 cm\({}^{-1}\) on the sample position. A CS\({}_{2}\) sample reference Z-scan trace to observe the correspondence between the positions of the RIKE signal maxima and those of the Z-scan trace peak and valley is also shown. In the presence of the pump pulse (see Figure 5), the overall shape of the trace does not change, but a slight reduction of the peak-valley amplitude is clearly seen: the corresponding nonlinear refractive index calculated for \(\Delta T_{pv}^{Pp}=3.9\%\) is \(\gamma_{Pp}=6.0\times 10^{-7}\) cm\({}^{2}\)/GW. The difference between \(\Delta T_{pv}^{Pp}\) (pump-probe) and \(\Delta T_{pv}^{P}\) (probe alone) is a negative nonlinear refractive index contribution caused by the presence of the pump pulse, i.e., by the coherent molecular motions. In order to observe the Raman (oscillatory) part of the nonlinear refractive index, we repeated the differential pump on/off measurements at several selected pump-probe delays. The resulting peak-valley amplitude difference \(\Delta T_{pv}^{Pp}-\Delta T_{pv}^{p}\) is shown in Figure 6 as a function of the pump-probe delay. Clear oscillations are visible, with a period equal to about 200 fs, as obtained by a sine fit of the experimental data; this period coincides within the experimental uncertainty with that (193 fs) of the oscillations due to the CH\({}_{2}\)Br\({}_{2}\) Raman mode at 173 cm\({}^{-1}\), thus unambiguously demonstrating that the Z-scan difference signal is produced by the RIKE effect due to the coherent Raman field established by the pump pulse.