## 2 Materials and Methods  
The experimental apparatus is based on the interferometer design used in [6] as modified with the fast scan mechanism proposed in [5], with further modifications to allow for MZ-scan measurements, and modifications in the signal detection assembly, as detailed below; the scheme is shown in Figure 1.  
Briefly, the excitation beam was produced by a femtosecond oscillator (MIRA 900 F, Coherent Inc., Santa Clara, CA, USA) operating at 780 nm wavelength, equipped with a cavity dumper (APE GmbH, Berlin, Germany) with electronic control for selection of the repetition rate; operation at 1 kHz was chosen to completely exclude cumulative thermo-optical effects. The laser bandwidth was 10 nm FWHM as measured with a spectrometer ([PERSON], Horiba SAS, Palaiseau, France), allowing impulsive excitation of Raman modes below approximately 200 cm\({}^{-1}\). After passing through a prism compressor for dispersion compensation, and through a half-wave plate for polarization control, the beam was fed into a [PERSON] interferometer with orthogonally polarized arms by using a polarizing beam splitter. To realize the scan averaging technique, one of the interferometer arms, the pump/Stokes arm, includes a fast scanning delay line, realized by a retroreflector mounted on an actuator driven by a triangular wave, capable of oscillating at a few tens of hertz, producing a delay up to several picoseconds, and placed on a computer-controlled linear stage. The two beams were recombined and focused by a 5 cm focal length lens onto the sample contained in a 1 mm-thick quartz cuvette placed on an actuator to allow oscillation of the sample around the focus position, as is necessary for MZ-scan measurements; the actuator itself was mounted on a manual linear stage to allow fine setting of the rest position of the sample. The beam on the sample had a 120 fs autocorrelator-measured pulse width with typical energies of a few nanojoules for each beam and a 10:3 pump/probe energy ratio. Figure 1: Layout of the experimental apparatus and picture of the ISRS interferometer with the schematics of the principles of operation of the Kerr lens and spectral shift detection assemblies. A photo of the interferometer and signal detection sections is also shown. After the sample, the pump/Stokes beam was filtered out by a Glan-laser polarizer, and the surviving probe beam was directed, using a 50/50 beam splitter, to two signal detection systems, in order to simultaneously detect the ISRS-induced spectral shift and the Raman-induced Kerr lens effects. The spectral shift detection system was composed of a collimating lens and a 780 nm long-wave pass edge filter (LP02-780 RU-25 Semrock, IDEX Health & Science, LLC, Rochester, NY, USA) tilted in order to transmit approximately 50% of the incoming beam to a large-area photodiode (DET100 A/M, Thorlabs GmbH, Bergkirchen, Germany). The Kerr lens detection system was composed of a closed-aperture Z-scan-like arrangement, i.e., a photodiode (DET100 A/M Thorlabs) placed in the beam far field after a pinhole, thus capable of detecting the changes in the beam profile. Due to the use of the cavity dumper, reducing the laser repetition rate, the signals generated by the photodiodes are well-isolated narrow pulses, different from the common high-repetition rate case, where, owing to the few-nanosecond pulse interval, a small amount of integration is sufficient to produce a continuous signal. Therefore, a fast resettable sample-and-hold module (611A-2-20-50, Analog Modules Inc., Longwood, FL, USA) was used to transform the low-duty cycle signals in quasi-continuous waveforms. A USB digitizer (USB1608 GX, Measurement Computing Corp., Norton, MA, USA) finally provided data acquisition and display under a LabView program which performs data averaging, as is necessary to exploit the scan averaging noise reduction and sensitivity enhancement [5], and data storage.