## 3 Results and Discussion
### Stimulated Rotational Raman Scattering in Compressed \(H_{2}\)
Due to the low Raman gain, at a hydrogen pressure of 1 MPa, only the first rotational Stokes line was  
Figure 3: The dependance of the SRS spectra on (**a**) the pump pulse energy at a hydrogen pressure of 3 MPa and (**b**) the hydrogen pressure at a pump pulse energy of 7 mJ. observed, while the number and intensity of higher-order Stokes components increased at higher pressures. It is noteworthy that even when the circular polarization of the pump beam made it possible to completely suppress the direct generation of vibrational SRS (Figure 2b, red solid line), at pressures above 3 MPa, the first rotational Stokes pulse in turn became a pump source for SVRS at -2012 nm (Figure 3b, blue line). When the hydrogen pressure reached 4 MPa, the cascade generation of SVRS from second-order rotational Stokes was also observed at -2074 nm (Figure 3b, green line). Thus, at increased hydrogen pressure, two vibrational Stokes components were generated at once (Figure 3b, green and violet line), corresponding to a Raman shift of 4155 cm\({}^{-1}\) from the first- and second-order rotational Stokes. It is also important to note that the nonlinear refractive index \(n_{2}\) of the medium increases with increasing hydrogen pressure [32]. As a result, a spectral pedestal (background) was formed between the rotational Stokes lines in the -1-1.4 \(\upmu\)m wavelength range, where additional spectral components appeared due to the self-phase modulation. The high pump pulse energy and hydrogen pressure not only contributed to the cascade generation of higher-order rotational Stokes comb but also significantly improved the overall SRRS conversion efficiency and lowered its threshold (Figure 4). The SRRS threshold decreased from 5 mJ to 0.95 mJ as the hydrogen pressure increased from 1 MPa to 5 MPa (Figure 4a,c). This dependence corresponded to the reciprocal function 4.9/p, where p is the H\({}_{2}\) pressure (Figure 4c, red dashed line). It is well known that the conversion efficiency of transient SRS strongly depends on the density of the Raman medium. Therefore, the best SRRS conversion efficiency achieved at saturation also increased rapidly from 1.5% to 42% (Figure 4c, black solid line). However, a further increase in gas pressure and pump pulse energy will lead to an increase in \(n_{2}\) and the instantaneous field intensity of the pump beam, respectively. This will cause stronger nonlinear effects such as SPM, multiphoton ionization, harmonic generation, etc., which will eventually suppress SRS. A similar behavior of SVRS was also observed (Figure 4b). Figure 4: Conversion efficiency of (**a**) SRRS and (**b**) SVRS at different hydrogen pressures; (**c**) dependance of the maximum SRRS conversion efficiency (black line) and threshold energy (red solid line) on hydrogen pressure. SRRS beam profile at 5 MPa hydrogen pressure: (**d**) with 1 mJ pump energy; (**e**) with 7 mJ pump energy. However, the intensity of vibrational Stokes modes became noticeable only starting from a hydrogen pressure of 3 MPa with a cascade energy transfer from rotational Stokes. This was also evident from the change in the slope of the SRRS efficiency curve (Figure 4c, black solid line). The best conversion efficiency of the pump pulse energy into vibrational Stokes modes was 3.2%. It is noteworthy that even with a maximum pump energy of 7 mJ and a maximum hydrogen pressure of 5 MPa, the beam still remained smooth after the spatial filter (Figure 4d,e).