## 3 Results and Discussion  
### Stimulated Rotational Raman Scattering in Compressed \(H_{2}\)  
In the steady-state SRS regime, the conversion efficiency to high-order Stokes increases with the elongated focusing of the pump beam [27]. In the transient SRS regime, when the pump pulse width is comparable to the molecular dephasing time (T\({}_{2}\)), which, for SRRS in hydrogen, is \(\sim\)1 ps [28], the threshold intensity increases drastically compared to the steady-state case [29], and the effects of SPM, self-focusing, and supercontinuum generation become predominant. Therefore, a loose focus with a long interaction length is most suitable for exciting cascade SRRS by picosecond or femtosecond laser pulses. On the other hand, loose beam focusing entails low peak power density. It is expected that the pump intensity should exceed the SRS threshold but remain below the self-focusing and  
Figure 1: Experimental setup for studying cascade SRRS in compressed hydrogen: \(\uplambda\)/2—half-wave retardation plates; \(\uplambda\)/4—quarter-wave retardation plates; TFP 1,2—thin-film polarizers; A—iris aperture; DM—dichroic mirror; F1,2,3—focusing lenses; F—long-pass interference filter; BD—beam dump; M1—45 deg steering mirror; M2 and M3—plane silver mirrors of delay line. self-phase modulation thresholds. The insufficient pump intensity caused by loose beam focusing is compensated by a longer interaction length. Thus, the focusing conditions and pump energy need to be optimized to excite more Stokes orders in SRRS and suppress parasitic nonlinear effects. At the beginning of the studies, the WLC seed was not used for SRS generation, as described later in this section. Since a loose focus with a long interaction length is preferred for generating high-order rotational Stokes with picosecond pump pulses, the focal length of the F3 lens was varied from 500 to 1500 mm at a constant pump energy of 2 mJ and an H\({}_{2}\) pressure of 3 MPa. Indeed, the SRRS threshold was passed, but unwanted supercontinuum was not observed under these conditions. Since there were no significant differences in the conversion efficiency or SRS spectrum envelope with different lenses, the optimal lens with a 750 mm focal length was selected. Although the most studied vibrational shift of 4155 cm\({}^{-1}\) in hydrogen shows the best steady-state gain, a rotational shift of 587 cm\({}^{-1}\) was also expected. Moreover, the SRRS can dominate in the highly transient regime as pump pulses approach -1 ps. However, with the linear polarization of the pump pulses, SVRS cannot be sufficiently suppressed (Figure 2). Regarding SRRS, although it is generally accepted that rotational SRS cannot be excited by a linearly polarized pump beam due to the parametric Stokes-anti-Stokes coupling [30], we confidently observed rotational Stokes components. Moreover, SRRS was reliably generated when the dichroic mirror (DM) and quarter-wave retardation plate (\(\lambda/4\)) were removed and when an additional thin-film polarizer was placed in the path of the pump beam to increase the polarization contrast. The windows in the cell were meticulously inspected not only for the absence of conventional depolarization but also for any manifestation of the nonlinear phenomenon of cross-polarized wave (XPW) generation. Finally, when a Glan prism was placed upon exit from the cell, the opposite polarization appeared strictly after the SRS excitation threshold was exceeded. The accompanying WLC generated by SPM is known to act as a seed beam for the generation of high-order rotational lines through four-wave Raman mixing. However, at the very threshold of SRS generation, one could expect only the first vibrational Stokes. With the circular polarization of the driving pulses, two units of angular momentum are transferred to hydrogen, which makes it possible to significantly increase the SRRS gain [23]. The dependence of the SRRS conversion efficiency on the pump energy for different polarizations of laser pulses at a hydrogen pressure of 3 MPa is shown in Figure 2a.