## 3 Results and Discussion
### Comparison between the Stokes and Anti-Stokes FSRS  
It is notable that both the Stokes and anti-Stokes Raman spectra can be conveniently captured by FSRS gain/loss measurement depending upon the relative wavelengths of the Raman pump and probe pulses, while the latter can be switched between various BUMA sidebands (e.g., shifting the pinhole position) or tuned within the same sideband (e.g., varying the time delay between FP and WL) with ease (see Figure 1). Based on partition functions in thermodynamics, there is less population on the first excited vibrational state (_i.e._, quantum number \(v=1\)) than that on the ground state (\(v=0\)). At room temperature the thermal energy 1 \(k_{B}T\) amounts to \(\sim\)200 cm\({}^{-1}\) so all the vibrational modes (e.g., \(>\)300 cm\({}^{-1}\) in Figure 3a) should display weaker anti-Stokes spontaneous Raman peaks than the corresponding Stokes peaks particularly for high-frequency modes. In contrast, FSRS signal strength is normalized by the probe intensity (see Equation (1)) but is typically proportional to Raman pump power [9; 39] and to the square of the SRS nonlinear coefficient for either the Stokes or anti-Stokes signal [40; 41]. Figure 4a shows that the ground-state FSRS anti-Stokes Raman spectrum we collected using S\({}_{+1}\) on the FP side as the probe (_i.e._, to the blue of the 402 nm pump pulse in Figure 2b) is much stronger than the Stokes spectrum. This unusual, opposite trend indicates that some other factors contribute to the Raman signal strength beyond the Raman pump power and third-order nonlinear polarizabilities [41]. Can it arise from resonance enhancement because this is a stimulated Raman technique [14; 42]? If so, how does the Raman pump wavelength compare to the 0-0 vertical transition energy between the electronic ground state and excited state of LD390 in both FSRS measurements?  
We list all the anti-Stokes over Stokes peak intensity ratios in Figure 4a insert and it becomes apparent that the two modes below 750 cm\({}^{-1}\) have a ratio below 1.8 while the modes above 1000 cm\({}^{-1}\) all have a ratio above 3.0. The overall trend is that the Raman peak gets stronger as the vibrational frequency increases. Given that the anti-Stokes process originates from the higher-lying vibrational state (e.g., \(v=1\)) and terminates at the lower-lying vibrational state (e.g., \(v=0\)), this experimental trend can be explained by the principle of resonance Raman enhancement because the 402 nm pump pulse being used still falls short of the LD390 electronic absorption peak of \(\sim\)355 nm (Figure 4b). As a result, for the anti-Stokes transition, the 663 (1615) cm\({}^{-1}\) modes correspond to an \"effective\" Raman pump wavelength of 392 (377) nm, making the latter Raman mode much stronger because a 377 nm pump is in closer proximity to the 355 nm electronic gap than a 392 nm pump. This reasoning is further corroborated by experimental data in Figure 3a, and paves the way to enhance higher-frequency Raman modes regardless of their intrinsic electronic polarizability. For the Stokes spectrum that starts from the ground state and ends on the \(v=1\) state in S\({}_{0}\), the vibrational transition frequency does not affect the energy relation between the 402 nm Raman pump and the 355 nm electronic energy gap (_i.e._, no addition of the vibrational frequency can occur to bring the 402 nm Raman pump closer to the solute \(S_{1}\) state, see Figure 4b), hence the intensity ratio between Raman peaks is mostly determined by the mode-dependent polarizability [13,43].