Time-domain modelling and thermometry of the CH4 ν1 Q-branch using hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering

The ro-vibrational ν2 mode spectrum of methane investigated by ultrabroadband coherent Raman spectroscopy

“…The modeling of the CH 4 v 2 coherent Raman spectrum follows the modeling approach of the CH 4 v 1 spectrum presented by Chen et al, 52 based on the assumption of impulsive excitation of the Raman coherence, and on a phenomenological description of the resulting third-order nonlinear optical susceptibility following Prince et al 47 This approach has been successfully demonstrated for both pure-rotational [61][62][63] and ro-vibrational 54,64 CRS of multiple combustion-relevant species. The main assumptions of the timedomain model can be outlined as follows: the nonlinear interaction of the electronically off-resonant pump, Stokes probe laser fields (at angular frequencies ω i with i = 1, 2, and 3 for the pump, Stokes, and probe, respectively) with the gas-phase medium induces the macroscopic third-order polarization:…”

“…[72][73][74] The resulting spectral database has been employed by multiple research groups to simulate the spontaneous CH 4 Raman spectrum in both the dyad 75 and pentad region, 21,30,76 and recently, its application has been extended to the v 1 CH 4 CRS spectrum. 52 According to the notation of Jourdanneau et al, the spontaneous Raman line intensities in the spectral database are computed as 76…”

“…Each of the v 2 mode transitions gives rise to a damped harmonic contribution that is computationally evaluated on a temporal grid up to 1 ns, with 8 fs step size, corresponding to a resolution of 0.03 cm −1 for the Fourier-transformed CRS signal. As pointed out by Chen et al, 52 the main challenge in the development of an accurate time-domain model for the CH 4 CRS spectrum is the staggering number of Raman transitions included in the MeCaSDa calculated spectral database computed at the University of Burgundy 72,73 (and accessible at the following url: http://vamdc.icb.cnrs.fr/PHP/methane.php) and the resulting computational cost. Implementing the calculation of χ (3) as a running sum for every transition input avoids exceeding memory limits of the available computational resources; each spectral calculation still needs to be iterated for different input values of temperature and, if the effects of molecular collisions are not negligible, species concentrations in the probe volume.…”

“…Hence, the calculation of spectral libraries for quantitative spectroscopy can be a cumbersome task, especially when the possibility of CH 4 CRS thermometry in non-equilibrium environments is considered. 21 The computational cost can be reduced by implementing a filter to exclude transitions whose intensity is lesser than the cut-off value of the strongest transition in the spectrum, 52 depending on both the strength of the associated instantaneous dipole and on the Boltzmann population. Figure 3(a) shows the transition polarizability for a small fraction of the Raman transitions considered in the database, corresponding to the fundamental band of the v 2 mode spectrum (0000 ← 0100) and its first two hot bands (0001 ← 0101 and 0100 ← 0002): the overall database spans more than 18 orders of magnitude in the Raman polarizability.…”

“…In the present linewidth model, the effect of the symmetry of ro-vibrational wave function is neglected 42 so that the linewidth computed for a specific value of the rotational quantum number J is applied to all its symmetry components in Table I; similarly, the same RET rate is assumed for all the vibrational hot bands. Following the work of Chen et al, 52 the species-specific constant a is set to 2, and the number of fitting parameters to be simultaneously determined is reduced by independently fitting α and β at room temperature, assuming δ = 1 and n = 0. While the MEG model has been successfully applied to isotropic v 1 Q-branch CRS spectrum of CH 4 in multiple studies, 44,45,52 the sum rule in Eq.…”