Comparative analysis of Herman‐Wallis factors for uses in coherent anti‐Stokes Raman spectra of light molecules

Abstract

The cross section of Raman processes involving light molecules takes into account the unavoidable coupling between rotational and vibrational modes. This coupling is quantified by the Herman-Wallis (HW) factor and its use was recently criticized in view of the known thermometric application of vibrational spectra of coherent antiStokes Raman scattering (CARS) of hydrogen. Following this line of research, this paper addresses the physical limitations of the HW factors employed ordinarily in Q-branch CARS measurements. Furthermore, new determinations of the vibration-rotation coupling are considered. These are based on a more realistic scenario consisting of anharmonic oscillations and polarizability variations during vibration. Numerical examples for fundamental diatomics, namely H 2 and N 2 , are given throughout the text. It is found that, as expected, the Raman cross section of H 2 is strongly dependent on the HW factor and the consequent correction to CARS line intensities is of the order of 10% or greater. Surprisingly, the analysis suggests that N 2 spectral data are also affected, to a certain extent, by the new HW factors. Usually, this correction is completely disregarded, but under the new understanding of the vibration-rotation coupling, Q-branch CARS lines of N 2 are predicted to undergo variations between 1 and 5% for rotational levels that are sufficiently populated at temperatures of interest for CARS studies. Oxygen is also prone to vibration-rotation corrections and is finally shown as an example between the two limits of hydrogen and nitrogen.

CARS thermometry revisited in lightof the intramolecular perturbation

“…But, it is important to emphasize that HW corrections to the line intensities become relevant for molecular transitions between high rotational levels that are usually populated at those temperatures characterizing combustion science 3, 10–14. In particular, laser spectroscopy for thermometric applications in harsh environments is dominated by coherent anti‐Stokes Raman scattering (CARS) and it seems surprising that, despite the well‐recognized knowledge of CARS spectra of simple molecules (diatomics, mainly), the understanding of VR perturbation in vibrational CARS intensities was not properly tackled until recently 15–17. The impetus to undertake the research came from the confusion prevailing among the CARS users as to the use of contradictory Q‐branch HW corrections to hydrogen CARS spectra 15.…”

Accurate temperature measurements in flames with high spatial resolution using Stokes Raman scattering from nitrogen in a multiple-pass cell

“…We also find comparisons [38,39] between this form of the Herman-Wallis factor and those given by Buldakov et al [26], as if they have separate origins. However, the expression given by Tipping and Bouanich [33] is an approximate form of the expression given by Buldakov et al [26], because the Herman-Wallis factor given by Tipping and Bouanich [33] is an approximation of the Herman-Wallis factors given by Tipping and Ogilvie [40], and Buldakov et al's expression is a function of v, which simplifies to Tipping and Ogilvie's expression, which is given only for v 0.…”

Advances In Understanding Of Coherent Raman Scattering For Diagnostic Uses

“…Recently, the research in coherent anti-Stokes Raman scattering (CARS) for thermometric uses has deepened the subject of vibration-rotation corrections [2][3][4][5] and it appears that the interpretation of the CARS signal of the most known diatomics is significantly affected by the HW factor. Examples are given in Figure 1.…”