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

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. Copyright (C) 2009 John Wiley & Sons, Ltd.