What are the intensities and line-shapes of the twenty four polarization terms in coherent anti-Stokes Raman spectroscopy?

Abstract

Coherent anti-Stokes Raman spectroscopy (CARS) is conventionally described by just one diagram/term where the three electric field interactions act on the ket side in a Feynman dual time-line diagram in a specific time order of pump, Stokes and probe pulses. In theory, however, any third-order nonlinear spectroscopy with three different electric fields interacting with a molecule can be described by forty eight diagrams/terms. They reduce to just 24 diagrams/terms if we treat the time ordering of the electric field interactions on the ket independently of those on the bra, i.e. the ket and bra wave packets evolve independently. The twenty four polarization terms can be calculated in the multidimensional, separable harmonic oscillator model to obtain the intensities and line-shapes. It is shown that in fs/ps CARS, for the two cases of off-resonance CARS in toluene and resonance CARS in rhodamine 6G, where we use a fs pump pulse, a fs Stokes pulse and a ps probe pulse, we obtain sharp vibrational lines in four of the polarization terms where the pump and Stokes pulses can create a vibrational coherence on the ground electronic state, while the spectral line-shapes of the other twenty terms are broad and featureless. The conventional CARS term with sharp vibrational lines is the dominant term, with intensity at least one order of magnitude larger than the other terms.