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

Kai Niu,Soo-Y Lee

doi:10.1063/1.4938102

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.

Highlights

INTRODUCTIONPulses has been used for gas thermometry of N2.13 Begley et al.[14] showed that Coherent anti-Stokes Raman spectroscopy (CARS) is useful for investigating biological compounds where background fluorescence is a problem for conventional spontaneous Raman studies
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
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

Summary

INTRODUCTION

Pulses has been used for gas thermometry of N2.13 Begley et al.[14] showed that CARS is useful for investigating biological compounds where background fluorescence is a problem for conventional spontaneous Raman studies. Much of the theory has relied on just the conventional CARS diagram with a pump, Stokes and probe pulse, in that order, interacting with matter. The pump and Stokes pulses are temporally coincident at the sample, and prepare a vibrational coherence on the ground electronic state, while the probe pulse acts after a delay time. In Prince et al.’s,29 CARS experiment, the central wavelengths of the pump and Stokes pulses are around 530 nm and the probe pulse central wavelength is 800 nm. Niu et al.[31] has provided a simulation of Prince et al.’s,29 experimental results using just the conventional single CARS term which is assumed to be dominant, as well as derived the Dlott phenomenological result using a three-state model and FIG.

THEORY

RESULTS AND DISCUSSIONS

CONCLUSION