Raman scattering and vacuum fluctuation: An Einstein-coefficient-like equation for Raman cross sections

Abstract

Since it was first predicted 100 years ago, Raman scattering has been a cornerstone of molecular spectroscopy with a widespread impact on science and technology. Nearly all theoretical frameworks have employed Raman cross sections (σRaman) to characterize and quantify molecular Raman response. The recently introduced absolute stimulated Raman scattering cross section (σSRS), on the other hand, provides an alternative way of interpreting molecular responses under two coherent laser sources. However, the theoretical connection between σRaman and σSRS remains unclear. Herein, we are inspired by Einstein’s A and B coefficients for spontaneous and stimulated emissions and derived an analogous equation [Eq. (16)] for Raman scattering from an approach along quantum electrodynamics. Equation (16) decomposes Raman cross sections into a contribution from the vacuum electromagnetic field and an underlying molecular response captured by stimulated Raman cross sections (in the unit of Göppert–Mayer). This theoretical relation is supported by recent experimental measurements on methanol as a model compound. Foremost, it provides a connection between experimentally defined σRaman and σSRS under certain approximations. In addition, it quantitatively shows that it is the weak vacuum field of the Stokes channel that makes Raman cross sections appear so small, corroborating the conventional Raman theory. Moreover, it suggests stimulated Raman cross sections to be a vacuum-decoupled intrinsic quantity for characterizing molecular response during Raman scattering. Remarkably, stimulated Raman cross sections turn out to be not weak when compared to two-photon absorption, narrowing the conventional gap of cross sections between spontaneous Raman and UV–vis absorption by more than 1010 folds.