The Duality of Raman Scattering.

Abstract

ConspectusFirst predicted more than 100 years ago, Raman scattering is a cornerstone of photonics, spectroscopy, and imaging. The conventional framework of understanding Raman scattering was built on Raman cross section σ_Raman. Carrying a dimension of area, σ_Raman characterizes the interaction strength between light and molecules during inelastic scattering. The numerical values of σ_Raman turn out to be many orders of magnitude smaller in comparison to the linear absorption cross sections σ_Absorption of similar molecular systems. Such an enormous gap has been the reason for researchers to believe the extremely feeble Raman scattering ever since its discovery. However, this prevailing picture is conceptually problematic or at least incomplete due to the fact that Raman scattering and linear absorption belong to different orders of light-matter interaction.In this Account, we will summarize an alternate way to think about Raman scattering, which we term stimulated response formulation. To capture the third-order interaction nature of Raman scattering, we introduced stimulated Raman cross section, σ_SRS, defined as the intrinsic molecular property in response to the external photon fluxes. Foremost, experimental measurement of σ_SRS turns out to be not weak at all or even larger when fairly compared with electronic counterparts of the same order. The analytical expression for σ_SRS derived from quantum electrodynamics also supports the measurement and proves that σ_SRS is intrinsically strong. Hence, σ_Raman and σ_SRS can be extremely small and large, respectively, for the same molecule at the same time. Our subsequent theoretical studies show that stimulated response formulation can unify spontaneous emission, stimulated emission, spontaneous Raman, and stimulated Raman via eq 10, in a coherent and symmetric way. In particular, an Einstein-coefficient-like equation, eq 12a, was derived, showing that σ_Raman can be explicitly expressed as σ_SRS multiplied by an effective photon flux arising from zero-point fluctuation of the vacuum. The feeble vacuum fluctuation hence explains how σ_SRS can be intrinsically strong while, at the same time, σ_Raman ends up being many orders of magnitude smaller when both compared to the electronic counterparts. These two sides of the same coin prompted us to propose "the duality of Raman scattering" (Table 1). Finally, this formulation naturally leads to a quantitative treatment of stimulated Raman scattering (SRS) microscopy, providing an intuitive, molecule-centric explanation as to how SRS microscopy can outperform regular Raman microscopy. Hence, as unveiled by the new formulation, a duality of Raman scattering has emerged, with implications for both fundamental science and practical technology.