Fundamental detectability of Raman scattering: A unified diagrammatic approach

Both spontaneous Raman scattering and stimulated Raman scattering (SRS) are cornerstones of modern photonics, spectroscopy, and imaging. However, a unified understanding of the ultimate detectability of Raman scattering is lacking, due to both historical and technical reasons. Starting from quantum electrodynamics, we formulate the fundamental detectability for both spontaneous Raman scattering and SRS. The key concept is recognizing spontaneous Raman scattering as stimulated Raman process driven by vacuum field fluctuation. A simple and unified expression, Eq. (17), is derived, which can be depicted on a two-dimensional phase-diagram-like graph with inherent symmetry. It turns out that the particle nature of light dictates the ultimate detectability of spontaneous Raman scattering, which can be represented by a line on this detectability diagram. Importantly, if provided with a reasonably strong Stokes photon flux, SRS can breach this fundamental limit and open uncharted territory of drastically accelerated measurement speed and much lower detection concentration relevant to biological imaging. Such new territory in the detectability diagram is otherwise forbidden by the spontaneous counterpart. Diagrammatical analysis explains the empirical observations, provides quantitative insights, and makes new predictions. Notably, recent experimental applications of SRS microscopy can almost entirely be captured by this diagram, further supporting the explanatory power of the theory. Thus, this unified diagrammatic approach outlines a framework to understand all Raman-based measurement and provides a theoretical explanation for the remarkable utility of the emerging SRS microscopy.