Fundamental detectability of Raman scattering: A unified diagrammatic approach

Abstract

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.

Stain-Free Histopathology with Stimulated Raman Scattering Microscopy

“…Despite the broad analytical applications in many research fields, spontaneous Raman scattering is too weak to be used for biomedical imaging. After the invention of the pulsed laser, CRS phenomena including CARS and SRS were discovered. , These coherent nonlinear optical processes could enhance the weak Raman scattering efficiency by up to ∼10 8 . − In the CRS process, both the pump and Stokes beams simultaneously interact with the target molecules; a strong optical resonance occurs when the beat frequency Δω = ω p – ω S matches the vibrational frequency Ω of a chemical bond. CARS photons of ω CARS = 2ω p – ω S are generated via a four-wave-mixing process.…”

The Duality of Raman Scattering

“…We can provide a semiempirical numerical evaluation of eq 5 to support the measurement results. 3 If we assume we excite small molecules whose electronic state lies around 200 nm by a third-order interaction unit in cm 2 (area) unit in cm 4 •s (Goppert-Mayer) vacuum-coupled vacuum-decoupled extremely small compared to the electronic counterpart (linear absorption) (see Figure 1) comparable to or exceeding the electronic counterpart (two-photon absorption) (see Figure 1) The summation over states can be relaxed, provided the single resonant state has a large enough transition dipole moment as in Albrecht's theory. 26 We assume both the laser excitation wavelength and the chromophore electronic absorption to be 700 nm and the electronic linewidth to be 700 cm −1 , take the transition displacement D as 1.6 Å, and assume Franck−Condon overlap to be 0.1 here.…”

“…Specifically, N p is the number of pump photons passing through the sample within the dwell time, and Λ, or Raman absorbance, is a dimensionless quantity defined by Λ = n · σ Raman A · true( ω normalp ω normalS true) , characterizing the strength of the Raman response. The detection limit of Raman microscopy can be recast into η · Λ · N p = 1 where η denotes the photon collection efficiency for spontaneous Raman Eq corresponds to the quantum limit that only a single photon is detected during the spontaneous Raman scattering process.…”

“…Fundamental Detectability of Raman Scattering: A Unified Diagrammatic Approach. The Journal of Chemical Physics 2024 , 160 (9), 094110 …”

“…The results paint a previously underappreciated dual nature of Raman cross section, which we call “the duality of Raman scattering” (Table ). The quest for the origin of such Raman duality not only reveals a unified theoretical framework for molecular spectroscopy, , which can be regarded as a generalization of Einstein’s A and B coefficients, but also leads to a quantitative treatment and appreciation of stimulated Raman scattering (SRS) microscopy for chemical imaging. , …”