Abstract

Raman scattering is most commonly associated with a change in vibrational state within individual molecules, the corresponding frequency shift in the scattered light affording a key way of identifying material structures. In theories where both matter and light are treated quantum mechanically, the fundamental scattering process is represented as the concurrent annihilation of a photon from one radiation mode and creation of another in a different mode. Developing this quantum electrodynamical formulation, the focus of the present work is on the spectroscopic consequences of electrodynamic coupling between neighboring molecules or other kinds of optical center. To encompass these nanoscale interactions, through which the molecular states evolve under the dual influence of the input light and local fields, this work identifies and determines two major mechanisms for each of which different selection rules apply. The constituent optical centers are considered to be chemically different and held in a fixed orientation with respect to each other, either as two components of a larger molecule or a molecular assembly that can undergo free rotation in a fluid medium or as parts of a larger, solid material. The two centers are considered to be separated beyond wavefunction overlap but close enough together to fall within an optical near-field limit, which leads to high inverse power dependences on their local separation. In this investigation, individual centers undergo a Stokes transition, whilst each neighbor of a different species remains in its original electronic and vibrational state. Analogous principles are applicable for the anti-Stokes case. The analysis concludes by considering the experimental consequences of applying this spectroscopic interpretation to fluid media; explicitly, the selection rules and the impact of pressure on the radiant intensity of this process.

Highlights

  • Raman scattering involving individual optical centers is a well-established molecular process used as a spectroscopic1–3 and microscopic tool4,5 with an ever-increasing range of applications, including surface-enhanced spectroscopy,6–11 sensing,12–14 the detection of environmental pollutants,15,16 and identification of disease.17 The theoretical basis for the underlying phenomenon is well-known and established with quantum electrodynamical techniques offering a insightful means of formulation.18 The concurrent annihilation and creation of a photon of two different radiation modes is involved, typically entailing some exchange in vibrational energy with the system and thereby corresponding to an inelastic process

  • Raman scattering is most commonly associated with a change in vibrational state within individual molecules, the corresponding frequency shift in the scattered light affording a key way of identifying material structures

  • The first is a change in the intensity of conventional Raman-allowed lines, which arise from vibrational transitions associated with two-photon interactions

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Summary

INTRODUCTION

Raman scattering involving individual optical centers is a well-established molecular process used as a spectroscopic and microscopic tool with an ever-increasing range of applications, including surface-enhanced spectroscopy, sensing, the detection of environmental pollutants, and identification of disease. The theoretical basis for the underlying phenomenon is well-known and established with quantum electrodynamical techniques offering a insightful means of formulation. The concurrent annihilation and creation of a photon of two different radiation modes is involved, typically entailing some exchange in vibrational energy with the system and thereby corresponding to an inelastic process. Utilizing methods detailed by Andrews et al., we extend this earlier Raman study, focusing on the experimentally more significant likelihood in which just one of the pair becomes vibrationally excited This analysis entertains contributions involving the transfer of either one or two virtual photons between the optical centers during. Subsequent subsections accommodate further tiers of complexity: explicitly one and two virtual photon exchanges, respectively At this juncture, we focus on the application of these spectroscopic techniques to fluid media, including the relevance of modified selection rules—with the appropriate symmetry analysis applied to an example system—and a consideration of pressure dependence. The context for this work is discussed with regard to a range of applications

Theory for single-center Raman scattering
Introducing the accommodation of neighbor interactions
Born-Oppenheimer development of the transition tensors
Raman scattering with virtual photon coupling to a neighbor
Raman scattering with coupling of two virtual photons to a neighbor
Scattering in fluid media
Exemplary systems
Pressure dependence of the rate of scattering
DISCUSSION
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