Calculation of off‐resonance Raman scattering intensities with parametric models

Bougeard, D.; Smirnov, Konstantin S.

doi:10.1002/jrs.2527

Cited by 11 publications

(13 citation statements)

References 104 publications

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“…In a simplified one-dimensional model the potential landscape of this state can be approximated as a displaced harmonic potential. Therefore, the vibrational levels separated by phonon frequency ω m can be quantized using the creation and annihilation operators b̂ and b̂ † . We can thus define a linear polarizability of the molecule along this coordinate as α̂ ν = R ν Q ν 0 ( b̂ + b̂ † ), where R ν is the element of the Raman tensor and Q ν 0 is the zero-point amplitude of the vibrations.…”

Section: Results and Discussionmentioning

confidence: 99%

Quantum Mechanical Description of Raman Scattering from Molecules in Plasmonic Cavities

et al. 2016

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Plasmon-enhanced Raman scattering can push single-molecule vibrational spectroscopy beyond a regime addressable by classical electrodynamics. We employ a quantum electrodynamics (QED) description of the coherent interaction of plasmons and molecular vibrations that reveal the emergence of nonlinearities in the inelastic response of the system. For realistic situations, we predict the onset of phonon-stimulated Raman scattering and a counterintuitive dependence of the anti-Stokes emission on the frequency of excitation. We further show that this QED framework opens a venue to analyze the correlations of photons emitted from a plasmonic cavity.Surface Enhanced Raman Scattering (SERS) is a spectroscopic technique in which the inelastic scattering from a molecule is increased by placing it in a hotspot of a plasmonic cavity, where the electric fields associated with the incident and the scattered photons are strongly enhanced (see the schematic in Fig. 1(a)). 1 The difference between the energy of those two photons provides a fingerprint of the molecule, i.e., detailed chemical information about its vibrational structure. Since the initial observation of Raman scattering from single molecules, 2,3 the use of a variety of plasmonic structures that act as effective optical nanoantennas over the last decades has allowed a tremendous advance of this molecular spectroscopy 4 . Metallic particles such as nanoshells 5,6 , nanorings 7 , nanorods 8 , nanowires 9 , or nano stars 10 , as well as plasmonic nanogap structures formed in particle dimers [11][12][13] , nanoparticle-on-a-mirror morphologies [14][15][16][17] , or nanoclusters 18 , are among the variety of structures that offer huge and controllable enhancements of the field intensity in their hotspots, boosting the inherently weak Raman scattering intensity, 1,19 and ultimately enabling the chemical identification and imaging of particular vibrational modes of a molecule with subnanometer resolution. 20 These results suggest that some experiments might have reached the regime where the quantum-mechanical nature of both the molecular vibrations and the plasmonic cavity emerges, 21 and call for an adequate theoretical description that goes beyond the classical treatment of the electric fields produced in plasmonic cavities. 1,22,23 In this work we address the underlying quantummechanical nature of Raman scattering processes by quantizing as bosonic excitations both the vibrations of the molecule and the electromagnetic field of a plasmonic cavity. The description of the vibrations through bosonic operators can be justified by considering the harmonic approximation to the energy landscape of the molecule along a generalized atomic coordinate ( Fig. 1(b)), such as the length of a molecular bond, e.g., C=O. 21,22 These vibrations interact with the cavity photons through a nonlinear Hamiltonian, reminiscent of that found in optomechanical systems. 24 In this description, the large enhancement of the Raman scattering from a molecule in the plasmonic cavity occurs thanks to ...

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Section: Results and Discussionmentioning

confidence: 99%

Quantum Mechanical Description of Raman Scattering from Molecules in Plasmonic Cavities

et al. 2016

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“…(86), one obtains the same expressions as Eqs. (18) and (19) in Dezfouli et al 12 We note that Dezfouli et al use as excitation 2E 0 cos(ω l t) instead of E 0 cos(ω l t), which introduces a factor 4 difference in the equations.…”

Section: Comparison With Generalized Optomechanical Modelmentioning

confidence: 99%

“…1(a)). Therefore, the vibrational levels separated by phonon frequency ω m 17,19 can be quantized using the phonon creation and annihilation operatorsb andb † :…”

Section: Introduction To Molecular Optomechanicsmentioning

confidence: 99%

Linking classical and molecular optomechanics descriptions of SERS

et al. 2017

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The surface-enhanced Raman scattering (SERS) of molecular species in plasmonic cavities can be described as an optomechanical process where plasmons constitute an optical cavity of reduced effective mode volume which effectively couples to the vibrations of the molecules. An optomechanical Hamiltonian can address the full quantum dynamics of the system, including the phonon population build-up, the vibrational pumping regime, and the Stokes-anti-Stokes correlations of the photons emitted. Here we describe in detail two different levels of approximation to the methodological solution of the optomechanical Hamiltonian of a generic SERS configuration, and compare the results of each model in light of recent experiments. Furthermore, a phenomenological semi-classical approach based on a rate equation of the phonon population is demonstrated to be formally equivalent to that obtained from the full quantum optomechanical approach. The evolution of the Raman signal with laser intensity (thermal, vibrational pumping and instability regimes) is accurately addressed when this phenomenological semi-classical approach is properly extended to account for the anti-Stokes process. The formal equivalence between semi-classical and molecular optomechanics descriptions allows us to describe the vibrational pumping regime of SERS through the classical cross sections which characterize a nanosystem, thus setting a roadmap to describing molecular optomechanical effects in a variety of experimental situations.

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“…Each contribution depends upon the bond type, orientation, and length. Bond polarizability models have been widely employed to represent the polarizability of single molecules, polymers, silica glasses, and nanotubes. ,,, For polymeric materials, only a few studies have focused on computing the Raman spectra of crystals and uses rather small molecular systems …”

Section: Bond Polarizability Modelmentioning

confidence: 99%

Predicting Raman Spectra of Condensed Polymer Phases from MD Simulations

Chen

Milner

2017

Macromolecules

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Raman spectroscopy is useful for probing conformational disorder and detecting rotator phases in nalkanes and polyethylene. Raman spectra do not give direct information about molecular conformations or phase structure, which are inferred from spectral signatures of previously identified phases. Here, we use molecular dynamics simulations to model polymer systems and predict their Raman spectra, so spectral and structural information can be obtained at once. Central to our method is the bond polarizability model, which represents molecular polarizability as a sum of individual bond contributions. We use two approaches for generating the Raman spectrum. First is normal-mode analysis, useful for identifying Raman modes in ordered phases. More generally, we compute the time-dependent polarizability and Raman spectra directly from simulation trajectories. Our results capture the main features of experimental spectra for crystalline, rotator, and melt phases of polyethylene.

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Calculation of off‐resonance Raman scattering intensities with parametric models

Cited by 11 publications

References 104 publications

Quantum Mechanical Description of Raman Scattering from Molecules in Plasmonic Cavities

Quantum Mechanical Description of Raman Scattering from Molecules in Plasmonic Cavities

Linking classical and molecular optomechanics descriptions of SERS

Predicting Raman Spectra of Condensed Polymer Phases from MD Simulations

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