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Physical Review A

Molecular Raman effect in an optical microcavity: A classical approach

Michele Marrocco

Published Oct 1, 1996• 4 citations
Publisher

Abstract

Spontaneous Raman scattering is investigated theoretically by considering a completely classical description of the process that takes place within the mirrors of a microscopic Fabry-P\'erot cavity. This analysis is based on the image method within the framework of the classical theory of light scattering. In order to account for the finite reflectivities of the mirrors, the result for the scattered field is presently determined analytically only in the limit of low finesse of the optical cavity. This leads to a general expression for the cross section of the Stokes transition that explains the results recently reported in the literature [F. De Martini, M. Marrocco, C. Pastina, and F. Viti, Phys. Rev. A 53, 471 (1996)]. Therefore, in the limit of low finesse of the cavity, one must accept that this effect has a fundamentally classical nature. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.3626

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Spontaneous Raman scattering is investigated theoretically by considering a completely classical description of the process that takes place within the mirrors of a microscopic Fabry-P'erot cavity. This analysis is based on the image method within the framework of the classical theory of light scattering. In order to account for the finite reflectivities of the mirrors, the result for the scattered field is presently determined analytically only in the limit of low finesse of the optical cavity. This leads to a general expression for the cross section of the Stokes transition that explains the results recently reported in the literature [F. De Martini, M. Marrocco, C. Pastina, and F. Viti, Phys. Rev. A 53, 471 (1996)]. Therefore, in the limit of low finesse of the cavity, one must accept that this effect has a fundamentally classical nature. \textcopyright{} 1996 The American Physical Society.
The spontaneous Raman scattering from liquid samples of C6{\mathrm{C}}_{6}C6​H6{\mathrm{H}}_{6}H6​ is investigated in the Casimir topology of a microscopic optical Fabry-P\'erot cavity terminated by Bragg reflectors tuned at the emitted Stokes wavelength. The given general quantum scattering theory is based on a complete set of mode functions describing the cavity-confined field in its vacuum state. The coupling of the field with the normal CH ring stretching mode at \ensuremath{\Delta}\ensuremath{\nu}=3062 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ (totally symmetric species A1g{\mathit{A}}_{1\mathit{g}}A1g​) of the benzene molecule is given via the related Raman tensor, which leads to the appropriate form of the coupling Hamiltonian. A detailed experimental investigation of the spontaneous Raman scattering for the mode is then reported. The results confirm the relevant predictions of the scattering theory, namely, the effect of the vacuum confinement on the enhancement and inhibition of the total and differential cross sections, on the angular distribution of the scattered radiation, and on the molecular depolarization ratio. \textcopyright{} 1996 The American Physical Society.
The temperature effect on the resonance Raman scattering from molecules is investigated. Considering a total system consisting of a molecular system, a heat bath, and the weak radiation field, a general expression for the relaxation processes is derived utilizing the Liouville operator technique for the time evolution of the density matrix of the total system. By using the perturbation method with respect to the radiation and matter up to second order, rate constants for zero photon (radiationless processes), one-photon and two-photon processes are derived after taking the long time limit in the Markoff approximation. Assuming a weak interaction between the molecular system and heat bath, a temperature-dependent resonance Raman scattering cross section is formulated in the adiabatic basis set for the molecular systems. In the displaced harmonic oscillator model, we obtain an analytical expression for the temperature-dependent Raman scattering cross section for the multimode case, which is suitable for both weak coupling and strong coupling cases. Analytical expressions for the Stokes and anti-Stokes bands of the jth order vibrational transition in the one oscillator model can easily be obtained from the general expression for the resonance Raman scattering cross section derived. An approximate Stokes to anti-Stokes ratio is given up to the second order of the dimensionless displacement Δ. The resonance Raman scattering cross section and the excitation energy profiles are numerically calculated as a function of physical constant such as temperature, molecular vibrational frequency and Δ. It is shown that the excitation profiles of the anti-Stokes band of the jth order vibrational transition have the similar envelope of the corresponding Stokes band shifted by jh/ω. The inverse Raman effect which is closely related to the ordinary Raman effect is also discussed.
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.
A compact and transparent plane-wave expansion of the complete Green function for an absorbing multilayered system is derived. The plane-wave solutions involved match, in the appropriate limit, the space-mode functions recently employed for quantization of the radiation field in a planar cavity and make this Green function particularly convenient for consideration of optical processes in realistic cavities and multilayers in general. This is illustrated by considering classically light scattering on a molecule in a planar cavity. It is demonstrated that the cross sections derived, besides generally describing light scattering on molecules embedded in a multilayer, correctly reproduce the effects of field confinement on light scattering in a planar cavity as predicted recently by the quantum-mechanical theory of Cairo et al. [Phys. Rev. Lett. 70, 1413 (1993)]. It is also pointed out that scattering into waves guided by the cavity lossy (metallic) mirrors may become an effective process in low-order microcavities. As a by product, a classical approach to spontaneous emission in absorbing planar cavities emerges from these considerations.
A theory for the resonance light scattering in a molecular system interacting with the heat bath is developed, taking into account the multilevel structure of the molecular system. An expression for the cross section of the resonance light scattering process is derived by using the Liouville operator method in the Markoff approximation; the cross section consists of three terms: resonance Raman scattering, resonance fluorescence, and their mixing. The mixing term vanishes in the limit of the zero vibrational dephasing constant. Analytical expressions for the resonance Raman scattering and resonance fluorescence cross sections are derived in the displaced harmonic oscillator model. Model calculations of the vibrational band structure in the resonance light scattering cross section are performed by using the expressions derived. Differences of the band intensity distribution in the resonance fluorescence from that in the resonance Raman scattering are illustrated.
We present a theoretical framework for spontaneous Raman scattering that fundamentally bridges quantum-mechanical and nonlinear-optical approaches. By conceptualizing spontaneous Raman scattering as a stimulated Raman gain or loss event seeded by the quantum vacuum field, we rigorously derive the spontaneous Raman cross-section directly from the third-order nonlinear susceptibility. Crucially, this framework predicts the existence of a hitherto unrecognized phenomenon: "spontaneous Raman loss" (sRL), which acts as the vacuum-seeded counterpart to stimulated Raman loss, complementing traditional spontaneous Raman scattering (spontaneous Raman gain, sRG). Furthermore, we establish a rigorous connection to the traditional Kramers-Heisenberg-Dirac (KHD) theory, revealing that the spontaneous process is governed by interference before a detector between the signal field emitted from molecules and the vacuum field itself that stimulates the molecules. This insight uncovers a direct correspondence between the sRG susceptibility and the rotating/counter-rotating interference terms in the KHD formula. Ultimately, we extend the foundational KHD theory by incorporating previously unrecognized essential terms, achieving perfect analytical agreement between the quantum mechanical and nonlinear optical descriptions of Raman scattering.