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Physical Review Letters

Resonance Fluorescence and Resonance Raman Scattering: Lifetimes in Molecular Iodine

Paul F. Williams, Denis L. Rousseau, S. H. Dworetsky

Published Feb 4, 1974• 164 citations
Publisher

Abstract

We report a significantly shortened scattering lifetime in molecular iodine when the frequency of a single-mode 5145-\AA{}A incident laser is tuned away from resonance with a discrete transition. This observation of a shortened scattering time is indicative of what has been conventionally called a Raman process. Off-resonance lifetime measurements, as reported here, may provide a means of determining the relative contribution to the absorption linewidth of homogeneous and inhomogeneous broadening.

DOI
10.1103/physrevlett.32.196

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We report a significantly shortened scattering lifetime in molecular iodine when the frequency of a single-mode 5145-\AA{}A incident laser is tuned away from resonance with a discrete transition. This observation of a shortened scattering time is indicative of what has been conventionally called a Raman process. Off-resonance lifetime measurements, as reported here, may provide a means of determining the relative contribution to the absorption linewidth of homogeneous and inhomogeneous broadening.
We address the distinction between resonance Raman scattering and fluorescence as the excitation source is continuously tuned through resonance. The experiments are performed in iodine vapor using a cw laser, whose intensity is electrooptically modulated in the 0.1-50-MHz frequency range. A lock-in amplifier is used to detect both the in-phase and out-of-phase response of the emission. The modulated signal is found to be the sum of two components. One component varies with angular modulation frequency ω, as (1 + ω2τ2)-1/2, where τ is the lifetime of the excited state. The other is found to be flat within the range of modulation frequency used in the experiment. Since the results of the modulation experiment are the Fourier transform of the response to pulsed excitation, the first component corresponds to exponential decay with the fluorescence lifetime and the second corresponds to a prompt response. A density matrix calculation shows that the prompt response would be absent if the absorption were independent of laser frequency. It exists as a result of the finite inhomogeneous linewidth and the laser detuning from the center of the transition. The amplitude of the delayed and prompt components is a function of laser frequency. This gives a full description of the dynamical response to the emission to linear excitation as the laser is tuned continuously through resonance. The response of the sample to nonlinear excitation is also discussed.
The review deals with various variants of classification of the types of secondary emission of light by molecules; cases are distinguished in which the secondary emission occurs without additional processes that find their way between photon emission and absorption; the advisability of differentiating between the cases of resonance fluorescence and resonance scattering is noted. Reference is made to papers that have made contributions to the development of quantum-mechanical and classical theory of Raman scattering and to the development of the concepts of the relations between electron-vibrational absorption spectra, fluorescence spectra, and scattering excitation near and near and far resonance. Conditions are considered of excitation of the spectrum at different relations between the electronic-oscillator damping constant, the atom vibration frequency, the rotational frequencies, and the difference between the frequency of the incident light and the frequency of the electronic transition. The conditions for the excitation of typical light scattering, typical resonance fluorescence, and certain intermediate types, in which individual features of scattering are combined with certain features of fluorescence (phenomena of the transition type) are noted. The results of investigations of different models of the scattering centers, their advantages, shortcomings, and limits of applicability are compared. The most interesting results of the experimental investigations of resonant scattering of light by molecules and crystals are noted.
Abstract If and only if spontaneous resonance Raman scattering is excited by irradiation upon a single, discrete and non‐degenerate energy level sufficiently distant from other levels can it be interpreted as resonance fiuorescence, i.e. a sequence of two independent one‐photon processes, an absorption and an emission in definte order of succession. This decomposition of the resonance scattering process is independent of the bandwidth of the exciting radiation relative to the widths of the combining levels. These widths however determine quantitatively the temporal decay of the resonance scattering (= resonance fluorescence) probability given explicitly in the paper.
Abstract A practical approach to understanding light scattering processes in the condensed phase is presented. First a theoretical discussion of the various parameters in resonance light scattering is given and there is a special emphasis on our simplified approach to this question. As with other approaches the two level density matrix in association with a quantum regression theorem leads to two types of emission from an ensemble of molecules at finite temperature (T2 ≠ 2T1). We have called one of these fluorescence and the other sharper emission Raman scattering because it results directly from the presence of a coherent polarization in the medium. A brief discussion of time dependent scattering is also given. An experiment that reproduces the main features of the theory is described for resonance scattering from azulene in naphthalene at 30 K. For all values of the laser frequency (near resonance) both a sharp (Raman) and diffuse (fluorescent) component occurs in the emission spectrum. These spectra when interpreted by the simplified theory yield a value of T2 = 0.7 ps from fluorescence linewidth, and T2 = 0.8 ps from the incoherent to coherent scattering ratio, for the 0–0 two level system of azulene in naphthalene. A discussion of practical aspects of the influence of inhomogeneous line broadening is also presented.
The response of emission in I2 vapor to intensity modulated light at radial frequency ω is measured and described in terms of the lifetime of the excited state, T1, the rate of phase interrupting collisions γ, and the inhomogeneously broadened absorption line. When the laser is tuned to resonance, the variation of amplitude of the modulated emission with ω corresponds to a single exponential decay with lifetime T1. Off resonance, the modulation is described as the sum of the above ‘‘delayed’’ component and a ‘‘prompt’’ in‐phase component which is independent of modulation frequency. The ratio of the delayed to prompt component for off resonant excitation is shown to be 2γT1. This relation is used to determine the rate of phase interrupting collisions in I2 vapor.
In this paper we present a quantum mechanical treatment of time resolved resonant and near resonant light scattering from a molecular system. The time resolved decay pattern is characterized by just two types of lifetimes, those specifying the molecular system and those characterizing the light pulse, while the off resonance energy parameter affects the total intensity and, in some cases, the relative intensities of the different decay components. The theoretical results for the ’’isolated’’ molecule are confronted with the recent experimental data of Williams, Rousseau, and Dworetzky [Phys. Rev. Lett. 32, 196 (1974)] for resonance and near resonance photon scattering from I2. Finally, we present a general scheme for handling photon scattering from a multilevel molecular system.