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The Journal of Chemical Physics

Lifetimes for resonance fluorescence and near resonance Raman scattering

Shaul Mukamel, Joshua Jortner

Published May 1, 1975• 95 citations
Publisher

Abstract

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.

DOI
10.1063/1.430956

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Physical Review A•Sep 1, 1975•71 citations
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.
Time resolved resonance and near-resonance light scattering is analyzed by means of Green’s operator formalism. We study the process of a photon wavepacket colliding with and scattered from a given molecule. Two decay components similar to those observed by Williams, Rousseau, and Dworetsky are obtained under appropriate conditions. Unlike other recent treatments of this problem, the light pulse is not treated as a pure quantum state (minimum uncertainty wavepacket) but rather as a mixture having characteristic time and energy profiles. It is shown that the nature of the light pulse may strongly influence the ratio of the short time to the long time decay intensities.
Pulses of laser light which undergo Raman scattering by a molecule at a resonance are observed to consist of two components: a short pulse which lasts as long as the driving pulse, and a long tail which falls off with the lifetime of the excited state. It is shown that the recent observations of Williams, Rousseau, and Dworetsky on I2{\mathrm{I}}_{2}I2​ can be fitted by theory; one has to suppose that the frequency spectrum of the driving pulses is broadened to an extent equivalent to a reduction of the stated rise and fall times by a factor of 10.
Light scattering by isolated small and intermediate-size molecules is studied theoretically. A quantum-mechanical model is developed that treats the molecule and the radiation field on equal terms and allows a nonperturbative solution for arbitrary wave forms and field strengths. The molecular states are described in terms of a basis set of zeroth-order states chosen so as to minimize the number of excited molecular states in the laser frequency range that combines radiatively with the initial (ground) state, i.e., that act as doorways for the field. Detailed calculations are restricted to the case of a single doorway. Closed-form expressions are obtained for the frequency-resolved scattering rates and time-resolved scattering spectra, including fluorescence and Rayleigh–Raman components, for a variety of conditions, including δ(t) excitation, excitation by a Lorentzian light pulse, by a coherent train of pulses and stationary excitation. The case of nonlinear scattering by very intense pulses is also investigated. Model calculations are reported for systems of 1–3 molecular levels. It is found that in general phase relations are maintained so that the coherence survives as long as the signal.
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.
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.
A theoretical study is presented of the effects of collisional perturbations on the time-resolved resonant and near-resonant photon scattering from a molecular system. The photon counting rate is formulated in terms of tetradic Green's functions in Liouville space. The collisional and radiative damping effects are handled by an effective-Liouvillian formalism. The formal expressions are disentangled by invoking a series of successive approximations, assuming short correlation times of the thermal bath, neglecting relaxation processes in the ground electronic state, considering rotational relaxation as providing the dominant damping mechanism in the excited electronic manifold, specializing to weak electromagnetic fields, neglecting some off-resonance processes and disregarding collision-induced radiative processes. The photon counting rate is expressed as a triple convolution of the photon counting rate for the free molecule with the Doppler Gaussian profile and with a Lorentz profile. The latter incorporates purely collisional effects due to intrastate cross relaxations and proper T2{T}_{2}T2​ processes. The theory accounts well for the recent experimental data of Williams, Rousseau, and Dworetsky on collisionally perturbed I2{\mathrm{I}}_{2}I2​ molecules.