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The Journal of Chemical Physics

On the theory of time resolved near-resonance light scattering

Horia I. Metiu, John Ross, Abraham Nitzan

Published Aug 1, 1975• 35 citations
Publisher

Abstract

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.

DOI
10.1063/1.431423

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Journal of Physics B Atomic and Molecular Physics•Jul 28, 1980•2 citations
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.
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.
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.
A thermal Green function theory of resonance long-laser-pulse scattering is developed, correctly taking account of the uncertainty-relation between the time-resolved and the energy-resolved experiments and the effect of the sample surface. The transient scattering efficiency can be calculated by folding the retarded Green's functions which are given by the thermal average of the chronological products of the pulse-current (or -density) and current operators into an uncertainty-principle broadening function. The theory is applied to resonance light scattering from a simple molecule in gas for steady and transient cases, where all the collision processes are treated quantum-statistically. At low pressure, the resonance scattering is mainly composed of Raman scattering (RS), final-state redistribution scattering (FRS), final-state transfer scattering (FTS) and collision-induced redistribution scattering (CIRS). In the steady state, it is shown that ordinary resonance Raman scattering is equivalent to RS in collisionless case, that absorption followed by emission contains RS, FRS and FTS, and that absorption followed by redistribution followed by emission is the same phenomenon as CIRS which is weighted by rotational population of excited molecules. Moreover, recent laser-pulse data by Roussea, Patterson and Williams are satisfactorily explained. Connection between this theory and other work is discussed.
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.
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.
The authors present a weak light field, scattering theoretical description of the intensity autocorrelation function for the scattered light from a many-atom (molecule) system. The theory considers both resonant and near-resonant scattering for atoms with many sublevels in both the ground and electronically excited states, and it incorporates the effects of the finite coherence time of the incident radiation. The theory is derived using incident two-photon wave packets with spatial dispersion among the target atoms. Purely anti-bunching contributions arise from single-atom-two-photon scattering and from successive two-atom-two-photon scattering events. However, there are interleaved two-atom-two-photon scattering processes which provide purely bunching contributions since both atoms may be scattering at the same time. Path length differences in the successive two-atom scatterings can also induce some bunching character to the correlation function. The dependence of the risetime and decay of the intensity correlation function upon the atomic excited state lifetimes and the coherence time of the incident light emphasises the correlation between photons which have been coherently and/or incoherently scattered.