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Journal of Raman Spectroscopy

Pulse shapes of Raman and Rayleigh scattering

V. A. Morozov, P. P. Shorygin

Published Feb 1, 1986• 1 citation
Publisher

Abstract

Abstract The expressions for the pulse shapes of secondary radiation in the frequency range of Rayleigh scattering and resonance fluorescence and in the range of Raman scattering and shifted resonance fluorescence are obtained on the basis of the quantum treatment of transformation of light pulses, the resonance conditions for Raman and Rayleigh scattering being considerably different. The characteristic cases of different pulse shapes of Raman and Rayleigh scattering are considered for the condition when the molecules are irradiated by light pulses which are shorter then the lifetime of the excited state of the molecule and are weak enough not to result in saturation.

DOI
10.1002/jrs.1250170125

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The Journal of Chemical Physics•Jun 15, 1986•5 citations
Abstract The expressions for the pulse shapes of secondary radiation in the frequency range of Rayleigh scattering and resonance fluorescence and in the range of Raman scattering and shifted resonance fluorescence are obtained on the basis of the quantum treatment of transformation of light pulses, the resonance conditions for Raman and Rayleigh scattering being considerably different. The characteristic cases of different pulse shapes of Raman and Rayleigh scattering are considered for the condition when the molecules are irradiated by light pulses which are shorter then the lifetime of the excited state of the molecule and are weak enough not to result in saturation.
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 Presupposing exponentially decaying states (with phenomenological lifetimes) of the particle system interacting with the radiation field, the shape and width of Raman lines is discussed on a quantum‐mechanical basis for the most important types of excitation: non‐resonance, pre‐resonance, rigorous resonance with a continuum level and with a discrete, non‐degenerate, and isolated level; monochromatic and non‐monochromatic irradiation. Attention is called to peculiar intensity distributions of the secondary radiation obtainable by sufficiently monochromatic excitation in near resonance to an isolated state (resonance fluorescence case) which deviate characteristically from those customary in traditional fluorescence and scattering spectra.
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.
The approximation of nonoverlapping lines is used to calculate spectra of resonance fluorescence and Raman scattering when two- and three-level atoms are pumped by a smooth pulse of duration comparable with the excited-state lifetime. The difference between the quasienergy terms, that determines the satellite frequency, depends on time and has the same value twice, at the pulse leading and trailing edges, so that interference may occur between the radiation produced in the appropriate parts of the pulse. However, the interference pattern is blurred since radiative broadening destroys the coherence. Relationships are obtained between the parameters for which interference may be observed. An analysis is made of the change to short pulses when allowance can be made for the scattered field using the first order of perturbation theory.
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.
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.