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Journal de physique

Resonant Raman scattering versus luminescence

S. Abraham-Ibrahim, B. Caroli, C. Caroli, Bernard Roulet

Published Jan 1, 1981• 2 citations
Publisher

Abstract

We study the competition, in the light scattering spectrum, between electronic resonant Raman scattering and luminescence, on a simple three-level model due to Takagahara et al., where electrons are assumed to couple, in the intermediate state, with a field of localized « phonons ». The model can be solved exactly. We show that the relative weight of Raman versus luminescence peaks is controlled by a single memory parameter γb /Γ — where γb and Γ are the damping rates of the intermediate electronic state and of the phonons. If γb/Γ >> 1, memory is quasi-perfect, and the spectrum is purely Raman; in the opposite limit luminescence predominates. For γb/Γ ∼ 1, both structures are present, as well as anomalous satellites characteristic of « hot » luminescence.

DOI
10.1051/jphys:019810042080113700

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We study the competition, in the light scattering spectrum, between electronic resonant Raman scattering and luminescence, on a simple three-level model due to Takagahara et al., where electrons are assumed to couple, in the intermediate state, with a field of localized « phonons ». The model can be solved exactly. We show that the relative weight of Raman versus luminescence peaks is controlled by a single memory parameter γb /Γ — where γb and Γ are the damping rates of the intermediate electronic state and of the phonons. If γb/Γ >> 1, memory is quasi-perfect, and the spectrum is purely Raman; in the opposite limit luminescence predominates. For γb/Γ ∼ 1, both structures are present, as well as anomalous satellites characteristic of « hot » luminescence.
Time dependent description of resonance Raman scattering is performed for a general system, by a density matrix reformulation of damping theory originally used for resonance fluorescence of atom. Radiative damping in the intermediate states can be described in terms of "damping operator" in realistic situations. In large ergodic systems, the scattering reduces to luminescence if the relaxation time within the excited states is much shorter than the radiative lifetime. In a typical case, time resolved emission spectra consist of various stages (i) scattering complex where absorption and emission are inseparable, (ii) dynamical and then (iii) kinetic relaxations giving rise to the hot luminescence, which finally converges to (iv) the ordinary luminescence from relaxed excited states. Hot luminescence does not appear within a motionally narrowed line. The interpretation of spectra depends also on the method of observation.
A general formula of the time-resolved optical spectrum for transient resonant light scattering is derived systematically by means of the operator algebra within the formalism of nonequilibrium thermo field dynamics (NETFD). The formula is applied to an analytically solvable model of the localized electron and phonon system, i.e., second-order light scattering due to the optically active three electronic states whose intermediate state is dynamically modulated by the phonon interaction mode. The derivation of the analytical expression for a four-point function, needed to obtain the spectrum, is performed with the help of the algebraic manipulations in NETFD, which showed the advantage of its methodology with respect to nonequilibrium transient phenomena. The three-dimensional profiles of the Raman and luminescence components in the time-resolved spectrum in the model are presented to show how the stochastic character comes out in the fast modulation limit, and how the dynamical behavior of the phonon system causing the modulation of the intermediate electronic state comes out in the slow modulation limit.
Various characteristics of frequency-integrated intensities of secondary radiation components near the resonance excitation region have been calculated for a three-level system coupled with a reservoir using a stochastic model. It has been found that the spectral and temporal characteristics of the resonant second-order optical processes can be understood consistently by considering that Raman scattering results from the average value of the induced-dipole moment with respect to the energy fluctuation due to the system-reservoir interaction, while luminescence results from its deviation from the average value. A simple method to determine parameter values that characterize the excited-state dynamics in condensed phases from the secondary radiation data is also discussed.
Resonance Raman scattering and luminescence under an intense excitation field are studied for both stationary and transient excitation regimes. By means of the Green function theory of resonance Raman scattering and luminescence we explain the characteristic features of the recent experiments on two-photon resonance Raman scattering via excitonic molecule in CuCl where the resonance dip and the asymmetry of the Raman yield around the resonance were observed. We ascribe the origin of the resonance dip of the Raman yield to the resonance enhancement of collisional damping of excitonic molecule and exciton states. The asymmetry of the Raman yield can be naturally understood in terms of the frequency and wave-vector dependent relaxation constants. Furthermore an approach is proposed which incorporates the coherence and correlation among excitonic molecules and excitons in their non-equilibrium state and clarifies their effects on the optical spectra.
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.