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Physical Review A

Relative intensities and time characteristics of Raman scattering and luminescence under nearly resonant light excitation

Takashi Kushida, Shuichi Kinoshita

Published Jun 1, 1990• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.41.6042

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Journal of the Physical Society of Japan•Aug 15, 1979•27 citations
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.
Time-resolved secondary-radiation spectra have been calculated for a three-level system coupled with a reservoir under pulsed-light excitation. It has been found that a dip is observed in the time profile of the secondary-radiation intensity near the resonance-excitation condition, when the spectral bandwidth of the detection system is increased. If the secondary radiation is divided into the Raman and luminescence components that are, respectively, due to the mean value and fluctuation of the photoinduced emission dipole, the dip is observed only in the former. A simple analysis reveals that this dip originates from the quantum interference between the resonant and nonresonant contributions to the Raman scattering.
The stochastic theory of intermediate state interaction developed in a preceding paper is applied to more realistic models to discuss the correlation between the incident and the scattered photons in more detail. Through these model calculations it is confirmed that the spectral characteristics of the second order optical process are determined by a few physical parameters of the radiative damping rate and the modulation amplitude and rate. In the slow modulation limit the relative intensity ratio between the broad Raman component and the luminescence is almost determined by the ratio between the radiative damping rate (γ b ) and the modulation rate (γ m ). In the fast modulation limit the ratio between the δ-shaped Raman component if it exists and the luminescence is given by the ratio between γ b and the dephasing relaxation rate Δ 2 /γ m ( Δ denotes the modulation amplitude.).
A general theory of transient light scattering is developed on the basis of our stochastic theory of intermediate state interaction. The transient behaviors of various components of the second order optical process under a pulsed irradiation are discussed and model calculations of the time-resolved emission spectra are performed. It is clarified that in the fast modulation limit the Raman component has a time constant determined by the phase memory time of the intermediate state while the time constant of the luminescence component is given by the radiative damping rate. The transient behaviors of the scattered light intensity are also discussed.
The perturbative density matrix formalism is used to study the time-dependent resonance Raman scattering (RRS) and resonance hot luminescence (RHL) components of the light-induced spontaneous emission process that has been called resonance secondary radiation (RSR). A three-level system coupled in a stochastic way to a bath is used to study the RSR emission driven by a coherent laser pulse with a variable Gaussian width in time. The spectral filter in a light detection system is explicitly included in the detection step of the problem. Observable time and frequency resolved RSR spectra are then calculated numerically. The spectral and temporal properties of the time-dependent RSR spectrum are very sensitive to the width of the driving pulse when the pulse width is of the same order of magnitude as the important system dephasing constants. In this domain the RRS contribution to the RSR spectrum weakens relative to the RHL as the light pulse is shortened. In the limit that the laser pulse becomes ‘‘delta function-like’’ the RSR spectrum consists essentially of RHL. When appropriate, the numerical results are compared to the stationary RSR problem as well as to the case where the RSR emission is driven by an exponential pulse. The analytical solutions to both of these cases are presented.
The effects of the finite correlation time of the external modulation on the secondary-emission spectra are clarified emphasizing the deviation from the motional narrowing limit or the impact approximation in the case of large off-resonance excitation. The dependences of the excitation spectrum of the secondary emission on the modulation parameters and on the inhomogeneous broadening are studied systematically. It is found that the excitation spectrum of the luminescence shows a faster decrease than that of the Raman scattering as the off-resonance frequency increases. The present theory is relevant for explaining the recent experiment by Watanabe, Kinoshita, and Kushida [Chem. Phys. Lett. 126, 197 (1986)] on the \ensuremath{\beta}-carotene in solutions. A general theory of the time-resolved spectra of the secondary emission is formulated to incorporate the effect of the finite correlation time. The luminescence component shows a slow temporal decay with the longitudinal relaxation rate. It is found for the first time that the difference is unexpectedly large between the transient behavior of the luminescence intensity and that of the intermediate-state population for the slow-modulation regime and that the difference indicates the effect of finite correlation time of the frequency modulation. On the other hand, the transient behavior of the Raman scattering contains a fast component that follows the envelope of the excitation-pulse intensity and the same slow component as the luminescence. The ratio of the slow component to the total intensity depends sensitively on the modulation parameters and the off-resonance frequency. The modulation parameters of the system in question can be estimated from these dependences in combination with the spectral characteristics of the emission under stationary excitation.
Competitive behavior of two channels of resonant Raman scattering and luminescence is discussed for the giant two-photon excitation of excitonic molecules in CuCl. The stochastic theory of intermediate state interaction is applied to describe the time-integrated and time-resolved emission spectra of the excitonic molecule excited resonantly by a short light pulse. Particularly as for the time-resolved spectrum, the frequency-time uncertainty due to the finite observation time is incorporated in the present theory. Our theory explains the observed characteristics of the emission spectra, and the relaxation constants of the excitonic molecule and the exciton in the final state are determined from comparison between the observed and calculated spectra.