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Physical review. B, Solid state

Distinction between resonance Raman scattering and hot luminescence

Y. R. Shen

Published Jan 15, 1974• 242 citations
Publisher

Abstract

Using density-matrix formalism which takes into account relaxation more correctly, we show that resonance Raman scattering and hot luminescence are two distinct physical processes, although they are always simultaneously present and can interfere with each other. The transient response of the two processes are, however, different.
DOI
10.1103/physrevb.9.622

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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.
Two complementary pictures for the resonance Raman scattering are presented, corresponding to two different ways of decomposing the four-time correlation function of dipole moment for this second-order process into a pair of two-time correlation functions. One is to take the auto-correlation of polarizability following the semi-classical picture for Raman scattering and expand it in powers of intra-system coupling; how the Raman spectra of higher orders approach the so-called luminescence is shown in the weak and strong coupling limits. Another is to study the correlation between absorption and emission processes; one can see how the relaxation of the strong coupled system after photoexcitation is reflected in the time-resolved emission spectra.
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.
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.
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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.