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Physical Review A

Redistribution of scattered light in resonant electronic Raman scattering from localized scattering centers

David L. Huber

Published Dec 1, 1984• 1 citation
Publisher

Abstract

An analysis is presented of the redistribution of scattered light in resonant electronic Raman scattering from localized scattering centers. Results are obtained for the integrated cross sections characterizing the coherently scattered and the redistributed radiation. A statistical $S$-matrix theory is outlined which relates the cross section for the redistributed radiation to the coherent-scattering cross section. For the theory to be applicable it is necessary that the absorption lines from the various initial and final states to the resonant intermediate state have identical shapes. The conditions for this to occur are discussed.

DOI
10.1103/physreva.30.3033

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An analysis is presented of the redistribution of scattered light in resonant electronic Raman scattering from localized scattering centers. Results are obtained for the integrated cross sections characterizing the coherently scattered and the redistributed radiation. A statistical SSS-matrix theory is outlined which relates the cross section for the redistributed radiation to the coherent-scattering cross section. For the theory to be applicable it is necessary that the absorption lines from the various initial and final states to the resonant intermediate state have identical shapes. The conditions for this to occur are discussed.
We outline a statistical model for the cross section characterizing the integrated intensity of the redistributed radiation resonantly scattered from a localized scattering center coupled to a thermal bath. The theory exploits a formal analogy between the resonant scattering of light and nuclear scattering in the compound-nucleus regime. Using statistical models developed for the nuclear problem, we express the cross sections describing the quasielastic scattering and the redistributed Raman scattering in terms of parameters which can be extracted from measurements of the coherent-scattering cross sections.
We have calculated the cross section for Raman scattering of light from a hydrogenic atom, for a wide range of photon energies. The calculation assumes the photon encounters the atom in its ground state and excites it to the 2s2s2s state. Since various contributions to the matrix element may be isolated in the computation, the calculation allows one to obtain a notion of the relative importance of various classes of intermediate states in a given frequency range. We also point out that the Raman efficiency SSS may be expressed in terms of the derivative of the electronic polarizability tensor with respect to a parameter that measures the degree of excitation of the atom. Thus, the formal expression for SSS assumes an appearance identical to the expression encountered in the phenomenological theory of the first-order Raman effect in solids.
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.
The theory of resonant Raman scattering in the presence of intense incident and scattered light waves has been developed, using the quantum-mechanical master-equation approach. When the optical matrix elements between the resonant intermediate state and the initial and final states of the atomic system are larger than the relevant relaxation frequencies, it is shown that instead of the usual power broadening and shift of the Stokes or anti-Stokes line, each line can split into as many as five or seven lines, depending upon whether both the fields are exactly at resonance or otherwise.