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Physical Review A

Incident-photon energy-distribution effects on radiationless resonant Raman scattering

G. Bradley Armen, Honghong Wang

Published Feb 1, 1995• 51 citations
Publisher

Abstract

In the experimental observation of radiationless resonant Raman scattering, features that differ from the idealized case can arise when the spectral width of the incident photon distribution is comparable to the width of pertinent atomic energy levels. These features include nonlinear dispersion of the peak maxima and changes in the symmetry and width of the ejected-electron lines with changes in the average incident photon energy. Under certain conditions, the electron line shapes can become highly asymmetric or even double peaked. The origin of these features in actual experiments is explored through a model calculation for large spectral widths. Some possible applications of these effects are pointed out.

DOI
10.1103/physreva.51.1241

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In the experimental observation of radiationless resonant Raman scattering, features that differ from the idealized case can arise when the spectral width of the incident photon distribution is comparable to the width of pertinent atomic energy levels. These features include nonlinear dispersion of the peak maxima and changes in the symmetry and width of the ejected-electron lines with changes in the average incident photon energy. Under certain conditions, the electron line shapes can become highly asymmetric or even double peaked. The origin of these features in actual experiments is explored through a model calculation for large spectral widths. Some possible applications of these effects are pointed out.
A theory of resonant Raman scattering spectroscopy of one-dimensional electronic systems is developed on the assumptions that (i) the excitations of the one-dimensional electronic system are described by the Luttinger-liquid model, (ii) Raman processes involve virtual excitations from a filled valence band to an empty state of the one-dimensional electronic system, and (iii) excitonic interactions between the valence and conduction bands may be neglected. Closed form analytic expressions are obtained for the Raman scattering cross sections, and are evaluated analytically and numerically for scattering in the polarized channel, revealing a ``double-peak'' structure with the lower peak involving multispinon excitations with total spin S=0S=0S=0 and the higher peak being the conventional plasmon. A key feature of our results is a nontrivial power-law dependence, involving the Luttinger-liquid exponents, of the dependence of the Raman cross sections on the difference of the laser frequency from resonance. We find that near resonance the calculated ratio of intensity in the lower energy feature to the intensity in the higher energy feature saturates at a value of the order of unity (times a factor of the ratio of the velocities of the two modes). We explicate the differences between the ``Luttinger-liquid'' and ``Fermi-liquid'' calculations of resonant Raman spectroscopy (RRS) spectra and argue that excitonic effects, neglected in all treatments so far, are essential for explaining the intensity ratios observed in quantum wires. We also discuss other Luttinger-liquid features which may be observed in future RRS experiments.
We solve for the electronic Raman scattering response functions on an infinite-dimensional hypercubic lattice employing dynamical mean-field theory. This contribution extends previous work on the nonresonant response to include the mixed and resonant contributions. We focus our attention on the infinite-dimensional spinless Falicov-Kimball model, where the problem can be solved exactly, and the system can be tuned to go through a Mott-Hubbard-like metal-insulator transition. Resonant effects vary in different scattering geometries, corresponding to the symmetries of the charge excitations scattered by the light. We do find that the Raman response is large near the double resonance, where the transfered frequency is close to the incident photon frequency. We also find a joint resonance of both the charge-transfer peak and the low-energy peak when the incident photon frequency is on the order of the interaction strength. In general, the resonance effects can create order of magnitude (or more) enhancements of features in the nonresonant response, especially when the incident photon frequency is somewhat larger than the frequency of the nonresonant feature. Finally, we find that the resonant effects also exhibit isosbestic behavior, even in the A1g{A}_{1\mathrm{g}}A1g​ and B2g{B}_{2\mathrm{g}}B2g​ sectors, and it is most prominent when the incident photon frequency is on the order of the interaction energy.
It is shown that the average energy of the emitted photons does not coincide with the average energy of the incident photons in the process of resonant photon scattering on an atom. This happens because of the asymmetry of the natural line profile caused by the nonresonant corrections and by the dependence of the transition rates on the frequency. In the case of the Lyman-α transition in hydrogen, . The effect can be much larger if ‘artificial’ asymmetry of the intensity distribution in the photon source with respect to the resonance frequency takes place. In the latter case, the difference is close to the accuracy of the recent experiments on the Lyman-α frequency measurements.
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 effects of different laser line shapes on the intensity and spectrum of resonance fluorescence from a two-level atom are investigated. The laser model considered is that of an ideal single-mode laser operating high above threshold, with constant amplitude and undergoing phase-frequency fluctuations analogous to Brownian motion. As the correlation time of the frequency fluctuations increases from zero to infinity, the laser line shape changes from Lorentzian to Gaussian in a continuous way. It is shown that for intermediate and strong fields, the average intensity of fluorescence in the case of a resonant broadband Lorentzian line shape is higher than that in the case of a Gaussian line shape with the same bandwidth and total power. This is in contrast to the weak-field case where the higher peak power of the Gaussian line shape makes it more effective than the Lorentzian line shape. It is also shown that in the case of a nonzero frequency correlation time (non-Lorentzian line shape) the intensity of fluorescence undergoes non-Markovian fluctuations. In relation to the spectrum of resonance fluorescence, it is shown that as the line shape is varied from Lorentzian to Gaussian the following changes take place: In the case of off-resonance excitation, the asymmetry of the spectrum decreases. In the case of resonant excitation, the center-peak to side-peak height ratio for the triplet structure increases. Moreover, the recently predicted center-line dip, which develops in the spectrum in the case of broadband excitation when the Rabi frequency and the bandwidth are nearly equal, becomes increasingly deeper.
In the presence of coherent saturated near-resonant two-photon excitation, the ordinary Raman scattering line is replaced by a dynamic Stark shifted or Stark split doublet, and Rabi nutations appear in the time-resolved ordinary Raman spectrum. The relative intensity of the peaks of the doublet depends on the shape and on the average frequency of the exciting pulse. Striking new features arise from the interfering contributions of the upper and lower states of the two-photon transition to the Raman scattering process. The theory is applied to Raman scattering in atomic Na in the presence of the 3 2 S 1 2/(F=1, M F =1) to 4 2 D 3 2,5/2/(F=3,M F =3) two-photon resonances.