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Physical review. B, Condensed matter

Resonance optical response of small dielectric clusters

Joel I. Gersten, Abraham Nitzan

Published Apr 1, 1984• 13 citations
Publisher

Abstract

The optical response of small clusters made of two-level molecules is investigated with particular emphasis on the near-resonance region. It is seen that the dielectric-function concept is still useful for describing first-order properties such as particle polarizability and particle-absorption profile; however, near resonance the dielectric response is strongly affected by dephasing and by the energy-level shifts resulting from clustering of molecules in space. Finite-size effects on the dielectric response are also more pronounced near resonance. Second-order response (light scattering) cannot be described by the dielectric function if dephasing processes are important (as they usually are near resonance) and different response functions must be used for different observables. For a cluster of $N$ molecules the light-scattering cross section is made of two contributions: a coherent part (proportional to ${N}^{2}$) which may be described by the dielectric-function concept and an incoherent part (proportional to $N$). Implications for surface effects on the optical properties of molecules adsorbed on such clusters are considered.

DOI
10.1103/physrevb.29.3852

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The optical response of small clusters made of two-level molecules is investigated with particular emphasis on the near-resonance region. It is seen that the dielectric-function concept is still useful for describing first-order properties such as particle polarizability and particle-absorption profile; however, near resonance the dielectric response is strongly affected by dephasing and by the energy-level shifts resulting from clustering of molecules in space. Finite-size effects on the dielectric response are also more pronounced near resonance. Second-order response (light scattering) cannot be described by the dielectric function if dephasing processes are important (as they usually are near resonance) and different response functions must be used for different observables. For a cluster of NNN molecules the light-scattering cross section is made of two contributions: a coherent part (proportional to N2{N}^{2}N2) which may be described by the dielectric-function concept and an incoherent part (proportional to NNN). Implications for surface effects on the optical properties of molecules adsorbed on such clusters are considered.
The authors present a weak light field, scattering theoretical description of the intensity autocorrelation function for the scattered light from a many-atom (molecule) system. The theory considers both resonant and near-resonant scattering for atoms with many sublevels in both the ground and electronically excited states, and it incorporates the effects of the finite coherence time of the incident radiation. The theory is derived using incident two-photon wave packets with spatial dispersion among the target atoms. Purely anti-bunching contributions arise from single-atom-two-photon scattering and from successive two-atom-two-photon scattering events. However, there are interleaved two-atom-two-photon scattering processes which provide purely bunching contributions since both atoms may be scattering at the same time. Path length differences in the successive two-atom scatterings can also induce some bunching character to the correlation function. The dependence of the risetime and decay of the intensity correlation function upon the atomic excited state lifetimes and the coherence time of the incident light emphasises the correlation between photons which have been coherently and/or incoherently scattered.
We investigate the effect of a linear host medium on the dynamics of a dense collection of resonant atoms. We find that near dipole-dipole interaction is enhanced by the presence of the host dielectric, resulting in a lower threshold density and a greater hysteresis area for intrinsic optical bistability. Cooperative decay terms appear that represent the interaction of near dipoles mediated by the absorptive component of the dielectric function of the host medium. These terms are part of the local response and correspond to local cooperative decay effects. \textcopyright{} 1996 The American Physical Society.
Existing theories of level crossing and modulation effects in the light scattered from optically thin vapours are restricted to cases where the light from different atoms is either completely incoherent (lateral scattering) or completely coherent (forward scattering). In the latter case the resonances are Doppler broadened equivalents of the well known Lorentzian forms predicted for lateral scattering. The more general case of partial coherence of the scattered light, which might be expected at small scattering angles, has not previously been considered. In this paper the degree of coherence of the scattered light has been formulated in terms of an autocorrelation function. For scattering from an ideal gas the autocorrelation function may be split into two terms representing complete incoherence and complete coherence. The predicted resonances for scattering into an arbitrary direction are mixtures of the Lorentzian and Doppler broadened forms, but the latter have a strong angular dependence that effectively restricted their observation to the small angular range associated with diffraction from the active volume of the vapour.
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.
We study the nonlinear optical response of molecular assemblies consisting of coupled two-level molecules with arbitrary geometry including inhomogeneous broadening and exciton dephasing. An analytical expression for the third-order optical susceptibility is derived based on a certain closure of the equation-of-motion hierarchy. An exact expression for the third-order response of small crystalline aggregates with exciton population relaxation is derived, and used to show that for low relaxation rate \ensuremath{\Gamma} the cooperative part of the nonlinear response scales as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}1/2}$ in d=1, and up to logarithmic corrections, as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}1}$ in d=2 and 3. We show that cooperative enhancement is caused by exciton scattering. This is to be contrasted to other cooperative effects such as superradiance, which are related to the size of molecular coherence domains and therefore scale as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}\mathit{d}/2}$. In a numerical study for dipole-dipole interactions in d=1, 2, and 3 dimensions we find that the local-field approximation is valid only in selected cases, and in general fails to reproduce the magnitude and the resonance structure of ${\mathrm{\ensuremath{\chi}}}^{(3)}$.