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Physical Review Letters

Resonant Scattering and Spontaneous Emission in Dielectrics: Microscopic Derivation of Local-Field Effects

Pedro de Vries, Ad Lagendijk

Published Aug 17, 1998• 105 citations
Publisher

Abstract

Resonant classical light scattering by impurity atoms inside dielectric cubic lattices is investigated in the point-dipole limit. Modifications to resonance frequencies and linewidths are shown to be different for substitutional and interstitial impurities. Spontaneous emission rates inside dielectrics exhibit the well-known empty-cavity and Lorentz local-field factors for substitutional and interstitial atoms, respectively. The results are generalized to disordered dielectrics, indicating that the substitutional case occurs prevalently for impurity atoms.

DOI
10.1103/physrevlett.81.1381

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Resonant classical light scattering by impurity atoms inside dielectric cubic lattices is investigated in the point-dipole limit. Modifications to resonance frequencies and linewidths are shown to be different for substitutional and interstitial impurities. Spontaneous emission rates inside dielectrics exhibit the well-known empty-cavity and Lorentz local-field factors for substitutional and interstitial atoms, respectively. The results are generalized to disordered dielectrics, indicating that the substitutional case occurs prevalently for impurity atoms.
Spontaneous emission and Lamb shift of atoms in absorbing dielectrics and dense atomic gases are discussed using a microscopic Green's-function approach. Uncorrelated and random atomic positions are assumed, and the associated unphysical interactions between different atoms at the same location are eliminated (local field correction). For the case of an atom in a purely dispersive medium, the spontaneous-emission rate is altered by the well-known Lorentz local-field factor. When the mean distance between atoms becomes less than the resonance wavelength, results different from previously suggested expressions are found. In particular, it is shown that nearest-neighbor interactions become important. The results suggest that, for large densities, absorbing disordered dielectrics cannot accurately be described by a macroscopic approach that neglects correlations between atomic positions.
We have calculated the effect of material absorption on the rate of spontaneous emission by an embedded atom using a macroscopic Green-function approach and a microscopic Hamiltonian method that includes reservoir damping. When local field effects are neglected, the free-space emission rate is modified by the real part of the refractive index at the transition frequency of the embedded atom. Local field effects are introduced via a local field correction factor. This modification of the spontaneous emission rate generalizes a well-known result for transparent media and is of crucial importance in assessing the degree of inhibition of spontaneous emission for frequencies close to the resonances of the dielectric.
The local-field correction experienced by an interstitial impurity in a crystal with cubic symmetry is derived by use of a rigorous, self-consistent, semimicroscopic description of spontaneous emission in a microcavity. We compute the local-field factor for various positions of the impurity inside the crystal. Furthermore, we demonstrate that the local-field factor can be computed from a simple electrostatic model as a rapidly converging lattice sum. We show that the agreement between the predictions of this simple model and the rigorous calculations is remarkable, opening the way to a simple, general theory of a local-field effect for an impurity in a crystal with arbitrary symmetry.
The recent first-principles derivation of Langevin-Bloch equations of motion for near-resonant atoms embedded in a linear dielectric host leads to a clear, direct physical reinterpretation of fundamental physical principles as applied to one of the most basic problems of quantum mechanics: the renormalization of the spontaneous emission rate of an atom in a dielectric host. Here we show the role of the Lorentz local field, the fluctuation-dissipation theorem, the wave number and wave vector, the density of states, Fermi's golden rule, the electromagnetic energy density, canonical quantization, and the classical constitutive relations in this context.