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Physical Review Letters

Spontaneous emission in absorbing dielectric media

Stephen Mark Barnett, B. Hüttner, R. Loudon

Published Jun 22, 1992• 216 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.68.3698

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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.
We present calculations of the rates of decay of an excited atom embedded in an absorbing dielectric. Decay can occur by spontaneous emission into transverse radiative modes of the electromagnetic field and by Joule heating via longitudinal coupling of the atom to the dielectric. The spontaneous emission (transverse) decay rate is modified in a dielectric, being the free-space rate multiplied by the real part of the refractive index at the transition frequency of the atom. There is a further modification due to the difference between the macroscopic dielectric field and the local field at the position of the atom. In addition there is a longitudinal decay rate which is proportional to the imaginary part of the dielectric constant and therefore vanishes in non-absorbing media. We derive expressions for each of these rates of decay and discuss the physical mechanisms leading to them.
We consider the spontaneous emission in an absorbing medium by calculating the quantum flow of energy from an emitting atom. For this purpose, we extend the analysis by Power and Thirunamachandran of quantized Maxwell fields in the vicinity of an atom in the free space to a situation where the emitter is in a dielectric medium. We represent the quantum flow in terms of the non-equal time commutators involving electric and magnetic fields, as well as the local displacement field. The commutators are calculated applying a previously developed microscopic theory of quantization of radiation in dielectrics. Consequently, we derive from first principles the rate of spontaneous emission in an absorbing medium containing local field factors and other refractive contributions. The results support the previous introduction of the (virtual cavity) local field correction by Barnett et al on a phenomenological basis, as well as our previous approach in which the spontaneous emission is considered as a resonance energy transfer to the far-zone atoms. A distinctive feature of the present formalism is that it deals with the spontaneous emission directly by calculating the quantum flow from the emitting atom. Therefore, the method is free from divergences appearing in other approaches analysing the spontaneous decay in absorbing media.
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 present a simple theory on the effect of optical dephasing on the spontaneous emission (SE) rate in a microcavity containing (absorbing) dispersive dielectric media based on a photon Green's-function formalism in which the reservoir damping of medium polarizations is included in a phenomenological way. The theory yields the well-known result that the SE rate in free space is modified by the real part of the refractive index at the transition frequency of an atom in a bulk dielectric. On the other hand, it turns out that the degree of the alteration of the SE rate in a high-Q microcavity with dispersive media is affected not only by the real part of the refractive index but also by the imaginary part of the refractive index that is associated with the dephasing of the photon field due to the reservoir damping, i.e., the destruction of self-interference of the photon field.
The lifetime of an excited atom near an absorbing dielectric surface is calculated from an exact solution of a microscopic Hamiltonian model, which includes the effects of dispersion, local-field correction, and near-field Coulomb interaction. Results for the total decay rate are shown to be in excellent agreement with those based on classical electromagnetic theory and to yield the well-known result for the rate of nonradiative energy transfer in the limit of very small distance from the surface. \textcopyright{} 1996 The American Physical Society.