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Bulletin of the American Physical Society

Spontaneous emission in dielectrics

Peter W. Milonni

Published May 1, 1993• 0 citations
OpenAlex

Abstract

The theory of spontaneous emission in dielectric media is extended to take proper account of dispersion and local field corrections. For the case of spontaneous emission in a plasma or radiative electron-hole recombination in a semiconductor, there are effectively no local field corrections. A shift of emission lines due to a dispersive host medium is predicted and interpreted. The corrections to spontaneous and stimulated emission due to dielectric interfaces in microcavity lasers are discussed.

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The theory of spontaneous emission in dielectric media is extended to take proper account of dispersion and local field corrections. For the case of spontaneous emission in a plasma or radiative electron-hole recombination in a semiconductor, there are effectively no local field corrections. A shift of emission lines due to a dispersive host medium is predicted and interpreted. The corrections to spontaneous and stimulated emission due to dielectric interfaces in microcavity lasers are discussed.
In this work the electromagnetic field in a dielectric medium is quantized in a simple and straightforward way based on the classical expression for the energy density for the case of weak absorption. The quantized field leads to expressions for spontaneous and stimulated emission rates, and gain and absorption coefficients, for the general case of a dispersive dielectric host medium. Local field corrections, when they apply, arise in the same manner as in classical electromagnetic theory. The theory also leads to a radiative level shift dependent on the dispersion of the dielectric, and this shift may be interpreted as a van der Waals interaction between the guest atom and the atoms of the host medium.>
We present a general, semimicroscopic, self-consistent treatment of spontaneous emission for a two-level atom in a dielectric microcavity with arbitrary shape. Both lossless and absorbing media are considered. Our approach is based on linear-response theory and the coupled-dipole method. We illustrate our method on spherical and cubic cavities. We discuss the Purcell effect, the frequency shift, the local-field effect, and the dipole-dipole coupling experienced by a source placed in a microcavity.
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.
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.
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.