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Optics Letters

Local-field correction for an interstitial impurity in a crystal

Adel Rahmani, Patrick C. Chaumet, Garnett W. Bryant

Published Mar 15, 2002• 16 citations
Publisher

Abstract

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.

DOI
10.1364/ol.27.000430

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 3, 2005•1 citation
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.
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.
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.
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.
This chapter presents simple theoretical models which take into account the effect of dephasing of the vacuum fields on the spontaneous emission in a microcavity. This would be necessary to evaluate the limit of the capability of microcavity-based solid-state optical devices. The dephasing of the quantized fields, i.e., the vacuum fields, which is our main concern, results from the energy exchange between fields and medium polarizations interacting with phonon reservoirs, that is, from the dispersion. A symmetric structure of the system allows us to use the one-way time-evolution of field b, in order to obtain a motion equation of the field, which is in general derived from a round-trip time-evolution of the field. The alteration of the spontaneous emission in a microcavity can be viewed as a manifestation of the self-interference of the quantized fields, which are vacuum fields.
The spontaneous emission rate (SER) of a single impurity molecule for the electric dipole transition has been found in the case where the birefringence of a host crystal is taken into account. SER depends on the orientation of the dipole moment with respect to the principal axes of the dielectric (permittivity) tensor of the host crystal and on the principal refractive indices of the crystal. We use the model where the average electromagnetic field in the crystal is classical and effective electric field vectors at the site of the impurity molecule are found for the interstitial impurity which is located in the center of the crystal cell. The results of calculations for seven biaxial host crystals (anthracene, chrysene, diphenyl, fluorine, naphthalene, phenanthrene, terphenyl) are presented. It is shown that values of SER form in the space a three- axial ellipsoid. Differences in the values of SER for the electric dipole transition in the same host crystal are up to 34%.