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Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences

Vacuum field fluctuations and spontaneous emission in a dielectric slab

Heidar Khosravi, R. Loudon

Published Feb 8, 1992• 77 citations
Publisher

Abstract

Abstract The electromagnetic field is quantized on the basis of the complete set of spatial modes of a plane dielectric slab of arbitrary thickness and refractive index but infinite transverse dimensions, located in otherwise empty three-dimensional space. The vacuum field fluctuations and spontaneous emission rates are evaluated as functions of position both inside and outside the slab. The source-field operator is derived for emission by atoms inside the slab, in the direction perpendicular to its surfaces. Particular attention is given to the possibility of suppressing spontaneous emission by placing atoms in, or close to, a dielectric slab.

DOI
10.1098/rspa.1992.0024

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Abstract The electromagnetic field is quantized on the basis of the complete set of spatial modes of a plane dielectric slab of arbitrary thickness and refractive index but infinite transverse dimensions, located in otherwise empty three-dimensional space. The vacuum field fluctuations and spontaneous emission rates are evaluated as functions of position both inside and outside the slab. The source-field operator is derived for emission by atoms inside the slab, in the direction perpendicular to its surfaces. Particular attention is given to the possibility of suppressing spontaneous emission by placing atoms in, or close to, a dielectric slab.
Abstract The electromagnetic field is quantized on the basis of the classical spatial modes of a system geometry in which half of space is filled by a dielectric of constant refractive index and the other half of space is empty. The vacuum field fluctuations and spontaneous emission rates are evaluated as functions of position and polarization both inside and outside the dielectric. Particular attention is given to the variations of these quantities in the vicinity of the interface. The source-field operator is derived for emission by atoms inside and outside the dielectric, in the direction perpendicular to the interface.
Spontaneous decay behavior from an assembly of atoms (or molecules) in a dielectric slab sandwiched by two dielectric semi-infinite spaces with arbitrary refractive indices is investigated. We introduce a lifetime distribution function to describe decay kinetics. The zero-point fluctuations of the electromagnetic field are calculated as a function of the position of atom in the slab. They display a symmetric profile with respect to the central plane of the slab in symmetric structure sample and the contributions of the guided modes and the radiation modes components both exhibit cosinelike variation with a base but with a phase difference of \ensuremath{\pi}. With the increase of the thickness of the slab, the oscillations become dense. In contrast, for the asymmetric structure case, the related curves are asymmetric with respect to the middle plane of slab and exhibit considerably distorted cosinelike oscillations. The dependence of the spontaneous emission rate of atoms on the thickness of the slab and the refractive indices of substrate also is surveyed. Our calculations show that quite wide or narrow lifetime distribution can occur for different thicknesses of the slab. The coexistence of both accelerated and inhibited decay processes appears. The calculated results are in good agreement with experimental results.
A complete set of cavity modes in planar dielectric multilayer structures is presented which naturally includes the guided modes. We show that most of these orthonormal fields can be derived from a coherent superposition of plane waves incident on the stack from the air and from the substrate. Using this set of cavity modes, we present a quantization scheme in idealized lossless stratified dielectric structures. This enables us to discuss the vacuum quantum fluctuations of the fields within the multilayer stack. The spontaneous emission of photons by a two-level atom located at any position inside the stratified planar structure is derived using the quantum approach and standard perturbation theory. The spontaneous emission rate as well as the radiation pattern in the air, in the substrate and in the guided mode are presented. Finally, a numerical analysis of the radiative properties of an erbium atom located in an asymmetrical Fabry - Perot multilayer structure is investigated. We show that a large part of the emitted power is directed in one half-space although a significant amount of light remains trapped in the guided modes of the structure.
The spontaneous emission of photons by an atom placed near the dielectric slab is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (traveling) and the modes trapped to a waveguide formed by the slab (trapped). To describe angular properties of spontaneous emission a parametrization of the traveling modes by the outgoing waves has been proposed. Angular characteristics of the traveling photon emission, distributions of the trapped photon emission, as well as global decay rates have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error in an earlier paper by Khosravi and Loudon [Proc. R. Soc. London Ser. A 436, 373 (1992)] affecting thin slabs and results near waveguide-mode thresholds has been improved.
The rate of spontaneous emission of an atom in the presence of an interface between two dielectrics was calculated using the quantum theory of electromagnetic radiation. Spatial distribution of the field for quasi-continuous spectrum inside an infinite cavity with ideally conducting walls was determined for multiple values of real refractive indices. Spontaneous emission in the continuous spectrum of the field was calculated using the known spatial Green’s function for a one-dimensional dielectric interface. The rate of spontaneous emission of an atom may either be higher or much lower than that in the free space, depending on the refractive indices and the distance between the atom and the interface between dielectrics.