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Optics and Spectroscopy

Spontaneous emission of an atom in the presence of an interface between two dielectrics

A. V. Kozlovskiĭ

Published Dec 1, 2001• 0 citations
Publisher

Abstract

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.

DOI
10.1134/1.1429702

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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.
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.
The spontaneous emission rate of two interacting excited atoms near a dielectric interface is studied using the photon closed-orbit theory and the dipole image method. The total emission rate of one atom during the emission process is calculated as a function of the distance between the atom and the interface. The results suggest that the spontaneous emission rate depends not only on the atomic-interface distances, but also on the orientation of the two atomic dipoles and the initial distance between the two atoms. The oscillation in the spontaneous emission rate is caused by the interference between the outgoing electromagnetic wave emitted from one atom and other waves arriving at this atom after traveling along various classical orbits. Each peak in the Fourier transformed spontaneous emission rate corresponds with one action of photon classical orbit.
The spontaneous emission rate of an atom in a dielectric system with a single interface is calculated using quantum electrodynamics and analyzed using ideas from closed-orbit theory. The spontaneous emission rate is shown to exhibit a damping oscillation as the atomic distance from the interface is varied. The calculated frequency of the oscillation matches very well with the prediction from closed-orbit theory. This study provides a different perspective on the spontaneous emission of atoms in the presence of environments.
We consider the spontaneous emission (SE) of radiation by an atom in a one-dimensional cavity which consists of two medium regions and a vacuum region between them. The medium regions are composed of a bulk dielectric material which has a continuous absorption spectrum. We quantize the electromagnetic field as well as the polarization fields of the material, and polaritons composed of infinite number of fields are obtained. Using the polariton solutions, we then study the SE for an atom in such an absorptive and inhomogeneous cavity. The SE rate is shown to depend strongly on the position of the atom, the length l of the vacuum region, and the complex refractive index \ensuremath{\eta}+i\ensuremath{\kappa}. It is found in particular that the position dependence of the SE rate disappears for some particular values of l, in either of the vacuum or medium region. We also find that unlike the three-dimensional case the SE rate in a homogeneous cavity depends on both \ensuremath{\eta} and \ensuremath{\kappa}. \textcopyright{} 1996 The American Physical Society.
Starting from a quantum Maxwell equation for the vector potential operator, we study the spontaneous emission properties of a two-level atom interacting with the electromagnetic field in a lossless and inhomogeneous dielectric structure and express the spontaneous emission rate, the external quantum efficiency, and the spontaneous emission factor in terms of the classical Green function of the dielectric structure. Comparing these results with the corresponding classical results, we show that the above quantities can be calculated from the radiation field of a classical dipole. Based on this correspondence, a numerical algorithm is developed to calculate the modification of spontaneous emission in microcavities. The line shape of the emission spectrum of the light source and the decay of the cavity resonant modes are automatically taken into account in this algorithm. The approximate expressions for the spontaneous emission rate and the spontaneous emission factor are discussed.