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Physical Review A

Spontaneous emission in a nonhomogeneous medium: Definition of an effective polarizability

André Reid, Michel Piché

Published Jul 1, 1992• 6 citations
Publisher

Abstract

The definition of an effective polarizability associated with a dipole transition is shown to result from the use of a dyadic Green's function in solving the electron equation of motion obtained from a classical model of spontaneous emission that takes into account the presence of nonhomogeneities in the electric permittivity. This polarizability provides access to the line shape associated with the transition; it also provides a generalized procedure for studying the effects of changes in the electromagnetic environment on line shapes, frequency shifts, and transition rates.

DOI
10.1103/physreva.46.436

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Considerations of a classical model for spontaneous emission in a nonhomogeneous medium

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The definition of an effective polarizability associated with a dipole transition is shown to result from the use of a dyadic Green's function in solving the electron equation of motion obtained from a classical model of spontaneous emission that takes into account the presence of nonhomogeneities in the electric permittivity. This polarizability provides access to the line shape associated with the transition; it also provides a generalized procedure for studying the effects of changes in the electromagnetic environment on line shapes, frequency shifts, and transition rates.
The spontaneous emission (SE) of the excited atoms in a two-dimensional (2D) arbitrary inhomogeneous environment has been systematically studied. The local density of states, which determines the radiation dynamics of a point source (for 3D) or a line source (for 2D), in particular, the SE rate, is represented by the electric dyadic Green's function. The numerical solution of the electric Green's tensor has been accurately obtained with the finite-difference frequency-domain method with the proper approximations of the monopole and dipole sources. The SE of atoms in photonic crystal and plasmonic metal plates has been comprehensively and comparatively investigated. For both the photonic crystal and plasmonic plates systems, the SEs depend on their respective dispersion relations and could be modified by the finite-structure or finite-size effects. This work is important for SE engineering and the optimized design of optoelectronic devices.
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.
A model for spontaneous emission in active dielectric microstructures is given in terms of the classical electric field Green's tensor and the quantum-mechanical operators for the generating currents. A formalism is given for calculating the Green's tensor, which does not rely on the existence of a complete power orthogonal set of electromagnetic modes, and the formalism may therefore be applied to microstructures with gain and/or absorption. The Green's tensor is calculated for an optical fiber amplifier, and the spontaneous emission in fiber amplifiers is studied with respect to the position, transition frequency, and vector orientation of a spatially localized current source. Radiation patterns are studied using a Poynting vector approach taking into account amplification or absorption from an active medium in the fiber.
Abstract “Spontaneous emission of radiation” calculates the rate of spontaneous electric-dipole emission of a photon by an excited atom or molecule. The calculation proceeds by using basic quantum mechanics (i.e. not using the short cuts of Chapter 19); it uses quantum electrodynamics but is not, on that account, particularly difficult. A 2p–1s transition in hydrogen is used as exemplar; the radiation is elliptically polarized. The spectral line profile (lineshape function) is approximately Lorentzian, but has a high-frequency cut-off, needed to prevent the power radiated from diverging. A radiation-induced frequency shift is negligible. The width of the line profile agrees with the Einstein A-coefficient. A high-frequency cut-off is shown to apply similarly in the derivation of Golden Rule Number Two.
We present a formalism for studying the influence of dispersive and absorbing dielectric bodies on a radiating atom in the framework of quantization of the phenomenological Maxwell equations for given complex permittivities of the bodies. In Markov approximation, the rate of spontaneous decay and the line shift associated with it can then be related to the complex permittivities and geometries of the bodies via the dyadic Green function of the classical boundary value problem of electrodynamics -- a result which is in agreement with second-order calculations for microscopic model systems. The theory is applied to an atom near a planar interface as well as to an atom in a spherical cavity. The latter, also known as the real-cavity model for spontaneous decay of an excited atom embedded in a dielectric, is compared with the virtual-cavity model. Connections with other approaches are mentioned and the results are compared.