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Journal of Modern Optics

Field Quantization and Radiative Processes in Dispersive Dielectric Media

Peter W. Milonni

Published Oct 1, 1995• 144 citations
Publisher

Abstract

The electromagnetic field in a dispersive dielectric medium is quantized in a straightforward manner based on the classical expression for the field energy away from absorption resonances. Results for spontaneous and stimulated radiative rates, and absorption and gain coefficients, are obtained and compared with other expressions in the literature. Local field corrections, when they exist, are included. A level shift for an atom in a host dielectric medium is obtained and interpreted as the van der Waals interaction between that atom and its neighbours in the host medium.

DOI
10.1080/09500349514551741

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The electromagnetic field in a dispersive dielectric medium is quantized in a straightforward manner based on the classical expression for the field energy away from absorption resonances. Results for spontaneous and stimulated radiative rates, and absorption and gain coefficients, are obtained and compared with other expressions in the literature. Local field corrections, when they exist, are included. A level shift for an atom in a host dielectric medium is obtained and interpreted as the van der Waals interaction between that atom and its neighbours in the host medium.
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After giving an outline of the quantization scheme based on the microscopic Hopfield model of a dielectric bulk material, we show how the classical phenomenological Maxwell equations of the electromagnetic field in the presence of dielectric matter of given space- and frequency-dependent complex permittivity can be transferred to quantum theory. Including in the theory the interaction of the medium-assisted field with atomic systems, we present both the minimal-coupling Hamiltonian and the multipolar-coupling Hamiltonian in the Coulomb gauge. To illustrate the concept, we discuss the input--output relations of radiation and the transformation of radiation-field quantum states at absorbing four-port devices, and the spontaneous decay of an excited atom near the surface of an absorbing body and in a spherical micro-cavity with intrinsic material losses. Finally, we give an extension of the quantization scheme to other media such as amplifying media, magnetic media, and nonlinear media.
The problem of quantizing the radiation field inside a nonlinear dielectric is studied. Based on the quantization of radiation in a linear dielectric which includes absorption and dispersion, we extend the theory in order to treat also nonlinear optical processes. We derive propagation equations in space and time for the quantized radiation field including the effects of linear absorption and dispersion as well as nonlinear optical effects. As a special case we derive the propagation equation of a narrow-frequency band light pulse in a Kerr medium.
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.