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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum theory of Cherenkov radiation in an anisotropic absorbing media

Wei Li, Chengxin Yu, Shibing Liu

Published Oct 2, 2009• 2 citations
Publisher

Abstract

A fully quantum mechanical treatment is presented for the Cherenkov radiation stimulated by a uniformly moving charge particle in both isotopic medium and anisotropic medium. The relation between Cherenkov radiation intensity and dielectric tensor is analyzed, and the result is compared with previous work.
DOI
10.1117/12.847455

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Cherenkov radiation is one of the problems in light- matter interaction that can be opened new ideas in quantum electrodynamic. A quantum mechanic approach is presented for Cherenkov radiation of a moving atom in uniaxial and biaxial anisotropic medium. A moving particle in a medium emits Cherenkov radiation when its speed be larger than the phase velocity of light in the medium. The electromagnetic field is quantized in the anisotropic media, using maxwell and related constitute equations, phenomenologically. The Cherenkov radiation for an moving charged particle in the anisotropic medium with arbitrary real permittivity tensor is obtained. The dielectric structure can be changed the Cherenkov radiation. For uniaxial media, we give a close form of the Cherenkov radiation for arbitrary dipole alignment. In this manner, the Cherenkove radiation of the biaxial media is calculated.. It is shown the Cherenkov radiation in an isotropic medium can be obtained from the form of an anisotropic medium.
There are both loss and dispersion characteristics for most dielectric media. In quantum theory the loss in medium is generally described by Langevin force in the Langevin noise (LN) scheme by which the quantization of the radiation field in various homogeneous absorbing dielectrics can be successfully actualized. However, it is invalid for the anisotropic dispersion medium. This paper extends the LN theory to an anisotropic dispersion medium and presented the quantization of the radiation field as well as the transformation relation between the homogeneous and anisotropic dispersion media.
The macroscopic electromagnetic field is quantized in the presence of a uniformly moving permeable dielectric medium. We begin with the Maxwell-Minkowski equations, and the fields are quantized with the help of the Green function scheme. It is shown that for a homogeneous material, though the medium is assumed to be isotropic in its rest frame, it displays anisotropic character for the observer who detects the field observables in the laboratory frame. The field operators are expressed in terms of two independent infinite sets of bosonic field operators. Special attention is paid to the vacuum field fluctuation in moving media.
Quantization of the phenomenological Maxwell theory of the electromagnetic field in dispersive and absorbing dielectrics has been of increasing interest over the last years since it allows for a consistent formulation of quantum optics in the presence of dielectric bodies. We show, using a Dyson-type integral representation of the Green tensor, that the quantization scheme is consistent with QED for both isotropic and anisotropic media and therefore applies to arbitrary linear Kramers-Kronig media including amplifying media.
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 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.