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Journal of Physics B Atomic Molecular and Optical Physics

A canonical approach to electromagnetic field quantization in a nonhomogeneous and anisotropic magnetodielectric medium

Fardin Kheirandish, Majid Amooshahi, Morteza Soltani

Published Mar 20, 2009• 16 citations
Publisher

Abstract

In this paper, by extending the Lagrangian of the Huttner–Barnett model an electromagnetic field in a nonhomogeneous and anisotropic magnetodielectric medium is quantized canonically. In this model, Maxwell equations in the medium are obtained and solved using the Green function technique. The noise operators are found and the results are compared with the phenomenological method.

DOI
10.1088/0953-4075/42/7/075504

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In this paper, by extending the Lagrangian of the Huttner–Barnett model an electromagnetic field in a nonhomogeneous and anisotropic magnetodielectric medium is quantized canonically. In this model, Maxwell equations in the medium are obtained and solved using the Green function technique. The noise operators are found and the results are compared with the phenomenological method.
The Huttner-Barnett model is extended to a magnetodielectric medium by adding a matter field to this model. The eigenoperators for the coupled system are calculated and electromagnetic field is written in terms of these operators. The electric and magnetic susceptibilities of the medium are explicitly derived and shown to satisfy the Kramers-Kronig relations. It is shown that the results obtained in this extended model are equivalent to their counterparts obtained in the phenomenological methods.
The electromagnetic field inside a cubic cavity filled with a linear magnetodielectric medium and in the presence of external charges is quantized by modeling the magnetodielectric medium with two independent quantum fields. The electric and magnetic polarization densities of the medium are defined in terms of the ladder operators of the medium and eigenmodes of the cavity. The Maxwell and constitutive equations of the medium together with the equation of motion of the charged particles have been obtained from the Heisenberg equations using a minimal coupling scheme. The spontaneous emission of a two-level atom embedded in a magnetodielectric medium is calculated in terms of the electric and magnetic susceptibilities of the medium and the Green function of the cubic cavity, as an application of the model.
A technique of canonical quantization in a general dispersive nonlinear dielectric medium is presented. The medium can be inhomogeneous and anisotropic. The fields are expanded in a slowly varying envelope approximation to allow quantization. An arbitrary number of envelopes is included, assuming lossless propagation in each relevant frequency band. The resulting Lagrangian and Hamiltonian agree with known propagation equations and expressions for the dispersive energy. The central result of the theory is an expansion of the quantum Hamiltonian in terms of annihilation and creation operators corresponding to group-velocity photon-polariton excitations in the dielectric.
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.
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielectric medium is developed. The classical Maxwell equations with spatially varying and Kramers-Kronig consistent permittivity are regarded as operator-valued field equations, introducing additional current- and charge-density operator fields in order to take into account the noise associated with the dissipation in the medium. It is shown that the equal-time commutation relations between the fundamental electromagnetic fields $\mathbf{E}^$ and $\mathbf{B}^$ and the potentials $\mathbf{A}^$ and $\stackrel{^}{\ensuremath{\varphi}}$ in the Coulomb gauge can be expressed in terms of the Green tensor of the classical problem. From the Green tensors for bulk material and an inhomogeneous medium consisting of two bulk dielectrics with a common planar interface it is explicitly proven that the well-known equal-time commutation relations of QED are preserved.