By modeling a linear polarizable and magnetizable medium (magnetodielectric) with two quantum fields, namely E and M, electromagnetic field is quantized in such a medium consistently and systematically. A Hamiltonian is proposed from which, using the Heisenberg equations, Maxwell and constitutive equations of the medium are obtained. For a homogeneous medium, the equation of motion of the quantum vector potential, A, is derived and solved analytically. Two coupling functions which describe the electromagnetic properties of the medium are introduced. Four examples are considered showing the features and the applicability of the model to both absorptive and nonabsorptive magneto-dielectrics.
A fully canonical quantization of electromagnetic field is introduced in the presence of an anisotropic polarizable and magnetizable medium . Two tensor fields which couple the electromagnetic field with the medium and have an important role in this quantization method are introduced. The electric and magnetic polarization fields of the medium naturally are concluded in terms of the coupling tensors and the dynamical variables modeling the magnetodielectric medium. In Heisenberg picture, the constitutive equations of the medium together with the Maxwell laws are obtained as the equations of motion of the total system and the susceptibility tensors of the medium are calculated in terms of the coupling tensors. Following a perturbation method the Green function related to the total system is found and the time dependence of electromagnetic field operators is derived.
By modeling a linear, anisotropic and inhomogeneous magnetodielectric medium with two independent set of harmonic oscillators, electromagnetic field is quantized in such a medium. The electric and magnetic polarizations of the medium are expressed as linear combinations of the ladder operators describing the magnetodielectric medium. The Maxwell and the constitutive equations of the medium are obtained as the Heisenberg equations of the total system. The electric and magnetic susceptibilities of the medium are obtained in terms of the tensors coupling the medium with the electromagnetic field. The explicit forms of the electromagnetic field operators are obtained in terms of the ladder operators of the medium.
A canonical relativistic formulation is introduced to quantize electromagnetic field in the presence of a polarizable and magnetizable moving medium. The medium is modeled by a continuum of the second rank antisymmetric tensors in a phenomenological way. The covariant wave equation for the vector potential and the covariant constitutive equation of the medium are obtained as the Euler-Lagrange equations using the Lagrangian of the total system. A fourth rank tensor which couples the electromagnetic field and the medium is introduced. The susceptibility tensor of the medium is obtained in terms of this coupling tensor. The noise polarization tensor is calculated in terms of both the coupling tensor and the ladder operators of the tensors modeling the medium. PACS No: 12.20.Ds, 42.50.Nn
The electromagnetic field inside a cubic cavity filled up with a linear magnetodielectric medium and in the presence of external charges is quantized by modelling the magnetodielectric medium with two independent quantum fields. Electric and magnetic polarization densities of the medium are defined in terms of the ladder operators of the medium and eigenmodes of the cavity. 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. Spontaneous emission of a two level atom embedded in a magnetodielectric medium is calculated in terms of electric and magnetic susceptibilities of the medium and the Green function of the cubic cavity as an application of the model.
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