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A quantization scheme for the phenomenological Maxwell theory of the fullelectromagnetic field in an inhomogeneous three-dimensional, dispersive andabsorbing dielectric medium is developed. The classical Maxwell equations withspatially varying and Kramers-Kronig consistent permittivity are regarded asoperator-valued field equations, introducing additional current- andcharge-density operator fields in order to take into account the noiseassociated with the dissipation in the medium. It is shown that the equal-timecommutation relations between the fundamental electromagnetic fields $\hat E$and $\hat B$ and the potentials $\hat A$ and $\hat \phi$ in the Coulomb gaugecan be expressed in terms of the Green tensor of the classical problem. Fromthe Green tensors for bulk material and an inhomogeneous medium consisting oftwo bulk dielectrics with a common planar interface it is explicitly proventhat the well-known equal-time commutation relations of QED are preserved

Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics