After giving an outline of the quantization scheme based on the microscopicHopfield model of a dielectric bulk material, we show how the classicalphenomenological Maxwell equations of the electromagnetic field in the presenceof dielectric matter of given space- and frequency-dependent complexpermittivity can be transferred to quantum theory. Including in the theory theinteraction of the medium-assisted field with atomic systems, we present boththe minimal-coupling Hamiltonian and the multipolar-coupling Hamiltonian in theCoulomb gauge. To illustrate the concept, we discuss the input--outputrelations of radiation and the transformation of radiation-field quantum statesat absorbing four-port devices, and the spontaneous decay of an excited atomnear the surface of an absorbing body and in a spherical micro-cavity withintrinsic material losses. Finally, we give an extension of the quantizationscheme to other media such as amplifying media, magnetic media, and nonlinearmedia.
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