Mode expansion and photon operators in dispersive and absorbing dielectrics

We present a one-dimensional quantization scheme for the electromagnetic fi eld in arbitrary planar absorbing and dispersive dielectrics, taking into a ccount explicitly the finite extent of media. The complete form of the elec tric field operator includes a part that corresponds to the free fields inc ident from the vacuum towards the medium and a particular solution which ca n be expressed by using the classical Green-function integral representatio n of the electromagnetic field. By expressing the classical Green function in terms of the light modes of the dielectric structure, we obtain a natura l generalization to absorbing media of the familiar method of mode expansio n which strictly applies to non-absorbing media. As an application of our m ode expansion, we obtain general quantum-optical input-output relations rel ating the output photon operators in vacuum to the input photon operators a nd to the reservoir noise operators. The input-output relations obtained ar e uniquely determined by the knowledge of the classical light modes of the planar system. We finally show that our quantization scheme for arbitrary p lanar dielectrics satisfies the prescribed equal-time commutation relations of QED.