Three-dimensional electromagnetic field quantization in absorbing and dispersive bounded dielectrics

We present a quantization scheme for the electromagnetic field in dispersive and lossy dielectrics with planar interfaces, incorporating propagation in all the spatial directions, and including both TE and TM polarized fields. Field quantization is carried out starting from a microscopic model for the polarization quanta interacting with the electromagnetic field. Dissipation is described by considering the coupling of the polarization quanta of the system with the reservoir oscillators in the usual Langevin approach. The method is applied to a semi-infinite medium and expressions for the electromagnetic field operators are obtained in the two different spatial regions, i.e., in the vacuum and in the dielectric. As a check of our quantization scheme, we have verified that the obtained vector potential operator and its conjugate momentum satisfy equal-time canonical commutation rules, giving rise to the prescribed transverse Dirac δ function.