Quantum optics of dispersive dielectric media

Abstract

We quantize the electromagnetic field in a polar medium starting with the fundamental equations of motion. In our model the medium is described by a Lorenz--type dielectric function $\ensuremath{\epsilon}(\mathbf{r},\ensuremath{\omega})$ appropriate, e.g., for ionic crystals, metals, and inert dielectrics. There are no restrictions on the spatial behavior of the dielectric function, i.e., there can be many different polar media with arbitrary shapes. We assume no losses in our system so the dielectric function for the whole space is assumed as real. The quantization procedure is based on an expansion of the total field (transverse and longitudinal) in terms of the coupled (polariton) eigenmodes, and this approach incorporates all previous results derived for similar but restricted systems (e.g., without spatial or frequency dependence of coupled modes). Within the same model, we also quantize the Hamiltonian of a nonretarded electromagnetic field in polar media. Particular attention is paid to the derivation of the orthogonality and closure relations, which are used in a discussion of the fundamental (equal-time) commutation relations between the conjugate field operators.