Mode expansions in the quantum electrodynamics of photonic media with disorder

We address two issues in the quantum electrodynamical description of photonic media with some disorder, neglecting material dispersion. When choosing a gauge in which the static potential vanishes, the normal modes of the medium with disorder satisfy a different transversality condition than the modes of the ideal medium. Our first result is an integral equation for optical modes such that all perturbation-theory solutions by construction satisfy the desired transversality condition. Secondly, when expanding the vector potential for the medium with disorder in terms of the normal modes of the ideal structure, we find the gauge transformation that conveniently makes the static potential zero, thereby generalizing work by Glauber and Lewenstein (1991) [15]. Our results are relevant for the quantum optics of disordered photonic crystals.

► We study the quantum electrodynamics of photonic media with some disorder.
► We derive a new integral equation for the normal modes in a disordered dielectric.
► To all orders in the perturbation, its solutions satisfy the desired gauge condition.
► In an alternative description, idealized modes get coupled due to disorder.
► We transform these idealized modes so that they satisfy the right gauge condition.