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We address two issues in the quantum electrodynamical description of photonicmedia with some disorder, neglecting material dispersion. When choosing a gaugein which the static potential vanishes, the normal modes of the medium withdisorder satisfy another transversality condition than the modes of the idealmedium. Our first result is an integral equation for optical modes such thatall perturbation-theory solutions automatically satisfy the desiredtransversality condition. Secondly, when expanding the vector potential for themedium with disorder in terms of the normal modes of the ideal structure, wefind the gauge transformation that makes the static potential zero, therebygeneralizing work by Glauber and Lewenstein [Phys. Rev. A 43, 467 (1991)]. Ourresults are relevant for the quantum optics of disordered photonic crystals.

Mode expansions in the quantum electrodynamics of photonic media with disorder