Mode expansions in the quantum electrodynamics of photonic media with disorder

TL;DR

This paper develops a new integral equation for optical modes in disordered photonic media, ensuring correct transversality, and finds a gauge transformation to eliminate the static potential, aiding quantum optics in disordered photonic crystals.

Contribution

It introduces an integral equation for optical modes satisfying transversality and generalizes gauge transformations for disordered media, advancing quantum electrodynamics in complex photonic structures.

Findings

Derived an integral equation for optical modes with disorder.

Identified a gauge transformation to remove the static potential.

Applicable to quantum optics of disordered photonic crystals.

Abstract

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 another 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 automatically 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 makes the static potential zero, thereby generalizing work by Glauber and Lewenstein [Phys. Rev. A 43, 467 (1991)]. Our results are relevant for the quantum optics of disordered photonic crystals.