Strong Coupling to Two-Dimensional Anderson Localized Modes

We use a scattering formalism to derive a condition of strong coupling between a resonant scatterer and an Anderson localized mode for electromagnetic waves in two dimensions. The strong coupling regime is demonstrated based on exact numerical simulations, in perfect agreement with theory. The strong coupling threshold can be expressed in terms of the Thouless conductance and the Purcell factor, thus connecting key concepts in transport theory and cavity quantum electrodynamics.