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It is shown that in dielectrics exhibiting a complete photonic band gap, quantum electrodynamics predicts the occurrence of bound states of photons to hydrogenic atoms. When the atomic transition frequency lies near a photonic band edge, the excited atomic level experiences an anomalous Lamb shift and splits into a doublet. One member of this doublet exhibits resonance fluorescence whereas the other level is dressed by the emission and reabsorption of near-resonant photons whose amplitude decays exponentially from the vicinity of the atom.
John et al. (1990) studied this question.