  We continue our study of the quantum optics of a single photon interacting
with a system of two level atoms. In this work we investigate the case of a
periodic arrangement of atoms. We provide a general structure theorem
characterizing the band functions of this problem, which comprise the spectrum
of the associated Hamiltonian. Additionally, we study atomic densities arising
as periodically arranged scaled inclusions. For this family of examples, we
obtain explicit asymptotic formulas for the band functions.
