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We study the light dispersion relation in a periodic ensemble of atoms atfixed positions in the Fano-Hopfield model (the atomic dipole being modeledwith harmonic oscillators). Compared to earlier works, we do not restrict tocubic lattices, and we do not regularize the theory by hand but we renormalizeit in a systematic way using a Gaussian cut-off in momentum space. Whereas noomnidirectional spectral gap is known for light in a Bravais atomic lattice, wefind that, for a wide range of parameters, an omnidirectional gap occurs in adiamond atomic lattice, which may be realized in an experiment with ultra-coldatoms. The long-wavelength limit of the theory also provides a Lorentz-Lorenz(or Clausius-Mossotti) relation for an arbitrary lattice.

Fano-Hopfield model and photonic band gaps for an arbitrary atomic lattice