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We study the effects of finite size and of vacancies on the photonic band gaprecently predicted for an atomic diamond lattice. Close to a $J_g=0\to J_e=1$atomic transition, and for atomic lattices containing up to $N\approx3\times10^4$ atoms, we show how the density of states can be affected by boththe shape of the system and the possible presence of a fraction of unoccupiedlattice sites. We numerically predict and theoretically explain the presence ofshape-induced border states and of vacancy-induced localized states appearingin the gap. We also investigate the penetration depth of the electromagneticfield which we compare to the case of an infinite system.

Photonic band-gap in a realistic atomic diamond lattice: penetration depth, finite-size and vacancy effects