Résumé
Physical Review A: Atomic, Molecular and Optical Physics 88, 033844 (2013) 033844 We study the effects of finite size and of vacancies on the photonic band gap recently 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$N\approx 3\times10^4$atoms, we show how the density of states can be affected by both the shape of the system and the possible presence of a fraction of unoccupied lattice sites. We numerically predict and theoretically explain the presence of shape-induced border states and of vacancy-induced localized states appearing in the gap. We also investigate the penetration depth of the electromagnetic field which we compare to the case of an infinite system.