It is rigorously shown that the rate of spontaneous emission of atoms placed in a dielectric is determined by a part of the local density of eigenmodes of the Maxwell equations: the local radiative density of states. Spontaneous emission is inhibited if the atom is located at a position where this local radiative density is vanishing, even when the total density of states is not small. The radiative density of states can be obtained from a purely classical calculation. We demonstrate this principle by a calculation of the optical bandstructure and density of states of a three-dimensional lattice of resonant two-level atoms in the dipole approximation. The formation of photonic bandgaps is exhibited. The bandstructure can be characterized by two dimensionless parameters. We find a longitudinal polarization mode as well as a class of vacuum modes that are unaltered by the interaction with matter.

World Scientific
H. B. van Linden van den Heuvell , J. T. M. Walraven , M. W. Reynolds

van Coevorden, D. V, Sprik, R, de Vries, P, & Lagendijk, A. (1997). Response of atoms in photonic lattices. In H. B van Linden van den Heuvell, J. T. M Walraven, & M. W Reynolds (Eds.), Atomic Physics 15 : Fifteenth International Conference on Atomic Physics, Zeeman-Effect Centenary, Amsterdam, The Netherlands, 5-9 August 1996 (pp. 313–327). World Scientific.