LAUSR

We study the polaritonic bandstructure of a two-dimensional (2D) atomic lattice coupled to a surface plasmon polariton mode in the single excitation regime. We adopt a Dirichlet-to-Neumann map based computational technique which can accurately model non-Markovian dynamics as well as narrow-bandwidth features associated with any periodic atom-photon system in general. Using this technique, we design a 2D atomic lattice using only two-level atoms, which has an isolated flat polaritonic band where the magnitude of the group velocity for the modes in the band approach zero across the whole Brillouin zone. Such a system could be employed to slow, store, and manipulate single photons in a 2D geometry.