Numerical studies of the interaction of an atomic sample with the electromagnetic field in two dimensions

We consider the interaction of electromagnetic radiation of arbitrary polarization with multilevel atoms in a self-consistent manner, taking into account both spatial and temporal dependencies of localfields. This is done by numerically solvingthe corresponding systemofcoupled Maxwell-Liouville equations forvarious geometries. In particular, we scrutinize linear optical properties of nanoscale atomic clusters, demonstrating the significant role played by collective effects and dephasing. It is shown that subwavelength atomic clusters exhibit two resonant modes, one of which is localized slightly below the atomic transition frequency of an individual atom, while the other is positioned considerably above it. As an initial exploration of future applications of this approach, the optical response of core-shell nanostructures, with a core consisting of silver and a shell composed of resonant atoms, is examined.