Theoretical treatment of the interaction between two-level atoms and periodic waveguides

Light transport in periodic waveguides coupled to two-level atoms is investigated theoretically. By using optical Bloch equations and a photonic modal formalism, we derive a convenient semi-analytical expression for calculating the scattering matrix of single atoms trapped in periodic waveguides. The expression that holds for both photonic and plasmonic waveguides represents a basic building block toward the study of collective effects arising from photonmediated multi-atom interactions in periodic waveguides.