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Light transport in periodic waveguides coupled to a two-level atom isinvestigated. By using optical Bloch equations and a photonic modal formalism,we derive semi-analytical expressions for the scattering matrix of one atomtrapped in a periodic waveguide. The derivation is general, as the expressionshold for any periodic photonic or plasmonic waveguides. It provides a basicbuilding block to study collective effects arising from photon-mediatedmulti-atom interactions in periodic waveguides.

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