Weak and strong coupling of a quantum emitter with a meta-surface

• We model a resonant meta-surface by an impedance operator.
• We model the coupling of the meta-surface with an emitter.
• We demonstrate the existence of Bloch surface modes.
• We demonstrate the strong coupling regime between the emitter and the meta-surface.

Meta-surfaces are the bidimensional analogs of metamaterials. They are made on resonant elements periodically disposed on a surface. They have the ability of controlling the polarization of light and to generalized refraction laws as well. They have also been used to enhance the generation of the second harmonic. It seems however that their near-field properties have not been investigated. In this work, the coupling of an emitter with a meta-surface made of a periodic set of resonant linear dipoles was studied. Bloch surface modes localized on the meta-surface exist due the resonance of the dipoles. The strong coupling regime with a emitter can be reached when the Bohr frequency of the emitter is in resonance with the Bloch modes of the meta-surface.