Transformation Optics for Plasmonics: from Metasurfaces to Excitonic Strong Coupling

We review the latest theoretical advances in the application of the framework of Transformation Optics for the analytical description of deeply sub-wavelength electromagnetic phenomena. First, we present a general description of the technique, together with its usual exploitation for metamaterial conception and optimization in different areas of wave physics. Next, we discuss in detail the design of plasmonic metasurfaces, including the description of singular geometries which allow for broadband absorption in ultrathin platforms. Finally, we discuss the quasi-analytical treatment of plasmon-exciton strong coupling in nanocavities at the single emitter level.