Transformation Optics for Plasmonics: from Metasurfaces to Excitonic Strong Coupling Paloma A. Huidobro1;∗, Antonio I. Fern´andez-Dom´ınguez2;y 1Instituto de Telecomunicaes, Insituto Superior Te´ecnico-University of Lisbon, Avenida Rovisco Pais 1,1049-001 Lisboa, Portugal 2Departamento de F´ısicaTe´orica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autnoma de Madrid, E-28049 Madrid, Spain ∗
[email protected] [email protected] August 1, 2019 Abstract 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 meta- material conception and optimization in different areas of wave physics. Next, we discuss in detail the design of plasmonic metasurfaces, includ- ing the description of singular geometries which allow for broadband ab- sorption in ultrathin platforms. Finally, we discuss the quasi-analytical treatment of plasmon-exciton strong coupling in nanocavities at the single emitter level. 1 Introduction The development of Transformation Optics [1, 2] (TO) has been instrumen- tal in the fast development that metamaterial science has experienced during the last years [3]. This theoretical tool exploits the invariance of macroscopic Maxwell's equations under coordinate transformations to establish a link be- tween an electromagnetic (EM) phenomenon, described by the transformation, and the material response required for its realization. Thus, TO determines the way in which the EM constitutive relations, and therefore the permittivity and permeability tensors, must be tailored in space in order to obtain a desired arXiv:1907.13546v1 [cond-mat.mes-hall] 31 Jul 2019 effect.