Multiscale models of electromagnetic and plasmonic metamaterials

In this chapter, we discuss paradigms central to electromagnetic metamaterials and their plasmonic counterparts. We start with a slab lens with unlimited resolution, which is made possible using the concept of negative refraction, when the permittivity and permeability of a medium change sign simultaneously. Pendry’s perfect lens heavily relies upon existence of surface plasmons that exist on its boundaries. Correspondences with acoustics are then investigated in light of spring-mass models which bridge the field of electromagnetic and acoustic metamaterials, which are composites within which light or other (e.g. elastic, liquid surface) waves experience inverted Snell-Descartes laws of refraction upon resonance of micro-scale resonators. Next, we explain how geometric transforms introduced for computational easiness in helicoidal fibres, were given a twist by Pendry’s team in 2006 in order to design invisibility cloaks. Finally, we apply these mathematical tools to the control of surface plasmons propagating at structured metal-dielectric interfaces. We illustrate transformational plasmonics with a broadband plasmonic invisibility carpet which has been experimentally validated by Quidant’s group in 2010 at near infrared frequencies.