Guiding light with conformal transformations

The past decade has seen a revolution in electromagnetics due to the development of metamaterials. These artificial composites have been fashioned to exhibit exotic effects such as a negative index of refraction. However, the full potential of metamaterial devices has only been hinted at. By combining metamaterials with transformation optics (TO), researchers have demonstrated an invisibility cloak. Subsequently, quasi-conformal mapping was used to create a device that exhibited a broadband cloaking effect. Here we extend this latter approach to a strictly conformal mapping to create reflection less, inherently isotropic, and broadband photonic devices. Our method combines the novel effects of TO with the practicality of all-dielectric construction. We show that our structures are capable of guiding light in an almost arbitrary fashion over an unprecedented range of frequencies.