Non-euclidean ideas for broadband invisibility

Invisibility and negative refraction are both applications of transformation optics where the material of a device performs a coordinate transformation for electromagnetic fields. The device creates the illusion that light propagates through empty flat space, whereas in physical space light is bent around a hidden interior or seems to run backwards in space or time. All the previous proposals for invisibility require materials with extreme properties. We show that transformation optics of a curved, non-Euclidean space, such as the surface of a virtual sphere, relaxes these requirements and can lead to invisibility in a broad band of the spectrum.