Broadband Invisibility by Non-Euclidean Cloaking

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 backward in space or time. All of the previous proposals for invisibility require materials with extreme properties. Here we show that transformation optics of a curved, non- Euclidean space ( such as the surface of a virtual sphere) relax these requirements and can lead to invisibility in a broad band of the spectrum.