Flattening of conic reflectors via a transformation method

This paper presents a general and rigorous transformation method to tailor planar conic reflectors. The proposed method enables the designed reflectors to scatter or reflect incident light in the same manner as a conic reflector while the whole device as well as the reflector would maintain planar profiles. In order to reduce the overall size, especially the aperture of the reflector, we further apply a set of compressed and folded spatial mapping to the planar reflectors. Planar reflectors with reduced sizes are finally obtained which may be useful in several optical and electromagnetic applications.