Metamaterials, transformation optics and its applications

The purpose of this paper is to introduce transformation optics and general relativity with metamaterials to design optical devices. To show how useful the transformation optics is, we propose photonic metamaterials or photonic crystal waveguide with the structure of honeycomb lattice to slow light. We also show that general relativity gives the theoretical tools for designing optical devices made of such exotic properties and man-made materials. The media with a desired device function facilitate space-time transformations and include negative refractive index. One of the applications of slow light is to design single photon source.