Electromagnetics: from Covariance to Cloaking

An overview of some topical themes in electromagnetism is presented. Recent interest in metamaterials research has enabled earlier theoretical speculations concerning electromagnetic media displaying a negative refractive index to be experimentally realized. Such media can act as perfect lenses. The mathematical criterion of what signals such unusual electromagnetic behavior is discussed, showing that a covariant (or coordinate free) perspective is essential. Coordinate transformations have also become significant in the theme of transformation optics, where the interplay between a coordinate transformation and metamaterial behavior has led to the concept of an electromagnetic cloak.