Extending transformation optics beyond 3D geometries

Transformation optics makes use of coordinate transformations to explore the possibilities offered by artificially structured metamaterials for the manipulation of a wide variety of electromagnetic phenomena. Since a decade, transformation optics has consistently extended its scope. Initially, coordinate transformations were only applied to the transformation of light in the simplest of optical setups, i.e., empty space. In particular, straight light trajectories were being transformed into curved ones, e.g., avoiding a specific region in space (invisibility devices), bending over a specific angle (benders and splitters), and focussing to a particular point (lenses). Today, research efforts go beyond the transformation of empty space, allowing metamaterials to further enhance our control on electromagnetic phenomena other than light propagation. In this contribution, I will review our work on transformation optics to manipulate guided modes along and optical forces between metamaterial waveguides, the emission of Cerenkov radiation due to fast charged particles, and the Goos-Hänchen shift at metamaterial surfaces.