Discontinuous Transformation Optics for Surface Phenomena

In this contribution, we introduce an innovative way of using discontinuous coordinate tranformations to extend the geometrical formalism of transformation optics beyond the manipulation of light ray trajectories inside bulk media. Specifically, we demonstrate how discontinuous transformation optics can be used to design electromagnetic surface phenomena at the interface of man-made materials. As a first application of our approach, we show how the Goos-Hänchen effect can be understood and tailored from a geometrical point of view. In addition, we propose a similar approach for transition radiation.