Design of layered transformation-optics devices of arbitrary shape

Transformation-optics devices of arbitrary shapes usually result in material parameters inside the device that feature level sets of different shapes. Consequently, these devices cannot easily be implemented using a layered architecture and thus are, generally, more difficult to realize in practice. We present a method of designing two-dimensional transformation-optics devices of arbitrary shapes characterized by material parameters of same-level sets, thus suitable to be implemented through concentric layers, each layer being made of a single type of material or metamaterial. Remarkably, we show that transformations leading to such designs are obtained from solutions to the well-known eikonal equation. This approach allows fabrication techniques developed for cylindrical designs of circular cross section to be directly applied to devices of other shapes.