Transformation Optics

Transformation optics shows great promise as a new way of designing novel optical and electromagnetic devices based on the idea of using coordinate transformations to generate descriptions of dielectric media. It allows for essentially complete control over the behavior of electromagnetic fields through a suitable choice of medium, determined by a transformation that can specify the trajectories of light rays, the orientation of phase fronts, or other geometrical features of the fields. Although the requisite parameters of the medium may be unnatural for a particular transformation, recent advances in metamaterials—that even allow for a negative effective index of refraction—optics–designed devices. The transformation approach has also been shown to be applicable to non-electromagnetic wave systems such as acoustic and elastic waves. Here we review the current state of transformation optics and its extensions to other wave systems, the construction of transformation optics devices using electromagnetic metamaterials, and provide an introduction to the important theoretical aspects of transformation optics, covering the coordinate transformation and covariant approaches, as well as the conformal and quasiconformal methods.