Metamaterials, i.e. artificial materials with rationally designed geometry, composition, and arrangement of nanostructured building blocks are opening a gateway to unprecedented electromagnetic properties and functionalities that are unattainable with naturally occurring materials. Metamaterials also enable transformation optics, which is a new paradigm for the science of light with a family of novel applications ranging from superlens to optical cloaking.
Metamaterials give enormous choice of material parameters for electromagnetic applications. So much so that we might ask if there is a new way to design electromagnetic systems exploiting this new flexibility. In an ideal world magnetic and electrical field lines can be placed anywhere that the laws of physics allow and a suitable metamaterial found to accommodate the desired configuration of fields. Transformation optics was developed to answer the question of what parameters to choose for the metamaterial.
The idea, as depicted above, is quite straightforward: start with a field pattern that obeys Maxwell’s equations for a system that is topologically similar to the desired configuration but confined either to free space or a simple configuration of permittivity and permeability, then distort the system until the fields are in the desired configuration.
For a more in depth description of transformation optics see John Pendry's description of Transformation Optics located on his group research page.
John Pendry is a condensed matter theorist. He has worked at the Blackett Laboratory, Imperial College London, since 1981. He began his career in the Cavendish Laboratory, Cambridge, followed by six years at the Daresbury Laboratory where he headed the theoretical group. He has worked extensively on electronic and structural properties of surfaces developing the theory of low energy diffraction and of electronic surface states. Another interest is transport in disordered systems where he produced a complete theory of the statistics of transport in one dimensional systems.
John Pendry (2010), "Transformation Optics at Optical Frequencies," https://nanohub.org/resources/8327.