Electromagnetic Devices with Transformation Optics

The fundamental interaction between light and matter enables to generate, manipulate and detect the properties of light. Traditional optical components already achieve this up to a very high degree: optical fibre connections that guide optical signals over long distances, lensing systems for optical imaging, dielectric microcavities to confine electromagnetic energy, or nonlinear devices that enable frequency manipulations are just a few examples.
The advent of metamaterials--man-made, subwavelength structures whose electromagnetic interaction can be designed--opens up a new world of possibilities. Whereas traditional materials interact with light only through the electric permittivity, metamaterials can have an effective permittivity and permeability different from unity at optical frequencies. Moreover, they offer the possibility to design left-handed materials, which exhibit simultaneously negative permittivity and permeability.
Transformation optics is a theoretical framework for the design of optical devices that uses the analogy between dielectrics and nontrivial geometries. Using the tools of differential geometry--the language of Einstein's general relativity--the free-space Maxwell's equations can be rewritten in arbitrary coordinates. It can then be shown that this set corresponds to the macroscopic Maxwell's equations of electromagnetic ?elds propagating inside a material on the background of a right-handed Cartesian coordinate system. Transformation media thus enable to bend the straight coordinates along which the electromagnetic waves propagate into curved lines. To achieve the exotic permittivities and permeabilities prescribed by the equivalence of transformation optics, these devices must be made with metamaterials. Transformation optics and metamaterials can thus be combined to create components that are unimaginable within the framework of traditional optics. The invisibility cloak, a device that renders even the strongest scatterers invisible, is perhaps the best example. In this contribution, we will review our research concerning the design of electromagnetic devices with novel properties by the use of transformation optics.