Optimal Design in Transformational Optics – OPTRANS

This project comes under fundamental research. It is at the crossing between two federative themes: the modelisation of metamaterials from on one hand, and Transformation Optics on the other hand. Metamaterials are artificial structures made of a set of elementary components (wires, split rings, nanorods) possessing at the macroscopic level effective electromagnetic properties that are not found in natural materials. This properties open the way to a great deal of possibilities of controlling light propagation (super-lens, invisibility cloaking). They constitute an emergent theme of research, that is part of a bundle of new themes forming a new domain mixing Plasmonics, Metamaterials, Nanophotonics with potential applications in biophysics, integrated optics, solar cells and so on.
Transformation Optics is an even more recent theme since the founding article dates back to 2006. Transformation Optics exploits the idea according which there is an equivalence between a geometrical transform (that is to say, a change of coordinates) characterized by a Jacobian matrix and the electromagnetic properties of materials. This property has been aboundantly used in the framework of invisibility cloakings. Unfortunately, the permittivites and permeabilities deriving from these techniques do not exist in Nature: they are in general strongly heterogeneous and completely anisotropic.
At the moment, there is no such thing as a systematic approach to answering the following question: • « given a ray path, what are the permittivity/permeability tensors whose geodesics have this path? »
• « given the permittivity and permeability deduced from Transformation Optics, by which metamaterial are they realized? »

The aim of this project is to develop systematic methods allowing to answer these questions, that is to say, to realize a conceptual synthesis between Metamaterials and Transformation Optics
To do so, we shall use direct methods (developped during a preceding ANR project) as well as inverse and optimisation methods.