Invisibility. Transformation of space and applications

Invisibility is an old human myth, probably dating back to the days when success in hunting or war depended on the ability to be as unobtrusive as possible. This invisibility, after having made the fortune of storytellers, writers and film-makers, became almost a reality in 2006 with the first practical realization of an electromagnetic invisibility cloak. The invariance of Maxwell's equations in the geometric transformation of coordinates thus became a hot topic that year with the first proposal for a cylindrical invisibility cloak by J.B. Pendry and U. Leonhardt. Experimental fabrication and characterization of this first cloak at microwave frequencies showed the tool to be highly effective. Following this realization, several applications of this transformation were proposed for concentrators, waveguides, transitions and bends, rotators, directional antennas, and even electromagnetic wormholes. This coordinate transformation therefore appears to be a powerful tool for the design of devices or components with special properties difficult to obtain from conventional geometries and materials. Theoretically, the coordinate transformation method consists in generating a new transformed space from an initial space where the solutions of Maxwell's equations are known. The first step is to imagine a starting space and a target space, with their topological properties, and link them through an analytic transformation. Most of this work is based on a continuous transformation that produces a final space with complex, heterogeneous and anisotropic electromagnetic parameters. The difficulty lies in then concretely realizing this new space. To make this easier, parameter simplification was proposed in early work, with the disadvantage of impedance mismatch between the material and its environment. More recently, a discrete transformation applied to multilayer structures has been proposed to further simplify this realization. In this article, we present the principles and main applications envisaged for this transform, to invisibility but also to antennas.