Exploring metamaterial horizons: New concepts and geometrical tools for the description of advanced electromagnetic phenomena

Einstein’s theory of general relativity has dramatically changed our world view, by describing gravity as an intrinsic deformation of space and time. About fifteen years ago, John Pendry and Ulf Leonhardt had the intriguing idea to emulate the behaviour of light in a deformed space by making use of carefully designed artificial metamaterials. Metamaterials consist of elements that are very small with respect to the characteristic length of light waves. By optimizing the shape, the density, and the size of these elements, metamaterials can control the trajectory of light rays in a very precise way that allows them to reproduce light trajectories inside a deformed space. The equivalence between a deformed space and specific metamaterial properties lies at the heart of the technique known as transformation optics and allows for a very intuitive understanding of the behaviour of light inside advanced metamaterials. For example, transformation optics has been used to design invisibility devices that hide an object by smoothly guiding light rays around it. In recent years, rapidly advancing fabrication methods have resulted in metamaterial designs that are not yet understood in an intuitive way, such as reconfigurable, two-dimensional, or quantum metamaterials. In this work, the author introduces new concepts to describe advanced metamaterial designs in an intuitive way, so that they can be used in future light-based applications.The author starts by reviewing the fields of metamaterials and transformation optics. Based on three hallmark elements, i.e., thin wires, split-ring resonators, and helices, the first chapter discusses the unusual behaviour of light inside negative-index, hyperbolic, and chiral metamaterials as well as their relevance to photonic applications. Subsequently, in the second chapter, transformation optics is shown to be a powerful design tool that naturally extends the principle of Fermat from simple dielectrics to the realm of metamaterials. In the following chapters, the author introduces several concepts to describe advanced metamaterial designs such as materials that implement vector potentials for photons, reconfigurable metasurfaces with fundamental speed limits, two-dimensional metamaterial waveguides that emulate a deformation of their surface, and metamaterial black holes