Beyond transformation optics: A new paradigm for the electromagnetic interaction of metamaterials

In the past decades, scientists have harnessed the optical properties of materials in order to create photonic applications that have profoundly altered our daily lives, such as LCD screens, solar cells, fibres, lasers, etc. Recently, new artificial materials--also called metamaterials--have been developed with optical properties that cannot be found in natural materials and that can be tailored to the needs of next-generation technological applications. In this project, we want to advance our understanding of the physics of such metamaterials.

We will use the mathematical techniques underlying Albert Einstein's theory of general relativity to study the propagation of electromagnetic waves through various exotic materials. In the theory of general relativity, spacetime has curvature that forces light to propagate along curved paths, and no longer along straight lines. Currently, the relation between light ray curvature and metamaterial properties is provided by a theoretical framework called transformation optics. However, this framework is not applicable to exotic materials, such as nonlinear optical crystals, two-dimensional materials like graphene, and semiconductors. We will conceive new frameworks to learn how these materials impose a curved geometry to light and how they inspire and improve metamaterial designs.