3D Topological Photonic Crystals: Theoretical Methods and Applications

Abstract

The concept of topology has revolutionized our understanding of condensed matter physics, leading to the discovery of novel electronic phases and the emergence of topological materials. In recent years, this concept has been extended to the field of photonics, where it has led to the design of a new class of materials known as topological photonic crystals. These materials possess nontrivial topological properties that can lead to unique and robust light propagation phenomena. This thesis presents a comprehensive study of 3D topological photonic crystals, with a focus on the discovery of novel topological phases and the development of new methods for their characterization and design. The main contributions of this work are the proposal and investigation of 3D topological photonic phases, which include: the 3D Chern photonic insulator; the axion photonic insulator; and the 3DWeyl semimetal with unpaired photonicWeyl points. These phases exhibit unique features, such as vectorial bulk-boundary correspondence, closed Fermi loops, chiral hinge channels, and forbidden surface Fermi arcs, which have not been proposed before in 3D photonic crystals. To approach topology in 3D electromagnetism, we propose dimension-specific characterization methods, including vectorial photonic Wilson loops and transversality-enforced tight-binding models. These methods allow us to overcome the theoretical challenges associated with the vectorial nature of light, and permit us to model and characterize the topological properties of 3D photonic systems in detail. Throughout this thesis, we also suggest possible implementations to realize these topological phases, which include PhC domain walls, gyrotropic structures, and quantum emitters coupled to PhCs. Our goal is to demonstrate their potential for applications in guided-light communication, optical switching, particle detection, magneto-photonics, and quantum simulations. Overall, this work aims to contribute to a deeper understanding of topological phenomena in 3D electromagnetism and proposes novel investigation methods and possible applications. We hope that the tools and designs developed in this thesis can be used as a starting point to realize these topological phases in real-world photonic devices.