Recent advances in 2D, 3D and higher-order topological photonics

Over the past decade, topology has emerged as a major branch in broad areas of physics, from atomic lattices to condensed matter. In particular, topology has received significant attention in photonics because light waves can serve as a platform to investigate nontrivial bulk and edge physics with the aid of carefully engineered photonic crystals and metamaterials. Simultaneously, photonics provides enriched physics that arises from spin-1 vectorial electromagnetic fields. Here, we review recent progress in the growing field of topological photonics in three parts. The first part is dedicated to the basics of topological band theory and introduces various two-dimensional topological phases. The second part reviews three-dimensional topological phases and numerous approaches to achieve them in photonics. Last, we present recently emerging fields in topological photonics that have not yet been reviewed. This part includes topological degeneracies in nonzero dimensions, unidirectional Maxwellian spin waves, higher-order photonic topological phases, and stacking of photonic crystals to attain layer pseudospin. In addition to the various approaches for realizing photonic topological phases, we also discuss the interaction between light and topological matter and the efforts towards practical applications of topological photonics. Topological photonics: Light and topology linked in theory and practiceThe structural property of materials known as their topology can be exploited to control the behavior of light in the emerging field of topological photonics, offering potential applications in areas including topology theory, optical communication and optical computing. Researchers in South Korea and the USA, led by Junsuk Rho at Pohang University of Science and Technology (POSTECH) in South Korea, review recent progress in this rapidly developing field. They consider detailed theoretical and practical aspects of the interaction of light with materials whose topology influences the behavior of light waves. These materials include 'photonic crystals' and 'metamaterials', which have structural features on scales shorter than the wavelength of light. The authors also discuss progress towards developing practical applications for topological photonics. The ability to achieve highly efficient light transmission without dissipation is particularly promising.