Three-dimensional topological photonic crystals

Abstract

Photonic crystals, often referred to as the “semiconductors of light,” have entered a new phase enabling exotic properties once exclusive to topological quantum matter such as topological insulators. While the development of the first three-dimensional (3D) photonic crystal marked the establishment of photonic crystals as an independent field, initial studies in topological photonic crystals focused mainly on one and two dimensions. Though a true photonic crystal counterpart of a 3D strong topological insulator remains elusive, significant progress has been made toward achieving 3D topological photonic crystals. Compared with their lower-dimensional counterparts, 3D topological photonic crystals reveal a richer variety of topological phases and surface manifestation, which enables more degrees of freedom for light manipulation. In this review, concentrating on the novel boundary states unique in 3D systems, we provide a brief survey of the 3D topological photonic crystals and recent advances in this field. We categorize and discuss various topological phases and associated phenomena observed in 3D photonic crystals, including both gapped and gapless phases. Additionally, we delve into some recent developments in this rapidly evolving area, including the realization of 3D topological phases through synthetic dimensions.