Topological Dirac-vortex modes in a three-dimensional photonic topological insulator

Recently, topological Dirac-vortex modes in Kekul\'e-distorted photonic lattices have attracted broad interest and exhibited promising applications in robust photonic devices such as topological cavities, lasers, and fibers. However, due to the vectorial nature of electromagnetic waves that results in complicated band dispersions and fails the tight-binding model predictions, it is challenging to construct three-dimensional (3D) topological photonic structures with Kekul\'e distortion and the photonic topological Dirac-vortex modes have thus far been limited to two-dimensional (2D) systems. Here, by directly mapping a 3D Kekul\'e-distorted tight-binding model in a 3D tight-binding-like photonic crystal exhibiting scalar-wave-like band structures, we theoretically propose and experimentally demonstrate topological Dirac-vortex modes in a 3D photonic topological insulator for the first time. Using microwave near-field measurements, we directly observe robust photonic topological Dirac-vortex modes bound to and propagate along a one-dimensional (1D) Dirac-vortex line defect, matching well with the tight-binding and simulation results. Our work offers an ideal platform to map tight-binding models in 3D topological photonic crystals directly and opens a new avenue for exploiting topological lattice defects to manipulate light in 3D space.