  The hallmark of topological insulators is the scatter-free propagation of
waves in topologically protected edge channels. This transport is strictly
chiral on the outer edge of the medium, and therefore capable of bypassing
sharp corners and imperfections, even in the presence of substantial disorder.
In photonics, two-dimensional topological edge states have been demonstrated on
several different platforms, and are emerging as a promising tool for robust
lasers, quantum devices, and other applications. However, three-dimensional
photonic topological insulators, specifically those supporting topologically
protected edge states in all 3D, have thus far remained out of experimental
reach. Here, we demonstrate a three-dimensional photonic topological insulator
with protected topological edge states. The topological protection is enabled
by a screw dislocation. For this purpose, we utilize the concept of synthetic
dimensions in a 2D photonic waveguide array by introducing an additional modal
dimension to transform the system into a 3D photonic topological insulator. The
lattice dislocation endows the system with edge states propagating along
three-dimensional trajectories, with topological protection akin to strong
photonic topological insulators. Our work paves the way for utilizing
three-dimensional topology in photonic science and technology.
