Photonic topological insulator induced by a dislocation in three dimensions.

The hallmark of topological insulators (TIs) is the scatter-free propagation of waves in topologically protected edge channels 1 . 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 (2D) topological edge states have been demonstrated on several different platforms 2-4 and are emerging as a promising tool for robust lasers 5 , quantum devices 6-8 and other applications. More recently, 3D TIs were demonstrated in microwaves 9 and  acoustic waves 10-13 , where the topological protection in the latter  is induced by dislocations. However, at optical frequencies, 3D photonic TIs have so far remained out of experimental reach. Here we demonstrate a photonic TI with protected topological surface states in three dimensions. The topological protection is enabled by a screw dislocation. For this purpose, we use the concept of synthetic dimensions 14-17 in a 2D photonic waveguide array 18 by introducing a further modal dimension to transform the system into a 3D topological system. The lattice dislocation endows the system with edge states propagating along 3D trajectories, with topological protection akin to strong photonic TIs 19,20 . Our work paves the way for utilizing 3D topology in photonic science and technology.