  In the development of topological photonics, achieving three dimensional
topological insulators is of significant interest since it enables the
exploration of new topological physics with photons, and promises novel
photonic devices that are robust against disorders in three dimensions.
Previous theoretical proposals towards three dimensional topological insulators
utilize complex geometries that are challenging to implement. Here, based on
the concept of synthetic dimension, we show that a two-dimensional array of
ring resonators, which was previously demonstrated to exhibit a two-dimensional
topological insulator phase, in fact automatically becomes a three-dimensional
topological insulator, when the frequency dimension is taken into account.
Moreover, by modulating a few of the resonators, a screw dislocation along the
frequency axis can be created, which provides robust transport of photons along
the frequency axis. Demonstrating the physics of screw dislocation in a
topological system has been a significant challenge in solid state systems. Our
work indicates that the physics of three-dimensional topological insulator can
be explored in standard integrated photonics platforms, leading to
opportunities for novel devices that control the frequency of light.

Optics