Routing light with different wavevectors using synthetic dimensions.

Synthetic dimensions have drawn intense recent attention in investigating higher-dimensional topological physics and offering additional degrees of freedom for manipulating light. It has been demonstrated that synthetic dimensions can help to concentrate light with different frequencies at different locations. Here, we show that synthetic dimensions can also route light from different incident directions. Our system consists of an interface formed by two different photonic crystals. A synthetic dimension ξ is introduced by shifting the termination position of the photonic crystal on the right-hand side of the interface. We identify a correspondence between ξ and the interface state such that light incident from a specific direction can be collected. Thus, routing incident light from different directions is achieved by designing an interface with a proper distribution of ξ. Traditionally, this goal is achieved with a standard 4f optical system using a convex lens, and our approach offers the possibility for such a capability within a few lattice sites of photonic crystals. Such an approach reduces the size of the system, making it easier for integration. Our work provides, to our knowledge, a new direction for routing light with different momentums and possibly contributes to applications such as lidar.