Topological Rainbow Concentrator Based on Synthetic Dimension

Synthetic dimension provides a new platform for realizing topological photonic devices. Here, we propose a method to realize a rainbow concentrator of topological photonic states based on the synthetic dimension concept. The synthetic dimension is constructed using a translational degree of freedom of the nanostructures inside the unit cell of a two-dimensional photonic crystal. The translational deformation induces a nontrivial topology in the synthetic dimension, which gives rise to robust interface states at different frequencies. The topological rainbow can trap states with different frequencies, controlled by tuning the spatial modulation of interface state group velocities. The operation frequency as well as the bandwidth of the topological rainbow can be easily tuned by controlling the band gap of the photonic crystal. The topological principle can be applied to photonic crystals of any symmetry and arbitrary material composition, as long as a complete band gap exists. This Letter provides a new and general scheme for the realization of a topological rainbow concentrator and will be useful for the development of topological photonic devices.