T-shaped topological polarization beam splitter based on a synthetic dimension.

In this study, we propose a 2D photonic crystal (PC) with a common bandgap (CBG) for both TM and TE polarizations. Based on the Jackiw-Rebbi theory, a pair of topological helical edge states along the domain wall can be found in the parity-inversion bandgap. Pseudospin-locked unidirectional propagation and backscattering immunity of topological edge states (TESs) of dual polarization are demonstrated. By employing translation parameters as a synthetic dimension, the evolution of TESs within a parameter space is investigated. In addition, we design a T-shaped topological polarization beam splitter (TPBS), and finite element method (FEM) simulations show that our TPBS achieves effective separation of dual-polarization TESs. Our work provides an alternate way toward the design of TPBS, providing a new perspective for the development of integrated photonic circuits and optical communication systems.