Design of a beam splitter based on an adjustable beam-splitting ratio of a hexagonal star-like topological photonic crystal

We propose a new, to the best of our knowledge, mechanism to realize topological phase transition, that is, in a hexagonal star-like honeycomb lattice photonic crystal (PC), the optical quantum spin Hall effect (QSHE) can be realized by changing the materials of the outer or inner ring dielectric rods in the cells. We calculated the energy band and analyzed the topological phase transition law of a hexagonal star-like honeycomb PC. By changing the permittivity of the PC, the disturbance is introduced to the edge state. It is found that with the decrease of the permittivity of the PC, the gap decreases, the lower boundary state gradually redshifts, and the maximum transmittance in the straight waveguide can reach 98.8%. On this basis, a topological beam splitter was designed and analyzed. Results show that the beam splitting ratio obtained by the system is in the wide range of 0.2–3.5. Our research enriches the implementation of topological photonics, provides potential applications for topological boundary states in terahertz technology, and offers a new avenue for the design of current optical integrated devices.