No abstract

The localization and transmission of light is the core of modern photonic integrated devices, and the proposal of topological photonics provides a new way for optical manipulation. Topological photonic structures based on the Quantum spin hall effect or Quantum valley hall effect have the properties of immunity to defects and suppress backscattering, so they play a key role in designing novel low-loss photonic devices. In this paper, we cleverly design a two-dimensional dielectric photonic crystal with time-reversal symmetry to achieve the coexistence of the Quantum spin hall effect and the Quantum valley hall effect in a photonic crystal. The design can be likened to an electronic system in which two pairs of Kramers simplex pairs are constructed to achieve a quadruple simplex pair in a photonic crystal. First, based on the method of shrinking and expanding the silicon pillars arranged in the honeycomb structure, the quadruple degeneracy point at the <i>Γ</i> point of the first Brillouin zone is opened, and the corresponding topologically trivial or non-trivial photonic band gap is formed,thereby realizing Quantum spin hall effect. The expanded honeycomb lattice evolves into a Kagome structure, and then positive and negative perturbations are added to the Kagome lattice to break the spatial inversion symmetry of the Photonic crystal. When mirror symmetry is broken, different chiral photonic crystals can be created, resulting in the degeneracy point of the non-equivalent valleys <i>K</i> and <i>K</i>' in the Brillouin zone is opened and a complete band gap appears, thus realizing the Quantum valley hall effect. In the common band gap, topologically protected edge states are induced by nontrivial valley Chern number at the interface between two photonic crystals with opposite chirality. Numerical calculations show that unidirectional transport and bending-immune topological boundary states can be realized on the interface composed of topologically trivial (non-trivial) and positively (negatively) perturbed photonic crystals. Finally, a four-channel system based on the coexistence of the two effects is designed, The system is a novel electromagnetic wave router that can be selectively controlled by pseudospin degrees of freedom or valley degrees of freedom. This system provides a potential method for optical encoding and robust signal transmission, providing greater flexibility for the manipulation of electromagnetic waves.