Analysis of influencing factors on Dirac-cone band structures in dual-band valley topological photonic crystals

The degeneracy of Dirac-cones constitutes a focal point in valley photonic crystal research. The modulation of band structures by material and geometric parameters, particularly the gap opening mechanism at Gap 2, represents a critical research frontier. In previous studies, we investigated the influence of variations in dielectric materials on the band structures of dual-band systems, as well as the excitation of edge states and valley bulk states. Building upon this prior work, the present study systematically examines the material parameters of triangular scatterers with intact C₃v symmetry and analyzes the effects of different structural parameters on the formation of double Dirac-cones and the modulation of band structures. Finite Element Method simulation results indicate that when the scatterer's material parameters approach those of a perfect electric conductor, it facilitates the formation of dual-band valley topological edge states. Regarding structural parameters, maintaining both Gap 2 and Gap 1 requires relatively large scatterer dimensions; otherwise, Gap 2 exhibits significant degradation. Moreover, breaking spatial inversion symmetry induces the opening of Dirac-cones, leading to a complete bandgap. This mechanism offers promising applications in optical topological insulators, including photonic computing, optical beam splitters, and invisibility cloaking devices.