Intensity tuning of the edge states in the imperfect topological waveguides based on the photonic crystals with the \(C_{3}\) point group symmetry

We explore the topological behavior of a two-dimensional honeycomb photonic crystal (2D HPC) based on the presence of double Dirac-cone connected the orbitals \(p\) and \(d\), due to the \(C_{6}\) point group symmetry. Removing the four-fold degeneracy between the bands at the Dirac point can be achieved by introducing three small dielectric rods near the bigger ones to realize the perturbed PCs with the \(C_{3}\) point group symmetry with different topological features. By proposing the unique structure involving two PCs with different topological effects, one may study the one-way light distribution along the local boundary in spite of the defects, cavities, and disorders. Moreover, we investigate the variation of the transmitted intensity values under different defect conditions and realize that the size, location and material type affect the transmitted light. In the other words, tunable intensity of the edge states can be achieved through adjusting the defects such that by decreasing the radius of rods, the intensity of the edge states can be decreased or by increasing their distance from the unit cell center, the intensity will be decreased too. Finally, topological rhombic resonator enables unidirectional filtering of guided mode. The fact that different light manipulation scenarios can be realized provides a unique aspect for topological photonic insulators.