Valley-Hall topological edge states in honeycomb photonic crystals with circular air holes: parameter optimization and edge state confinement

We study valley-Hall topological photonic crystals based on a honeycomb lattice of circular air holes in a silicon background with a relative permittivity of 12. Using the plane wave expansion method, we compute the transverse electric (TE) polarized band structure and demonstrate that breaking the inversion symmetry by assigning different radii to the two sublattice holes opens a local gap at the K and K′ valleys. We systematically scan the two-hole-radius parameter space and identify an optimal tradeoff between K-point gap width and valley Chern number. For the selected parameters r1=0.24a0, r2=0.16a0 (with lattice constant a0=470 nm), the K-point local gap reaches 15.21 THz (9.84%) centered at 154.6 THz. Berry curvature integration over the one-third Brillouin zone yields valley Chern numbers Cv=−0.167 (band 2) and Cv=+0.455 (band 3) at 100×100 grid resolution. Supercell calculations with M=30 layers (15 per domain) confirm topological edge states at the zigzag interface, with the strongest confinement achieving 83.6% of the field energy within ±3 layers of the interface. We analyze the physical origin of the valley Chern number asymmetry between bands 2 and 3 and discuss the implications for topological photonic edge transport. We introduce a figure of merit quantifying the gap-topology tradeoff and assess fabrication tolerance, demonstrating that the K-point gap survives under ±5 nm radius perturbations.