Inverse Design of the Topology Bandwidth Tradeoff in Valley Photonic Crystals

Abstract: Integrated on-chip photonics increasingly relies on wave propagation that remains stable in the presence of fabrication imperfections, tight bends, and dense routing. Valley photonic crystals (VPCs) offer an attractive path: by opening a gap at the Dirac points of a hexagonal lattice, one can engineer guided modes confined to domain walls that thread around corners with reduced backreflection. We develop a design framework that co-optimizes the photonic bulk band gap and valley Chern number using a modified particle-swarm optimization (PSO), while evaluating the photonic band structure via plane-wave expansion and the topological characteristics using a gauge-invariant lattice discretization to compute the Berry-curvature. The optimized structures exhibit a clean valley-Hall gap with edge bands traversing the gap and high interface transmission in full-wave simulations. These results consolidate topology-aware geometry optimization for robust on-chip guiding.