Inverse Design of the Topology–Bandwidth Trade-Off in Valley Photonic Crystals

Valley photonic crystals provide a route to broadband domain-wall guiding, but increasing the bulk gap can delocalize Berry curvature and reduce the nonquantized valley-Chern number. We introduce a mixed-integer particle-swarm framework that searches polygonal VPC unit cells and maps the Pareto trade-off between normalized bandgap and valley topology using the bulk objectiveT=(Δf/f0)2|Cv|. The selected designs are then evaluated independently using full-wave transport simulations through disorder-averaged propagation-length extraction in 200a domain-wall waveguides with positional disorder σ = 0.01a. Across the studied design ensemble, the extracted propagation length exhibits a positive empirical association with |Cv|, providing a direct multidesign connection between the patch-integrated valley-Chern number and quantified disorder-limited transport in this VPC family. The framework therefore treats bandwidth, valley topology, and device robustness as distinct but connected quantities, enabling balanced inverse design rather than optimization of a single transport metric alone.