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Designing photonic topological insulators is highly non-trivial because itrequires inversion of band symmetries around the band gap, which was so fardone using intuition combined with meticulous trial and error. Here we take acompletely different approach: we consider the design of photonic topologicalinsulators as an inverse design problem and use topology optimization tomaximize the transmission through an edge mode with a sharp bend. Two designdomains composed of two different, but initially identical,C$_\text{6v}$-symmetric unit cells define the geometrical design problem.Remarkably, the optimization results in a photonic topological insulatorreminiscent of the shrink-and-grow approach to quantum-spin-Hall photonictopological insulators but with notable differences in the topology of thecrystal as well as qualitatively different band structures and withsignificantly improved performance as gauged by the band-gap sizes, which areat least 50 \% larger than previous designs. Furthermore, we find a directionalbeta factor exceeding 99 \%, and very low losses for sharp bends. Our approachallows for the introduction of fabrication limitations by design and opens anavenue towards designing PTIs with hitherto unexplored symmetry constraints.

Designing Photonic Topological Insulators with Quantum-Spin-Hall Edge States using Topology Optimization