Designing photonic topological insulators with quantum‐spin‐Hall edge states using topology optimization

Designing photonic topological insulators (PTIs) is highly non‐trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of PTIs as an inverse design problem and use topology optimization to maximize the transmission through an edge mode past a sharp bend. Two design domains composed of two different but initially identical C 6ν ‐symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a PTI reminiscent of the shrink‐and‐grow approach to quantum‐spin‐Hall PTIs but with notable differences in the crystal structure as well as qualitatively different band structures and with significantly improved performance as gauged by the band‐gap sizes, which are at least 50% larger than in previous designs. Furthermore, we find a directional β‐factor exceeding 99% and very low losses for sharp bends. Our approach allows the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto‐unexplored symmetry constraints.