Inverse design of photonic and phononic topological insulators: a review.

Photonic and phononic topological insulators (TIs) offer numerous opportunities for manipulating light and sound with high efficiency and resiliency. On the other hand, inverse design methodologies, such as gradient-based approaches, evolutionary approaches, and deep-learning methods, provide a cost-effective strategy for developing photonic and phononic structures with unique features in steering light and sound. Here, we discuss recent advances and achievements in the development of photonic and phononic TIs employing inverse design methodologies, including one-dimensional TIs, TIs based on the quantum spin Hall effect (QSHE) and quantum valley Hall effect (QVHE), and high-order TIs in lattices with diverse symmetries. Several inversely designed photonic and phononic TIs with superior performance are exhibited. In addition, we offer our perspectives on the future of this emerging study field.