Creating acoustic topological insulators through topology optimization

Abstract For the realization of topologically protected wave propagation, engineering artificial structures of topological insulators (TIs) inspired by quantum mechanics has attracted extensive attention over the last few years. However, the existing structures commonly compose of a regular shape of inclusions for the limited arrangements in the unit cell. This paper develops a topology optimization approach for designing novel structures of acoustic TIs. With the mechanism of acoustic TIs based on the quantum spin Hall effect (QSHE), topology optimization first seeks sonic crystals (SCs) with double Dirac cones of dipolar and quadrupolar modes. Then, topology optimization creates topological trivial and non-trivial SCs by breaking the double Dirac cones, which freely assemble into acoustic TIs. The optimized structures exhibit the typical functionalities of acoustic TIs, the robust propagation and spin-locked unidirectional transmission of topological edge states, verifying the effectiveness of the proposed approach.