The effect of symmetry on the optimal design of two-dimensional periodic materials

Topological distribution of dielectric materials within a unit cell has a significant effect on how waves propagate through the material. Through topology optimization, the configuration of a periodic material´s unit cell can be designed to specification. In many applications, it is desired to have a unit cell with as large a band gap as possible. In this paper we use Genetic Algorithms (GA) to optimize the design of unit cells in order to maximize the material´s band gap. We explore a number of approaches for the parametrization of the unit unit cell design. All of these approaches exploit different symmetries on the unit cell. We have examined transverse-electric and transverse-magnetic wave propagation with the aim to maximize the first band gap. The results show that the specialized GA operators have a dramatic effect on optimization performance. The results also imply that the type of symmetry constraint has a significant effect on the unit cell design and band gap size.