Optimizing Finite Structures to Suppress the Photonic Density of States

We propose a topology-optimization framework for optimizing finite structures of arbitrary shape by combining density-based methods with level-set approaches. We first optimize regular polygonal structures to suppress the photonic density of states and find that the best performing polygon is consistent with a tiling of space with hexagonal unit cells. We next show that introducing cavities into hexagonal structures further suppresses the photonic density of states, particularly when the cavity is also hexagonal. Such a result would find application in the design of fiber-optic cables. We then describe an approach for optimizing arbitrary x-simple or y-simple designs that can recover finite supercells of a hexagonal unit cell. Our approach can therefore discover the symmetry of photonic-crystal primitive unit cells that significantly suppress the photonic density of states for a given set of material parameters within a single optimization.