Topology‐Optimized 3D Photonic Structures with Maximal Omnidirectional Bandgaps

Abstract

Three-dimensional photonic crystals with large omnidirectional bandgaps are critical for diverse device applications, but have been challenging to design due to their structural complexity. A topology optimization algorithm based on the evolutionary topology optimization method to design omnidirectional bandgaps on demand is proposed. Considering an asymmetric simple cubic lattice, large bandgaps between any two neighbor bands are successfully realized and novel 3D photonic structures obtained. The topology-optimized designs have a uniform bicontinuous character, which originates from the orthogonal distribution of electric fields at the bounds of the bandgaps. The distribution of the dielectric material follows the directions of the wave vectors of the maximum frequencies at the lower bounds. Consequently, the macroscopic effective properties, such as permittivity, exhibit corresponding directionality. The isotropy of effective permittivity indicates the flatness of the lower bound and photonic crystals with large bandgaps tend to have isotropic effective permittivity.