Topologically evolved photonic crystals: Breaking the world record in band gap size

Using topology optimization, a photonic crystal (PtC) unit cell can be designed to exhibit favorable electromagnetic wave propagation properties. Among these is the opening of a band gap (BG) with the largest possible ratio of width to midgap frequency. In this paper the aim is to maximize the relative size of the first and fourth relative BGs of two-dimensional (2D) PtCs with a square lattice configuration. In addition, we examine the effects of the degree of unit cell symmetry on the relative BG size and on the geometric traits of the optimized topologies. We use a specialized genetic algorithm (GA) for our search. The results show that the type of symmetry constraint imposed has a significant, and rather subtle, effect on the unit cell topology and BG size of the emerging optimal designs. In pursuit of record values of BG size, we report two low-symmetry unit cells as an outcome of our search efforts to date: one with a relative BG size of 46% for TE waves and the other with a relative BG size of 47% for TM waves.