Optimized structures for photonic quasicrystals

A photonic quasicrystal consists of two or more dielectric materials arranged in a quasiperiodic pattern with noncrystallographic symmetry that has a photonic band gap. We use a novel method to find the pattern with the widest TM-polarized gap for two-component materials. Patterns are obtained by computing a finite sum of density waves, assigning regions where the sum exceeds a threshold to a material with one dielectric constant, 1, and all other regions to another, 0. Compared to optimized crystals, optimized quasicrystals have larger gaps at low constrasts 1/0 and have gaps that are much more isotropic for all contrasts. For high contrasts, optimized hexagonal crystals have the largest gaps.