Phoamtonic designs yield sizeable 3D photonic band gaps

We show that it is possible to construct foam-based heterostructures with complete photonic band gaps. Three-dimensional foams are promising candidates for the self-organization of large photonic networks with combinations of physical characteristics that may be useful for applications. The largest band gap found is based on 3D Weaire-Phelan foam, a structure that was originally introduced as a solution to the Kelvin problem of finding the 3D tessellation comprised of equal-volume cells that has the least surface area. The photonic band gap has a maximal size of 16.9% (at a volume fraction of 21.6% for a dielectric contrast of 13) and a high degree of isotropy, properties that are advantageous in designing photonic waveguides and circuits. We also present results for two other foam-based heterostructures based on Kelvin and C15 foams that have somewhat smaller but still significant band gaps.
See Klatt, Steinhardt, Torquato PNAS (2019) https://doi.org/10.1073/pnas.1912730116