Dielectric metamaterials with hexagonal lattice

We consider all-dielectric photonic structures with electric response consist of dielectric rods arranged in a hexagonal lattice. We construct gap map as a function of rod permittivity for a constant filling factor by analyzing photonic band diagrams. A near-boundary phase with a strong spatial dispersion is found, whereas in the case of a square lattice this phase does not exist. We observe epsilon-near zero modes in a metamaterial phase, which do not depend on a lattice orientation and a structure boundary.