Transport properties of electromagnetic waves in dielectric photonic quasicrystals

The transport properties of electromagnetic waves change at the transition of high-index dielectric photonic structures to the metamaterial regime. Here, we demonstrate the changes in the properties of the waves traveling through photonic quasicrystalline structures made of dielectric rods arranged in the nodes on a Penrose tiling lattice with ${C}₅$ rotation symmetry. We cannot use Bloch theorem in the study of aperiodic structures, so we consider full-scale structures to reveal Bragg- and Mie-type band gaps. A real-space metric allows us to define the period of the effective crystallographic planes in the quasicrystal and to relate the Bragg band gap to the lattice nodes in reciprocal space. We compared the quasicrystal structure with photonic crystals and found that transmission spectra in the band gap have similar profiles for both types of structures. The analysis of the magnetic field distribution in quasicrystal structures with high dielectric permittivity allowed us to recognize $\ensuremath{\mu}$ near-zero modes, which indicates that the structure acquires the metamaterial regime. The constructed phase diagram specified the metamaterial regime for the structure. Our results reveal the transport properties of photonic quasicrystalline systems in the metamaterial regime.