Unfolded band structures of photonic quasicrystals and moiré superlattices

We apply the band-unfolding approach to explore the dispersions of different types of photonic quasiperiodic structures, including photonic quasicrystals that have high-rotational symmetry but lack translational symmetry, and moir\'e superlattices, which are a twist of two primary lattices. The band-unfolding approach provides a simple picture to get the band structure of such quasiperiodic structures, which can be directly compared with experimental results. We envision this approach will be a basic method for introducing the rich concepts of photonics in condensed-matter physics to photonic quasiperiodic systems.