In this study, we explore the photonic band gap properties of two-dimensional quasiperiodic tiling approximants: the Ammann-Beenker tiling, the square-triangle tiling, and the Hexagon-Boat-Star (HBS) tiling. Air cylinders are placed at every vertex of the prototiles on a dielectric background, and the plane-wave method is used to calculate both TE and TM gaps. We confirm the existence of a complete gap in the square-triangle tiling and the HBS tiling. Notably, the HBS photonic approximant exhibits the first complete gap observed in a quasiperiodic structure with 10-fold rotational symmetry. To enhance the band gap, secondary air cylinders are introduced at the center of each star prototile in both the Ammann-Beenker and HBS tilings, increasing the point density. As a result, a small complete gap emerges in the Ammann-Beenker tiling, while the HBS tiling shows a significant enlargement of the gap. We further analyze the structural properties of these quasiperiodic tilings through the hyperuniformity and discuss how an ideal structure, characterized by high point density and low complexity, contributes to photonic band gaps. This work paves the way for more efficient designs in photonic technologies, with potential applications in optical sensors and novel laser systems.
Takemori et al. (Thu,) studied this question.