Band gap properties and self-collimation in a tenfold quasicrystal structure photonic crystals applying multicircular ring scatterers

In this paper, a kind of tenfold photonic quasicrystals based on the Penrose puzzle theory with the application of multicircular ring scatterers (MCRSs) is presented. It is divided into four kinds of square supercells and employed in a square lattice to constitute the first-order (1st), second-order (2nd), third-order (3rd), and fourth-order (4th) tenfold quasicrystal structure photonic crystals (TFQCSPCs) accordingly. In an attempt to evaluate the dispersion maps and equifrequency contour (EFC) profiles of such long-range ordered but not really periodic TFQCSPCs, an enhanced plane wave expansion (PWE) method is adopted. The photonic crystals (PCs) discussed in this paper are first classified into two major categories, air hole and dielectric column types which will be referred to as type 1, type 2 respectively in the following. The varying features of photonic band gaps (PBGs) of TFQCSPCs are inquired about by changing the refractive index (n) of the relevant medium and the number of rings (H) of MCRSs under two broad prerequisites of type 1 and type 2 PCs. The results are also compared with the associated properties of PBGs of traditional square lattice PCs (TSLPCs) and traditional triangular lattice PCs (TTLPCs) which employ MCRSs. Then, the 1st and 2nd TFQCSPCs and TSLPCs are fabricated in the form of hollow air holes dug in the silicon plate, and the transformation of their PBGs and EFCs is researched when the width (W) and H of the ring are adjusted. The possibility of implementing the phenomenon of polarization-insensitive self-collimation (PISC) in TFQCSPCs and TSLPCs is explored by examining the smoothest EFCs in EFC mappings. Eventually, our work actualizes the PISC phenomenon at seven normalized frequency (NF) values of 0.074, 0.168, 0.170, 0.172, 0.265, 0.270, and 0.297, which fills the gap of the PISC phenomenon in the low-frequency domain.