Relative permittivity dependence of photonic band gaps for unit cells of the basic structural unit of two-dimensional decagonal photonic quasicrystals

In the basic structural unit of two-dimensional (2D) decagonal photonic quasicrystals (PQCs), the photonic band gaps (PBGs) of the four square unit cells in two constructions have been calculated as functions of relative permittivity. The different unit cells possess different PBG structures and different relative permittivity threshold values. For a given unit cell, the type of PBG and the variation in the center frequency of the PBG depend on the construction and the effective relative permittivity, respectively. We propose a qualitative relationship, Fεr=Fεr(q,εreff−1/2), for the PBG impact factors, where the construction-dependent factor q determines the PBG type. Depending on the relative values of the relative permittivity of the scatterers (εra) and the background medium (εrb), either the TM band gap dominates (εra>εrb) or the TE band gap and complete band gap dominate (εra<εrb). The variation in the center frequency of the PBG depends on the inverse square root of the effective relative permittivity εreff, i.e., εreff−1/2.