The Mie resonance and dispersion properties in the two-dimensional superconductor photonic crystals with fractal structure

In this paper, the Mie resonance and dispersion properties in the two-dimensional (2D) superconductor photonic crystals (SPCs) with fractal structure under a transverse-magnetic (TM) wave are theoretically investigated by a modified plane wave expansion method, whose equations of calculations also are deduced. The configuration of 2D SPCs is the dielectric rods embedded into the superconductor Nb background with square lattices according to the iteration rule of Thue-Morse sequence (Th-MS). The calculated density of states and band structures are used to elaborate the Mie resonance in the proposed SPCs and the properties of photonic band gap (PBG) and defect mode, and the influences of configurational parameters on the dispersion properties are studied in detail as well. The calculated results demonstrate that the lower edge of PBG is flattened, which is originated from the Mie resonance, and two defect modes (quasi-localized states) appear in the PBG since Th-MS has the self-similarity and non-periodicity at the same time. The PBG and defect modes can be obviously trimmed off by changing those parameters.