Investigations on the two-dimensional aperiodic plasma photonic crystals with fractal Fibonacci sequence

摘要

In this paper, the properties of photonic band gaps (PBGs) and defect modes of two-dimensional (2D) fractal plasma photonic crystals (PPCs) under a transverse-magnetic (TM) wave are theoretically investigated by a modified plane wave expansion (PWE) method. The configuration of 2D PPCs is the square lattices with the iteration rule of the Fibonacci sequence whose constituents are homogeneous and isotropic. The proposed 2D PPCs is filled with the dielectric cylinders in the plasma background. The accuracy and convergence of the present modified PWE method also are validated by a numerical example. The calculated results illustrate that the enough accuracy and good convergence can be achieved compared to the conventional PWE method, if the number of meshed grids is large enough. The dispersion curves of the proposed PPCs and 2D PPCs with a conventional square lattice are theoretically computed to study the properties of PBGs and defect modes. The simulated results demonstrate that the advantaged properties can be obtained in the proposed PPCs compared to the 2D conventional PPCs with similar lattices. If the Fibonacci sequence is introduced into the 2D PPCs, the larger PBGs and higher cutoff frequency can be achieved. The lower edges of PBGs are flat, which are originated from the Mie resonances. The defect modes can be considered as the quasi-localized states since the Fibonacci sequence has the self-similarity and non-periodicity at the same time. The effects of configurational parameters on the characters of the present PPCs are investigated. The results show that the PBGs and defect modes can be easily manipulated by tuning those parameters.