Analyzing the photonic band gaps in two-dimensional plasma photonic crystals with fractal Sierpinski gasket structure based on the Monte Carlo method

In this paper, the properties of photonic band gaps (PBGs) in two types of two-dimensional plasma-dielectric photonic crystals (2D PPCs) under a transverse-magnetic (TM) wave are theoretically investigated by a modified plane wave expansion (PWE) method where Monte Carlo method is introduced. The proposed PWE method can be used to calculate the band structures of 2D PPCs which possess arbitrary-shaped filler and any lattice. The efficiency and convergence of the present method are discussed by a numerical example. The configuration of 2D PPCs is the square lattices with fractal Sierpinski gasket structure whose constituents are homogeneous and isotropic. The type-1 PPCs is filled with the dielectric cylinders in the plasma background, while its complementary structure is called type-2 PPCs, in which plasma cylinders behave as the fillers in the dielectric background. The calculated results reveal that the enough accuracy and good convergence can be obtained, if the number of random sampling points of Monte Carlo method is large enough. The band structures of two types of PPCs with different fractal orders of Sierpinski gasket structure also are theoretically computed for a comparison. It is demonstrate that the PBGs in higher frequency region are more easily produced in the type-1 PPCs rather than in the type-2 PPCs. Sierpinski gasket structure introduced in the 2D PPCs leads to a larger cutoff frequency, enhances and induces more PBGs in high frequency region. The effects of configurational parameters of two types of PPCs on the PBGs are also investigated in detail. The results show that the PBGs of the PPCs can be easily manipulated by tuning those parameters. The present type-1 PPCs are more suitable to design the tunable compacted devices.