External Magnetic Field The Two-dimensional Magnetic Photonic Crystal Absolute Band-gap Structures

The band structures of the photonic crystal (PC) are difficult to be calculated, when the dielectric function or permeability of the composed materials is dependent on the frequency of light wave. Generally, the permeability of ferrite is related to the frequency of light wave. In thiswork, the effects of the external magnetic field (H_ex) on the properties of the two-dimensional(2D) magnetic photonic crystal (MPC), which is composed of ferrite materials, are investigated by the use of the expanded basis method.Firstly, the effects of the external magnetic field (H_ex) on the absolute photonic band gap(PBG) structures of the 2D ferrite MPC with a triangular lattice are investigated. The scatterers are air rods in the ferrite material media. The calculated results show that the width of the absolute PBG, the middle-frequency of the absolute PBG (it is called gap-mid), and the gap-midgap ratio are increased as H_ex is increased, when the filling factor (f) of the 2D MPC is 0.843.However, the values of the above quantities are smaller than that without external magnetic field. Furthermore, the absolute PBG is not closed by the change of the external magnetic field. In thecase with f =0.650, the behaviors of the absolute PBG in the low frequency range are similar to that of the case with f = 0.843 under the influence of H_ex. At the same time, there is a new absolute PBG in the high frequency range after the external field H_ex is applied. Both the width of absolute PBG and the gap-mid gap ratio decrease as H_ex increases, however, the middle-frequencies increase as H_ex increases. It should be noted that the absolute PBG is closed when H_ex is larger than 3.0(2πc·a^-1).Secondly, the effects of the external magnetic field (H_ex) on the absolute PBG structures ofthe 2D ferrite MPC with a square lattice are investigated. There are three kinds of scatterers: air rods in ferrite material media, square air rods in ferrite material media and square ferrite material media rods in air. The calculated results show that there are common features in the threestructures, i.e. the absolute PBG can be closed when the external field H_ex is applied. In addition to this, the width of the absolute PBG, the middle-frequency and the gap-mid gap ratio nearly increase as H_ex increases. However, there are some different features in these structures.The ranges of H_ex are different when the absolute PBGs are being closed, the range of H_ex forthe close of the PBG in the structure of air rods in media is the largest, that in the structure of the square air rods in media is the smallest and that in the structure of the square media rods is between them. Both the width of the absolute PBG and the gap-mid gap ratio in the structure ofthe air rods in media are increased as the H_ex increases, and they reach the largest valves at thesame time. The values of them are larger than that without external magnetic field. However, the middle-frequencies of the absolute PBG are smaller than that without external magnetic field.