Magnetic Photonic Crystal Heterostructure And The Local Density Of States Of Two-dimensional Photonic Crystal

The properties of photonic crystals are investigates in this thesis. The contents include the following sections:(1)Photonic band gap (PBG) structures of two-dimensional magnetic photonic crystals (MPCs) in square lattice;(2)Guide modes in MPCs heterostructures in two-dimensional square lattices;(3)The density of states and local density of states of two-dimensional photonic crystals composed of circular cylinders in square lattice.Firstly, The PBG structures of the two-dimensional MPCs are calculated by use of the plane-wave expansion method. The MPCs consist of magnetic pillars in shapes of rectangular, square, hexagon and circular, respectively embedded in dielectric medium in square lattice. The optimal MPCs samples that possess the largest gap-mid gap ratio for every type of MPCs are obtained by scanning the three parameters (permeability, filling factor and rotating angle). The changes of the PBG structures are investigated when varying independently every one of the parameters and fixing the rest. The calculated results show that, in each sample, the middle-frequency of the PBG changes hardly with the variation of the filling factor or rotating angle, but decreases monotonously with the increase of the permeability. The PBG width increases to a top value and then decreases with the increase of each parameter. These results are helpful for understanding the PBG properties of the two-dimensional MPCs.Secondly, we construct theoretically the new type of mixed MPCs heterostructures composed of square lattice with the pillars in different shapes (rectangular, square, hexagon and circular). The photonic band structures are calculated by use of the plane wave expansion method in combination with supercell technique and the guide modes at interface are investigated. The guide modes at the interface of the MPCs heterostructures can be generated without any lattice distortion when the scattering pillars are in shapes of rectangular, hexagon, and circular. This result is quite different from the case in the non-magnetic PCs heterostructures in which the generating of guide mode needs the lattice distortion.Finally, the density of photonic states (DOS) and local density of photonic states (LDOS) of the two-dimensional photonic crystals composed of circular cylinders setting on square lattice are investigated by use of the plane wave expansion method. The calculated results show that the DOS and LDOS exhibit inconsiderably values in the pseudogap. The LDOS takes much larger values in the air cylinders areas and drops down suddenly at the boundary between the air cylinders and dielectric medium background. These characteristics of the LDOS are similar to that found in the two-dimensional photonic crystal composed of square air rods.