Theory Of The Electromagnetic Characteristics Of Three-dimensional Anisotropic Photonic Crystal Research

Since the pioneering work of Yablonovitch and John, there appears a growing interest in the research of photonic crystal (PC) which is a lattice structure composed of basic building blocks arranged periodically in another background medium. There appears, in such lattice structures, photonic bandgap (PBG) that is a frequency range in which electromagnetic waves are forbidden from propagation and the spontaneous emission can be prohibited as well. The above property offers us the unprecedented degrees of freedom in the manipulation and control of photons, consequently, leading to many potential applications in photonics.As semiconductor crystals affect the properties of electron, PCs affect the properties of photons in much the same way, accordingly, it is called the semiconductors of light. Considerable efforts have been made theoretically and experimentally in search of the PCs with complete PBG. Previous studies concentrating on the isotropic constitutes have proved that, for the PCs consisting of spherical dielectric material, the complete PBGs can be found in diamond structure and inverse opal structure.Introduction of anisotropy, either in shape or in dieletricity can break down the symmetry, leading to the lift of degeneracy, which may result in the appearance of complete PBGs. Researches have been performed before within the framework of the plane wave expansion and the finite difference time domain method, the results have shown that in the two dimensions case anisotropy are effective in opening up complete PBGs, however, in three dimensional case the efficacy of dielectric anisotropy is limited. The dissertation is devoted to the study of the effectiveness of dielectric anisotropy on the creation of the PBGs in simple lattice structures. It is organized as follows.In chapter one we present the background introduction, which is made up of four parts: concept of PCs; new physics and application of PCs; fabrication method; scheme of the dissertation. In chapter two we have extended the Mie theory to handle the scattering properties of 4 kinds of dielectric sphere with anisotropy (magnetically gyotropic anisotropy, electrically gyrotropic anisotropy, uniaxially dielectric anisotropy, biaxially dielectric anisotropy), the scattering matrices are obtained. The merit of this method lies in that the boundary conditions are taken into account exactly, therefore, it is rigid. In chapter three we have deduced KKR method within the framework of multiple scattering theory, by incorporating the scattering matrix of dielectric sphere, the photonic band structure can be calculated. Furthermore, the numerical calculation guarantees good convergence and reliable results can be obtained.In chapter four we have investigated the capability of uniaxially/biaxially dielectric anisotropy in modulating the photonic band structure. The results demonstrate that for fcc lattice structure there exist two partial PBGs among which the lower one lies between the 2nd and the 3rd bands and the upper one lies between the 4th and the 5th bands. The lower PBG exists in one third of the first Brilloin zone while the upper one can appear, simultaneously and complimentarily, in the rest two thirds of the first Brillouin zone. In addition, our calculation results suggest that the lower one prefers smaller anisotropy and the upper one prefers larger anisotropy. With the variation of the anisotropy, the photonic band structures are modulated, the evolution of the PBGs in different situations are discussed. Compared with uniaxial case, biaxial anisotropy can offer much more flexibility in modulating band structures, which leads to the appearance of desired PBG.In chapter five we have calculated the photonic band structures of PCs consisting of uniaxially/biaxially dielectric spheres with extraordinary axis along [111] direction. Our results demonstrate that complete PBGs can be found in both fcc and sc lattice structures which are absent in PCs composed of isotropic dielectric spheres. Moreover, compared with uniaxial case biaxially dielectric anisotropy could enhance the anisotropy further, leading to the lift of the degeneracy atΓpoint between the 3rd and the 4th band, which results in the appearance of a newly created partial PBG. The relation between gap to midgap ratio and the filling fraction is studied as well for fcc PCs consisting of biaxially dielectric spheres.