| In recent years, there has been a growing interest in studying periodic dielectric materials which have a gap in the density of states for electro-magnetic waves. These materials are now called photonic band gap (PBG) materials. They not only exhibit fundamentally new physics such as photon-atom bound states, but also offer many new technological application.; This dissertation is aimed at developing a theoretical understanding of these novel materials. Specific calculations include the following area. First the Korringa-Kohn-Rostoker (KKR) method has been extended to electro-magnetic waves in 2D for the computation of the photonic band structure. The results obtained by using KKR method and the plane-wave method are compared and in excellent agreement with each other. Second a method, which is commonly used in studying low-energy electron diffraction in conventional crystals, is presented to calculate the complex band structures and transmission spectra of two-dimension PBG materials. The matrices involved in this method are substantially smaller than those required for the plane-wave method. With this method, the attenuation lengths for frequencies within the forbidden bands are computed automatically with the band structure calculation. Reflection and transmission characteristics of crystals of finite thickness are also computed. Comparisons of our results with the available experimental data in general show rather good agreement. The application to frequency-dependent or complex dielectric functions are also discussed.; Then another on-shell method, which combines plane-wave and finite-difference techniques and shares the advantages of plane-wave and layer-KKR methods, is developed for the calculation of dispersion curves and transmission spectra. Results of the calculation are compared with experimental data measured using ultra-wide band microwave pulses for a two-dimensional PBG crystal. |
