Date of Award
Doctor of Philosophy (PhD)
Electrical and Computer Engineering
Dr. W. -P. Huang
Phonetic crystal waveguides and fibers are emerging waveguides that are formed based on relatively large-scale periodic dieletric materials, also known as the photonic band-gap materials. Modeling and simulation of such waveguide structures will help to gain understanding for the modal and transmission characteristics and their dependence on the key design and operation parameters. In this dissertation, the multilayer slab and circular photonic crystal waveguides are investigated theoretically with emphasis on their modal characteristics and transmission properties relevant to broad-band telecommunication systems and networks. Key performance parameters (e.g., the modal field, the modal effective index, the group-velocity dispersion, the confinement loss, the mode effective area, as well as the confinement factor, etc.) are simulated and analyzed by using both analytical and numerical methods. For the sake of completeness, a comprehensive review of the different mathematical methods for simulation and analysis of optical waveguides in general and photonic crystal waveguides in particular is presented. The theoretical frameworks for rigorous methods such as the finite difference method and the plane wave expansion method and for approximate methods such as the effective index method and the envelope approximate method are discussed, and their merits and shortcomings in modeling and analysis of photonic crystal waveguides and fibers are examined in great detail. The one-dimensional (1D) slab photonic crystal waveguides (PCWs) are the simplest to model and analyze, yet can offer deep insight into the salient features of photonic crystal waveguides and fibers. A somewhat exhaustive study for the modal properties of 1D PCWs is carried out with the help of the rigorous transfer matrix method. Four different guiding regimes due to the total internal reflection (TIR) and the photonic band-gap (PBG) are recognized, and their unique features are revealed and discussed. Further, scope of validity and level of accuracy for two insightful approximate methods (i.e., the effective index method and the envelope approximation method) are examined in detail by comparison with the exact solutions. Furthermore, new results about the effects of the number of unit cells (i.e., layer-pairs), the layer size-to-pitch-raio, and the core thickness on the modal properties are obtained and discussed. The two-dimensional (2D) photonic crystal waveguides such as the air-hole-filled photonic crystal fibers (PCFs) find more practical applications and also much more difficult to model and analyze. In this context, the modal analyses with different theoretical frameworks such as the scalar, semi-vector, and full-vector formulations are presented and discussed with the help of the finite difference method. It is demonstrated that the vector nature of the guided modes of the PCFs needs to be considered in analyzing the modal characteristics such as the dispersion. Based on the band structure of 2D photonic crystals, modal characteristics of the PBG-PCFs and TIR-PCFs are obtained and their physical behaviors are easy to explain. Also one new parameter is proposed to judge the single-mode operation of the PCFs, and the bending loss of the PCFs is calculated by the numerical method for the first time. Furthermore, the effects of finite number of air holes and size of interstitial holes on modal properties of the PCFs are investigated. Some scaling transformations of modal properties related to the design parameters of the waveguide structures are derived. Based on the rigorous analysis model and scaling transformations for the modal properties, a general procedure for design and optimization of the PCFs with desired modal properties is proposed. In comparison with the conventional design method, the new design procedure is more efficient and can be readily automated for the purpose of design optimization. Several applications of the design procedure (e.g., the design optimization for the dispersion shifted fibers, the dispersion flattened fibers, and the dispersion compensation fibers) are demonstrated.
Shen, Linping, "The Semiclassical Few-Body Problem" (2003). Open Access Dissertations and Theses. Paper 1251.