Study On The Characteristics Of Photonic Crystals Waveguide And Its Functional Devices

Photonic crystals waveguide (PCW) works in any frequency range as long as the working wavelength and the structure size are in the same scale. It has the advantages of wide bandwidth, narrow wave-packet at optical wavelength. It is widely used in optics communication to construct integrated optical functional devices. Therefore, it has realistic significance to carry out study on the dispersion characteristics of the functional devices which is designed based on such structures. In this dissertation, based on the dispersion relation and its application in two dimensional (2D) PCW, we made further study on the dispersion of transmittance mode of photonic crystals slab waveguide (PCSW). This study could provide some theoretical guide lines for the applications of photonic crystals in the future integrated optics systems. Some important and valuable results which bring forth some new ideas are accomplished, as listed below:1. The plane wave expand method (PWE) is used to investigate the dispersion and band-gap peculiarity for different structures of two dimensional photonic crystals (2D PCs). The relationships among Q quality, defect frequency of the two dimensional PCs and defect radius are analyzed. The dispersion peculiarity of 2D PCs linear waveguide and the transmission spectrum of the double defect waveguide are investigated. A channel drop filter with feedback structure in the 2D PCs is designed. When the phase difference between the feedback and drop structure is odd number of?, by suitable tuning of the Q quality between the drop waveguide and the main waveguide plus the double cavities, a 100% drop efficiency is achieved.2. The dispersion relationship of the coupled cavities waveguide (CCW) is investigated. Taking into account the fact that interaction occurs only between consecutive cavities, the coupled cavities dispersion curve is fitted by the tight-binding (TB) formalism. The theoretical modal of the group velocity, group delay, dispersion, dispersion slope are obtained from the dispersion formula. Simultaneously, the transmission spectrum of the straight waveguide and bend waveguide are studied by the means of finite difference time domain method (FDTD). A 3dB coupled cavities beam splitter is designed based on this study. Based on the slow-wave effect (low group velocity), a directional coupler (DC) is designed and the length of the coupler is decreased by making use of the strong interaction of the light and material. Comparing to the directional coupler which is designed based on linear waveguide, an additional parameter of the radius with the coupled defect zone is introduced and that makes the design of coupled cavities waveguide directional coupler more flexible. By optimizing the parameters, the coupling length is reduced to 1/3 of a standard coupler. The obtained extinction ratio -36.08dB is about the same as that of the linear defect photonic crystals waveguide directional coupler.3. Firstly, the three dimensional band diagram and equifrequency surface (EFS) are derived from the plane wave expand method (PWE). From the EFS, the maximum flatness half width (MFHW) and the normalized frequency are obtained. The relationship between (MFHW) and filling fraction Pf , dielectric ratio?b?aare alse determined. Secondly, the relationship between the parameters of the 2D air ring PCs self collimation effect and the inner and outer radius are investigated by the PWE with modified dielectric equation. Lastly, based on the self collimation effect, the transmission of the imaginary waveguide is studied. By taking inner radius r = 0.3R, outer radius R = 0.3a of the basal structure and r?= 0.48R, R?= 0.4R of the edge structure, the maximum transmission obtainable is 94.86% at the central normalized frequency?= 0.270.4. In order to make the PCs useful in a real integrated optics system, the super-cell PWE is employed to analyze the dispersion of the photonic crystals slab (PCS). By analyzing the parameters of the PCs effect on the photonic band gap and the thickness impact on the width of the photonic band gap, the PCs with square lattice dielectric rods type and triangular lattice air holes type are chosen as the fundamental structure to investigate the dispersion of the photonic crystals slab waveguide (PCSW). The dispersion of the transmittance modes are analyzed with the radius of the defect bigger or smaller than the fundamental PCS. These studies could provide some useful information on the applications of PCs to integrated optics.