Theoretical Reseach On Two Dimensional Photonic Crystal Slab And Optical Logic Devices

In this thesis, we focus our research on guided resonances in two dimensional photonic crystals slabs: how these resonances couple with modes outside the slabs, and design functional devices based on these optical properties analyzed; Then we design an air waveguide which is based on one dimensional photonic crystal and two dimensional photonic crystal slab combined-structure, and light propagation in this waveguide is analyzed; Finally we design an optical'not'logic gate device, and combined with the devices we design in this thesis, we expect to achieve more compact optical logic devices.The main works are listed below:(1) Programs to study optical properties of photonic crystals both in time domain and frequency domain are developed. Plane wave method is used to obtain band diagrams of photonic crystals in frequency domain. Scattering Matrix method is used to study transmission properties and guided resonance in two dimensional photonic crystal slabs. Finite Difference of Time Domain method is used to study light transmission properties, it can be used for analysis of photonic crystal of various shape. We can compare the results obtained by the frequency domain method with the results obtainded by the time domain method.(2) Optical properties of two-dimensional photonic crystal films'Brewster angle distribution are analyzed. Photonic crystal films are drilled with elliptical holes. If the films'parameters are properly set, it is found that their optical behaviors are similar with Brewster angles of conventional homogenious films, but Brewster angle distribution is quite different from that determined by conventional Brewster's law. Applications may be found in polarized and others modern optical devices.(3) Phase effect on the guided resonances in photonic crystal slabs is analyzed. We present an analysis in the case of a mirror symmetric system and an asymmetric system irradiated from both sides, as well as the more realistic and interesting case of a system bounded from one side by a perfect mirror. Gain is incorporated in the system, mainly to exemplify the results. Finally we find that phase effects persist in the asymmetric system resulting in a periodic response for the reflectivity versus the distance from the mirror, which is the main parameter controlling the phase relationship between the two incident waves. This effect still persists in two dimensional photonic crystal slab with point defect, which has leaky mode in the vertical direction.(4) A combined one dimensional photonic crystal and two dimensional photonic crystal slab hetero-structure is designed. It is shown that air line defect and 60 degree bend line defect in the two dimensional photonic crystal slab support lossless light propagation. The structure is more easily to be fabricated than three dimensional photonic crystals.(5) Optical filters based on dielectric omnidirectional reflectors are theoretically analyzed both in frequency domain and in time domain. It is shown that an optical filter can be made by drilling periodic air holes in a dielectric omnidirectional reflector. The filter's optical properties can be controlled by varying the lattice constant and the radius of air holes without changing the reflector's thickness. Thus different filters can be easily integrated in one reflector. A flat-top optical filter is also designed with few changes of the structure. This kind of filter is expected to be used in optical communication devices and vertical cavity surface emitting lasers.(6) A'not'logic gate device is designed and analyzed. When input wavelength of light isλ1, the output wavelength of the light isλ2 and keeps this state, and vice versa. Time needed to changing the two states is about 0.1ns.