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Research On The Optical Properties Of Photonic Crystals Used Right-hand And Left-handed Materials

Posted on:2008-12-26Degree:DoctorType:Dissertation
Country:ChinaCandidate:Z J JianFull Text:PDF
GTID:1118360215979779Subject:Materials Physics and Chemistry
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The information industry in the 20th century bases on the electrommunication, but the electron as one kind of information carrier, can't meet with the high-speed communication. People find one faster carrier, the photon, to replace the electron. The material that can control the photon is photonic crystal. There are broad applications with the perfect photonic crystal, but the photonic crystal with defect is more popular for researchers. We can use the defect in the photonic crystal to guide the electromagnetic wave, and this photonic crystal with defect can be used to make photonic crystal devices. Studies of left-handed materials open a series of new challenging problems for theoreticians as well as for experimentalists. The complete understanding of the properties of left-handed materials requires the reevaluation of some well-known facts of the electromagnetic theory. There are no formulas with negative permeability in classical textbooks of electromagnetism. Application of the existing formulas to the analysis of left-handed materials may lead to some strange results. The theory of electromagnetic field has to be reexamined assuming negativeεandμ. So, guided by this point, we performed some studies relative to left-handed materials.The main contents of this dissertation are described as follows.(1) The band structures of square lattice photonic crystal and hexagonal lattice photonic crystal have been computed in the second chapter. The results indicate that there is a smooth and isolated band in the band gap if photonic crystal has a dot defect. Appearance of this isolated band means that there will be a very high transmission rates for electromagnetic wave with certain frequency. We have developed a new numerical method—the impedance analytical method, which can be used to analysis the reflection coefficient, character equation and field distribution of one dimensional photonic crystal waveguide. The calculated results of transmission coefficient indicate that this new method can be applied to compute photonic crystal and total internal reflection. We also get the relation between normalized propagation constant and wavelength of the first forth modes by solving the character equation of one dimensional photonic crystal waveguide with the impedance method. The results are identical with the relevant papers. We have calculated the band structure and localized modes of two dimensional photonic crystal straight waveguide with finite difference time domain method. Localized modes of photonic crystal waveguide are very different from those of photonic crystal with dot defect. We have designed and analyzed some kinds of demultiplexers with FDTD.(2) Based on analyzing the relation of the width of the frequency band gap and parameters of grafted branches, the affecting of dielectric and the length of grafted branches on the width of band gap were studies and numerical calculation results were given.(3) Based on the transfer matrix for the bilayer structure, we compute the density of states along the axis of the finite one-dimensional photonic crystal, which is constructed out of N such bilayer structures periodically. The computations show that, under some conditions, there appear some unusual densities of states in the band gaps. These unusual densities of states are due to the discrete propagation modes peculiar to the photonic crystal composed of alternative left-handed and right-handed materials, and can be used to make very narrow filters totally different from any conventional types of filters. From the dispersion relation of the one-dimensional photonic crystal with alternative left-handed and right-handed materials, we calculate its band structure, discuss its peculiar discrete modes and photon tunneling modes, compare its peculiar zero-(?) band structure with the conventional Bragg band structure, and obtain some interesting results.(4) We have demonstrated the strong focusing effects of a point source and a plane wave by 2D photonic crystal structure formed by air holes in dielectric background with concavo-concave interface with the finite-difference time-domain technique. The far-field focus of a plane wave is obtained out of the photonic crystal structure while a strong focusing beam is also formed for a point source placed in the far place from the photonic crystal interface. Negative refraction is expected to be a significant step towards the novel imaging optics and can lead extensive applications in optical system design. Focusing of good quality is expected to be of great important for novel imaging optics and can lead to considerable changes in optical system design.(5) We take further research into the property of spontaneous emission of a two-level atom embedded in photonic crystals, one-dimension comblike photonic crystals for example. The properties of spontaneous emission depend not only on the relative position of the resonant frequency from the edge of the photonic band gap and the photonic mode density but also on the relative distance of the atomic space position from the sideband. The control of spontaneous emission of a three-level atom embedded in photonic crystals was investigated. As it shows, the properties of spontaneous emission depend not only on the relative position of the resonant frequency from the edge of the photonic band gap and the photonic mode density but also on the initial atomic state.
Keywords/Search Tags:photonic crystal, band structure, defect, waveguide, density of states, transmission coefficient, dispersion equations, left-handed material, transfer matrix, localized states, spontaneous emission, atomic population, emission spectrum
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