Study On The Bandgap Structure And Dispersion Characteristic In Two-dimensional Photonic Crystals

Recently, research on photonic crystal has become one of a focus all over the world. The basic characteristic of photonic crystals is its photonic bandgap. Therefore, it can provide novel mechanisms to control the flow of light, as a result, photonic crystal will. possess widely application prospect in optics communication and photonic integrated circuits. A new type of fiber, known as photonic crystal fiber, has emerged in the past several years, which have resulted in some unusual properties unattainable with conventional optical fibers. In particular, photonic crystal fibers can display near zero and flat dispersion in the visible and near-infrared. wavelength range, therefore, ithas great potential application.The bandgap structure in two-dimensional photonic crystal and dispersion properties of photonic crystal fibers are investigated theoretically in the dissertation by using the plane wave method and the finite-difference time-domain method. The theoretical research is given in the following.In chapter 1, the concept, characteristic and application of the photonic crystals is introduced. In addition, the concept, classifications, guiding light mechanism and dispersion characteristic of the photonic crystal fibre is also introduced in detail.In chapter 2, the bandgap distribution characteristic of hollow-core photonic bandgap guiding fibers with triangular and square structure is analyzed by using plane waves method. The condition of air-guiding of light in PBG-PCF are deduced, in order to guide light in the air-core of-the PBG-FCFs the ratio d/Λshould be larger than some specific values. In addition, we analyzed the influence on filling into medium in rods of cladding. The result indicate that the bandgaps increase with the ratio d/Λ. when increasing, the relatiye dielectric constant of the medium in rods of cladding, the width of bandgap is decrease. With the given normalized propagation constant, the filling coefficient has a best value, which the bandgap is maximal.In chapter 3, the total dispersion of photonic crystal fibers is obtained by summing up material dispersion and waveguide dispersion. A near zero and flat dispersion photonic-crystal fiber ranging from 1350 nm to 2010 nm can be designed by adjusting the diameter of the small air rod in the centre and the first ring of air rods, and the variety of dispersion is less than 0.5ps/(km·nm).In chapter 4,the bandgap of triangular structure two-dimensional photonic crystal composed of air rods with circular cross-section and the hexagonal cross-section is calculated by using plane wave method. The result indicate that the shape of cross-section of air rods is also one of factors that affect the position and width of the bandgap,if the ratio d/Λis same and the shape of the cross-section is different, its bandgaps are also different. The size of absolute bandgaps in two dimensional photonic crystals is often limited by band degeneracies at the lattice symmetry points. In order to gain the maximal bandgaps, we can reduce the lattice symmetry by introducing the addition different diameter rods and different shape of rods into the unit cell of two-dimensional photonic crystals. A two-dimensional compound lattices photonic crystal with rotating cylinders is designed, the bandgap of this structure is calculated by using plane wave method. The result indicate that a large absolute bandgap of this structure can be found by optimizing the parameters.In chapter 5,the composite two-dimensional photonic crystal is designed, the result indicate that the bandgaps of this structure are the result of superposing of other two photonic crystal bandgaps, so the bandgaps become wider, In addition, a new kind of defect structures in two-dimensional photonic crystals is designed, the transmission characteristics of light wave in two-dimensional photonic crystals including point defects and line defects are analyzed by using the finite-difference time-domain method. Based on this structure, a six-channel wavelength division multiplexing can be made with two-dimensional photonic crystals of micrometer scale, which has high transmission coefficient in the channels.In chapter 6,a two port wavelength division device in two-dimensional photonic crystals wave-guide is constructed based on self-imaging effect of multimode interference. The optical properties of two port wavelength division device have beendemonstrated theoretically by finite-difference time-domain method and plane wave method, in addition, we study the transmission rate in the output port of this device under a given coupling length, the result indicate that choosing the appropriate coupling length can make light to export in the two output ports. Further research shows, the transmission rate in the output port of this device can be improved by changing the radius of a medium rod in photonic crystals.