Properties Of Defect Modes In One-dimensional Photonic Crystals Containing Metamaterials

Recently, metamaterials in which both permittivityεand permeabilityμare negative, or only one of the two parametersεandμis negative, have been realized in microwave and near-infrared. When the metamaterials are introduced in one-dimensional photonic crystals, new types of photonic band gaps appear. Since the properties of such photonic band gaps are different from those of the Bragg gap, and they can lead to potential applications, one-dimensional photonic crystals containing metamaterials have become a subject of great interest for optical physics.When impurities are inserted into the one-dimensional photonic crystals, defect modes will emerge in the photonic band gap and have been used for the design of the filters, including single channel filters and multiple channel filters. To vary the structures by introducing the metamaterials is an effective way to obtain defect modes with unique properties. In this thesis, by means of numerical stimulations and theoretical analysis, the properties of the defect modes in one-dimensional photonic crystal containing metamaterials are investigated. The most important results are given as follows.(1) Defect modes inside the zero-n gap of one-dimensional photonic crystals stacking with positive- and negative-index materials are shown to possess three types of angle dispersion: positive, negative and near-zero types. The relations between the dispersion type of the defect modes and the structure parameters of the photonic crystal are given. Omnidirectional defect modes for TE or TM wave are obtained by the optimization of structure parameters of the photonic crystal.(2) An expression of the dispersion of the defect modes inside the Bragg gap or the zero- n gap of one-dimensional photonic crystals containing negative-index materials is derived. It is found from the expression that, the dispersion of the defect mode approaches to zero when the phase change on reflection from periodic stacks of the photonic crystals can cancel out the change of the optical phase thickness of the defect layer. Practical designs of defect modes with weak angle dependence for both TE and TM waves are given according to the conditions of the near-zero dispersion. In addition, narrow frequency and sharp angular defect mode is designed by combining two photonic crystals with defect modes of the positive and the negative types of dispersion, respectively.(3) Twin defect modes are found in one-dimensional photonic crystals stacking with two kinds of single-negative (permittivity- or permeability-negative) media layers, and a single-negative defect layer. The frequency interval of the two defect modes can be changed by merely varying the thickness of the defect layer or the ratio of the thicknesses of the two stacking layers. Conditions for the emergence of such twin defect modes are given by the analysis of the effective phase thickness of the defect layer and the two stacking layers.(4) Multiple omnidirectional resonance modes are generated in the periodic arrangement of photonic crystal (PC) heterostructures with two sub-PCs consisting of single-negative (permittivity- or permeability-negative) materials. From numerical simulations it is found that, the resonance transmission modes inside the zero-φeff gap of this periodic heterostructures are insensitive to incident angle. Moreover, as the periods of the heterostructure increases, the resonance transmission modes will split.