Optical Transmission Properties Of Photonic Crystals Containing Metamaterials

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 into 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 which leads to potential applications, photonic crystals containing metamaterials have become a hot issue in present research. In this thesis, by means of numerical stimulations and theoretical analysis, we investigate transmission properties of photonic crystals containing metamaterials. The major contents and most important results are given as follows.(1) Frequency response of photonic heterostructures consisting of single-negative materials is studied. We structure heterostructures by useing two photonic crystals with different band gap. The results show that the interface modes emerge on every interface of the heterostructures when the heterostructure is zero effective refractive index. Due to coupling between interface modes, waves can propagate by tunneling. In the case of zero effective refractive index, tunneling mode is independent of incident angles and polarizations and periods and have zero phase delay, which can be utilized to design zero-phase-shift omnidirectional multiple-channeled filters. With the increase of incident angles and period number of unit structure , the frequency of the tunneling mode situated the center of thezero-φ_eff gap is unchanged, while the frequency of the tunneling modes situated bothsides of the center of the zero-φ_eff gap shift to the center.(2) Multiple-channeled filters of photonic heterostructures containing single-negative materials are investigated. The results show that the number oftunneling modes inside the zero-φ_eff gap is equal to the number of heterojunction M, and can be used as M channels filter. When losses are involved, the results show that the electric fields of the tunneling modes decay largerly with the increase of the number of heterojunction and damping factors. Besides, the relation between the quality factor of multiple-channeled filters and the number of heterojunction M is linear, and the quality factor of multiple-channeled filters decreases with the increase of the damping factor, these results provide a feasible method to adjust the quality factor of multiple-channeled filters.(3) We study the local modes of one-dimensional photonic crystals consisting of single-negative permittivity and single-negative permeability media using transfer matrix methods. The results show that there exists a pair of resonant tunneling modes in this structure. The separation of the pair of tunneling modes can be tuned by varying the ratio of thicknesses of the two single-negative layers or the thickness of the defect layer. The electric field intensity of the resonant tunneling modes enhance exponentially with the increase of the ratio of thicknesses of the two single-negative layers. With the increase of the ratio of thicknesses of the two single-negative layers, the electric field of the tunneling modes becomes more localized, and the full width at half maximum of the tunneling modes becomes narrower. Besides, the pair of tunneling modes is insensitive to incident angle and thickness variation. These properties will be used for the design of tunable omnidirectional double-channel filter with high quality factor.(4) Transmission properties studies of one-dimensional photonic crystals consisting of mu-negative and positive index materials are presented by using transfer matrix methods. The results show that transmission properties of TE wavesdepend onε, while transmission properties of TM waves depend onμ, there exists atransmission band inside single-negative gap in this structure, and the transmission band is insensitive to the incident angle for the transverse electric waves but sensitive for the transverse magnetic waves. The position of the center axis of the transmission band is sensitive to the thickness of the positive-index layers, while the width of the transmission band is only dependent on the thickness of the mu-negative material layers. The position and width of the transmission band can be modulated independently by varying the thicknesses of positive index material and mu-negative material layers respectively. The tunneling mode is localized strongly inside positive index material layer, and the electric field enhance exponentially with the increase of the thickness of the mu-negative layers. We derive theoretically analytical expression of the resonant tunneling condition.