The Study Of Light Propagation In One-dimensional Photonic Crystal Containing Metamaterials

Photonic crystals are periodically arranged dielectric structures, the essentialproperty of the photonic crystals is photonic band gap. The propagation ofelectromagnetic waves with frequencies within the gap is forbidden. The property canbe used to control the propagation of photon which is analogous to the case ofelectrons in semiconductors. So, the photonic band gap materials are deemed tointending photo-electricity materials. In recent years, metamaterials have attractedmuch attention theoretically and experimentally. Metamaterial is an artificiallymaterial which have specially response to electromagnetic field. The metamateialsinclude double-negative materials whose permittivity and permeability aresimultaneously negative, and single-negative materials which containpermittivity-negative medium or permeability-negative medium. They have manyelectromagnetic properties which are different from ordinary photonic crystals, suchas negative refraction, reversed Doppler shift, reversed Cerenkov radiation, focuswith plane slab, and so on.The important function of photonic crystals is to control the propagation of light.Generally, signal of light propagates in a form of serials of light pulses. Thepropagation of a pulse is related with material's dispersion. Material's dispersion canartificially change by constructing "artificially atom" and arraying these atomsproperly. Metamaterial is an artificially dispersive material, the behavior of pulse'spropagation is interrelated with frequency in this dispersive material. The dispersionof material originates from the interaction of light with matter.In this thesis, we consider the case that the dispersive media are put into theone-dimensional photonic crystal where the Bragg scattering and the materialdispersion influence the propagation of the light. We study the combined effect of thestructural dispersion and material dispersion on the light pulse propagation throughone-dimensional photonic crystals containing metamaterials.In chapter 2, by solving Maxwell equation, we get the transfer matrix which issuitable for photonic crystals containing positive refraction indices, negativerefraction indexes, or single-negative materials for monochromatic plane wave. The temporal-spatial behavior of light pulses is calculated by integrating all frequencycomponents.In chapter 3, we introduce the effective refractive index by means of thecomplex transmission coefficient. We study the influence of material dispersionoriginating from atom's oscillatory and structural dispersion originating from Braggscatter in photonic crystals containing the refractive index material withDrude-Lorentz model. We consider photonic crystals containing a Drude-Lorentzdispersive defect. When the defect is a negative dispersive material, find that theeffective refractive index depend on material dispersion and structural dispersion. Ifincreasing periods of dielectric media beside the dispersive defect, the effectiverefractive index increases. If increasing the defect thickness or oscillator strength, theeffective refractive also increase, and have an anomalous dispersion region betweenthe electric resonance and magnetic resonance frequency. When the defect which is apositive material with Drude-Lorentz model. Increasing periods of dielectric media,the defect thickness or oscillator strength, the group velocity can change between thesuperluminal propagation and subluminal propagation. So, we can freely tailormaterial's dispersion by suitability adjusting dispersive parameter and structuralparameter.In chapter 4, we consider the propagation of pulses through one-dimensionalphotonic crystals containing negative materials, and the temporal-spatial behavior ofthe pulse and Poynting vector. Because of existing a wider band gap in this photoniccrystals and the effective dispersion is smooth in the band gap, we find thetransmitted pulses is approximately kept its shape if pulse's carrier frequency lying inthe band gap of the photonic crystals. But for same short-pulse through ordinaryone-dimensional photonic crystals, the transmitted pulses are distorted. Whenconsidering the negative materials is dispersive, the pulse' propagation issuperluminal for the pulse's carrier frequency lying in zero-(?) gap and Bragg gap. Ifthe pulse' carrier frequency lying in the band edge, the propagation is subluminal.And we study the temporal-spatial evolutions behavior of Poynting vector. It is clearto know of the transport of energy within photonic crystals.In chapter 5, we consider the transmission behaviors of optical pulses through one-dimensional photonic crystals composed of alternating layer of two kinds ofsingle-negative materials. The material in which only the permittivity or thepermeability is negative is called single-negative materials. We find the transmissionshort-pulses can keep the shape by adjusting the ratio of the thicknesses of the twokinds of single-negative material. And we have also proved that the Hartman effectexists in the structure.