光子晶体能带理论及创新设计

摘要光子晶体是由不同种介电常数的材料间隔周期性排列而成的人工材料，它对光或者电磁波存在光子带隙PBG),在此频率禁带中的光子无法在该光子晶体中传播。由于光子晶体的能带结构有关于光线的频率，光线在晶体内的传播又与其能带结构相关，不同的能带有着不同的特性，例如负折射效应等独特的光学性质，具有广阔的应用潜力。本文的主要研究内容有：1.介绍了光子晶体的概念以及负折射效应和慢光效应这两个光子晶体的重要光学性质，研究了平面波展开法和有限时域差分法(FDTD)这两个光子晶体常用的计算方法。2.研究了等频法在判断光子晶体是否产生负折射效应，通过调制光子晶体的折射率实现光子晶体的负折射现象，改变其色散关系，通过二维正方晶格、三角晶格的能带仿真验证了光子晶体的负折射效应的研究方法。在研究以半径为0.30a的Si介质圆棒的二维正方晶格时，在归一化频率为0.231到0.2576处可能发生负折射效应，并通过软件Rsof的FullWAVE验证了光线折射路径，确认归一化频率为0.2443处的确发生了负折射效应。最后说明了一部分基于光子晶体负折射效应和正负折射效应的一些实际应用。3.介绍了光子晶体慢光效应的背景知识和研究过程及慢光产生的原理，通过破坏光子晶体的周期性，将以半径为0.20a的Si介质圆棒破坏（引入了半径为0.13a的缺陷介质棒)，发现了晶体在归一化频率为0.305发生强烈色散从而验证了慢光效应，详细介绍了目前基于慢光效应的部分应用。关键词：光子晶体、负折射效应、慢光效应ABSTRACTA photonic crystal is an artificial material composed of different dielectric constantmaterial intervals.It has a photonic band gap(PBG)for light or electromagnetic waves,and the photon in this frequency forbidden band cannot propagate in the photoniccrystal.Because the band structure of photonic crystal has the frequency of light,thepropagation of light in the crystal is related to its band structure,different energy hasdifferent characteristics,such as negative refractive effect and other unique opticalproperties,has broad application potential.The main research contents of this paper are:1.The concept of photonic crystal and the important optical properties of thenegative refractive effect and the slow light effect are introduced,and the commoncalculation methods of the plane-wave expansion method and the method of finitetime-domain difference (FDTD)are studied.2.The equal frequency method is studied to determine whether the photoniccrystal produces negative refraction effect,realize the negative refraction phenomenonof the photonic crystal by modulating the refractive index of the photonic crystal,change its dispersion relationship,and verify the negative refraction effect of thephotonic crystal through the energy band simulation of two-dimensional square latticeand triangular lattice.When studying the two-dimensional square lattice of Si mediumcircular rods with a radius of 0.30a,a negative refraction effect may occur at thenormalized frequencies of 0.231 to 0.2576,and the light refraction path was verified bythe FullWAVE of the software Rsoft,confirming that the negative refraction effect didindeed occur at the normalized frequency of 0.2443.Finally,we illustrate somepractical applications of the negative and negative refractive effect of photoniccrystals.3.This paper introduces the background knowledge of slow light effect and theresearch process of slow light production principle,by destroying the periodicity ofphotonic crystal,the radius of 0.20a Si medium round rod damage (introduced theradius of 0.13a defect medium rod),found that the crystal in the normalized frequencyof 0.305 strong dispersion to verify the slow light effect,the current application basedon slow light effect is introduced in detail.Keywords:photon crystal,Negative refraction effect,slow light effectⅢ目录1绪论………1.1研究背景.11.1.1光子晶体的研究历程11.1.2