二维光子晶体的带隙结构和缺陷态研究

【作者】 肖清武；

【导师】 李晓春；

【作者基本信息】 中南大学 ， 光学， 2007， 硕士

【摘要】 光子晶体是一种介电常数呈周期性排列的人工复合材料，光波或电磁波在其中传播时会出现“禁带”现象，利用光子晶体的禁带特性可以控制光的传播，从而在光信息处理方面带来潜在的巨大应用，光子晶体也因此成为世界性的研究热点和前沿。本文在详细推导平面波展开法和时域有限差分方法(FDTD)的基础上，以二维光子晶体为模型，运用平面波展开法和时域有限差分方法，研究了介质参数、晶格结构、组元、缺陷等因素对光子晶体带隙及电磁波传播的影响。首先，研究了二维二组元体系中介电常数比、填充率、柱体形状和排列方式对光子晶体带隙宽度的影响，发现：介电常数比越大越容易形成宽带隙；随着填充率的增大，带隙宽度先增大后减小；柱体形状和排列方式对带隙结构也有很大的影响。对二维三组元GaAs／玻璃／空气包层体系的研究发现：在相同的晶格排列下，三组元体系较二组元体系更容易得到宽带隙，且第三组元GaAs圆柱芯体系的最低带隙较方柱芯体系的大，但它们的带隙宽度随填充率的变化规律基本相同；通过对圆柱芯体系三个组元填充率的优化组合可以得到△ω=0.1848的宽带隙。其次，研究了二维二组元体系中点缺陷、线缺陷的透射频谱和电场幅度分布，以及实缺陷柱填充率变化对带隙结构的影响。发现玻璃／空气和GaAs／空气两体系中，由于不同的组元体系，其带隙结构也明显的不同，但都会在原完整体系的带隙中出现缺陷态，且这些缺陷态都是局域化的，电磁波将被局限在缺陷位置进行传播。因此，利用点缺陷、线缺陷可制作光滤波和光波导器件。缺陷带的频率位置和宽度受实缺陷柱填充率的调制。最后，研究了二维三组元异质缺陷柱体系和三组元包层体系中的缺陷模及电场幅度分布。研究表明：在二组元体系中引入第三组元异质线缺陷后，原二组元体系的带隙频率位置、宽度可能发生一定的变化，同时会出现缺陷态；缺陷态频率主要受第三组元物性参数的影响，它们的缺陷态都具有较好的波导特征。三组元包层体系中，由于存在较宽的带隙，引入缺陷后，其缺陷态的调节更加容易；通过对缺陷结构的设计，不同频率的光波在传输过程中，由于缺陷的耦合作用不同，而具有不同的空间输出行为，从而实现特定频率光波的引导传播和分频滤波功能。更多还原

【Abstract】 Photonic crystal is a kind of manufactural composite material withperiodic arrangement of dielectric constant. Either light-wave orelectromagnetic wave can appear photonic band gap when they propagatein the photonic crystal. The propagation of light-wave can be controlledby using the characteristic of band gap. And many potential applicationsin photonic communications can be expected. So the research of photoniccrystals becomes the worldwide hotspot and foreland.In this paper, based on the particular introduction of the plane waveexpansion and FDTD method, the influences on photonic crystal bandgap and propagation of electromagnetic wave were investigated in 2Dphotonic crystal by the dielectric medium parameter, structure of crystallattice, material component, defect and so on.Firstly, the influence on photonic crystal band gap was investigatedby the ratio of dielectric medium constant, the filling fraction, the shapeof insertion and the manner of arrangement. It was shown that the biggerthe ratio of dielectric medium constant, the easier the band gap appeared.The band gap became wider at first and narrower later with theaugmentation of filling fraction. And the band gap of PC was closelyrelated with the shape of insertion and the manner of arrangement. Theresearch of 2D three-component GaAs/glass/air envelope-system showedthat three-component system got the wide band gap more easily thantwo-component system in same arrangement of crystal lattice. And thelowest band gap of the third component GaAs with column core waswider than with square core in the three-component system, but thechange trend of band gap with filling fraction was the same. The bandgap of optional design of the three components’ filling-fraction in columncore system reached△ω=0.1848.Secondly, the transmission and the distribution of electric field of 2Dtwo-component system with point cavity defect/linear defects wereinvestigated. And the influence of defect rods filling fraction on band gapstructure was also studied. The results showed that the band gap structures in glass/air system is obviously different from that in GaAs/airsystem, but the defect states were produced in formerly band gap of thetwo integrated system, and these defect states were all localized. So thepropagation of electromagnetic wave will be localized in the defectposition. Therefore, some special filter states/guided states would beformed. The position and width of defect bands were modulated by thefilling fraction of defect rods.Finally, the defect states and the distribution of electric field werestudied in 2D three-component heterogeneous pole system andthree-component envelope-system. It was shown that the third componentmaterial was introduced into two-component system as defect, theposition and with of band gap would be perhaps changed and produceddefect states. The defect states/bands frequency was affected by the thirdcomponent material’s physical parameter. And their defect states hadgood wave-guide character. In three-component envelope-system, themodulation of defect states became easier by introducing defects in wideband gap. Owing to the coupling effects among defects which light-wavepropagated in, light-wave with different frequency had differentpropagation behavior, and light propagating of wanted frequency can beallowed by designing suitable combined defects.更多还原