【作者】 赵永林；

【导师】 闫珂柱；

【作者基本信息】 曲阜师范大学 ， 理论物理， 2011， 硕士

【摘要】 光子晶体(Photonies crystals)是一种能够产生光子禁带的周期性光学微结构材料。它具有极其独特的光学性质和导光机制,在实际生活中具有多种潜在的应用价值。目前,关于光子晶体的研究已经成为光学和光电子学领域最前沿的项目之一。本文第一章详细介绍了光子晶体的概念、性质、应用领域和研究现状。由于此论文主要是利用平面波展开方法对二维光子晶体能带结构进行数值计算。因此,在第二章中对平面波展开法及其数值算法的推导做了详细的分析。第三章中,在二维正三角晶格光子晶体的基础上,通过改变晶体的晶格基矢构造了-种全新的周期结构。该周期结构的最小周期单元不再是传统意义上的等边三角形,而是一种更为优化的斜三角形结构。利用平面波展开法理论模拟了二维斜三角品格光子晶体完全带隙的情况,发现所设计结构的完全带隙宽度是二维正三角晶格光子晶体完全带隙宽度的4.32倍。分析了介质柱宽度,介质柱旋转角度以及相对介电常数对所构造结构的完全带隙的影响,所得结果对二维光子晶体的理论研究和实际应用有所帮助。为任意角度的二维光子晶体集成波导的研究和制作提供了理论基础。最后一章的主要研究工作是研究光子晶体波导的能带结构。同时,结合超原胞技术,计算出二维光子晶体波导的能带结构,并且根据计算讨论了介质柱宽度和缺陷介质柱介电常数对能带结构的影响。这些研究对光子晶体波导的设计具有实际指导意义。更多还原

【Abstract】 Photonic crystals were periodic optical micro-structure that were capable of generating photonic band gaps. It has many peculiar optical properties and unique light-guiding principle, so it has a number of potential applications in real life. Presently, the researching of PC has become the most advanced project in the optical and optoelectronic field.In chapter one, initial introduction about the concept, properties, application domain and research status quo of PC. In this thesis, Photonic band struetures of Two-dimensional (2D) Photonic crystals have been calculated based on Plane-wave expansion (PWE) method. So the plane-wave expansion method (PWE) and it’s numerical arithmetic are analyzed in the second chapter.In chapter three, Based on the two-dimensional equilateral triangular lattice photonic crystals, a new periodic structure is constructed by changing the unit cell-vector of the photonic crystals. The minimum construction unit of the periodic structure is no longer the traditional equilateral triangle, but an optimal oblique triangle. With the method of plan wave expansion, the band gap of two-dimensional oblique triangular lattice photonic crystals were simulated. The result shows that the absolute band gap width be 4.32 times wider than it produced by the two-dimensional equilateral triangular lattice photonic crystals. The influence on oblique triangular lattice photonic crystals by changing the width, rotation angle and relative dielectric constant of the dielectric column is analyzed. The results are very useful to the theoretical research and practical application of two-dimensional photonic crystals, and also provide a rationale for the research and fabrication of integrated two-dimensional photonic crystal waveguide at any angle.The main work of the last chapter is the analysis of Photonic Band Structures with photonic crystal waveguides. Then, combined with supercell technique, Photonic Band Structures of 2D photonic crystal waveguides were calculated. And, the influence factors on photonic band structures, such as width of Medium column and dielectric constant of defective Medium column, were discussed. These results have practical function to direct waveguide designing.更多还原