光子晶体的能带结构研究及大带隙设计

【作者】 葛祥友；

【导师】 李平；

【作者基本信息】 山东大学 ， 光学工程， 2006， 硕士

【摘要】 光子晶体是一种具有周期性介电常数的介电材料。它最主要的特征就是具有光子带隙。频率落在光子带隙中的电磁波在光子晶体中无法传播，这样人们就可以根据实际需要来设计不同结构的光子晶体以实现对光的控制。由于光子晶体独特的性能和潜在的巨大应用，已经吸引了越来越多的关注，成为一个迅速发展的新的科学领域。 为了研究光子晶体的各种性质，我们首先需要在理论上对它的能带结构和性质进行研究。因此利用目前所知的处理复杂电介质结构中的Maxwell方程组的各种数值计算方法研究光子晶体的能带结构和带隙是本文的主要内容。光子晶体的理论研究发展了许多不同的理论计算方法，本文主要介绍平面波展开法及其在光子晶体中的应用。使用基于平面波展开的频域块迭代方法的计算机模拟软件计算二维及三维光子晶体的能带结构，并对其带隙规律进行研究。 第一章对光子晶体的基本概念及研究光子晶体所用到的基本原理进行了说明，并把光子晶体能带结构和电子的能带结构进行了比较。然后简要介绍了光子晶体的几项应用。第二章是光子晶体的能带理论与数值模拟，理论方法部分的主要内容是平面波法在光子晶体中的应用。数值模拟部分主要对二维和三维情况中的计算机模拟步骤作了说明，对模拟要用到的基于平面波的频域块迭代方法作了介绍。 计算结果部分首先给出了二维三角晶格各偏振模式的能带结构和场分布，根据场分布图分析了带隙出现的原因。然后分析了晶格参量对TM偏振带隙结构的影响。计算了三角晶格空气柱型光子晶体的完全带隙，并对影响完全带隙的各种因素进行了分析。此外还对一种各向异性介质二维三角晶格结构的能带结构进行了计算，与各向同性介质的晶格相比这种晶格具有更高的带隙。提出了一种相互嵌套的长方晶格正方介质柱的二维光子晶体模型，在介电常数比为12时得到了15.68％的大带隙，这种模型在一定参数范围内具有很好的稳定性，适合实际制作。同时还介绍了一些其他的具有大带隙的二维光子晶体的晶格结构。由于三维光子晶体在理论分析和实际制作上的困难，在三维光子晶体的讨论中，主要对面心立方晶格和钻石品格的能带结构进行了分析。钻石晶格可以看作两个简单的面心立更多还原

【Abstract】 Photonic crystals are periodically structured electromagnetic media, generally possessing photonic band gaps: ranges of frequency in which light cannot propagate through the structure. This periodicity, whose length scale is proportional to the wavelength of light in the band gap, is the electromagnetic analogue of a crystalline atomic lattice, where the latter acts on the electron wave function to produce the familiar band gaps, semiconductors, and so on, of solid-state physics.Photonic band structure calculations are performed for several two dimensional and three dimensional photonic crystal geometries. Using a plane wave expansion method, Maxwell equations are solved numerically with a frequency-domain computational method that takes the vector nature of the electromagnetic field into account.It is found that photonic band gaps exist in both two dimensional and three dimensional photonic crystal geometries. Specifically, we study the photonic band structure of the two dimensional triangular lattice and analyze qualitatively the influences of the structure parameters of photonic crystal lattice on its TM polarization band gap. Then the complete photonic band gaps of the two dimensional triangular lattice photonic crystal with air columns in dielectric materials are investigated and the maximum gap ratio is found to be 16.19% when the dielectric constant is 12. The influencing factors of the lattice are also summarized. In the last section of the chapter on two dimensional situation a new model composed of square rods in two rectangular lattices nested each other with large complete band gap is proposed and some other new models with large complete band gaps are also mentioned. In the new model with dielectric constant being 12 a complete band gap with 15.86% gap ratio is found and it is also found that to a certain extent the model has good stability. Moreover the complete photonic band gaps of the anisotropic triangular lattice photonic crystal are computed and much larger gaps than that of isotropic photonic crystals are found.In Chapter four photonic band structures of three dimensional face-centered更多还原