光子晶体禁带特性的研究

【作者】 曾辉；

【导师】 杨亚培；

【作者基本信息】 电子科技大学 ， 光学工程， 2006， 硕士

【摘要】 光子晶体是一种新型的光学材料,它是将不同介电常数的介质材料在一维、二维或三维空间内组成具有光波长量级的周期性结构。由于其独具特色的传光机理,人们对光子晶体的理论分析和实验研究产生了极大的兴趣。目前,对光子禁带特性的研究仍然是该领域的研究热点之一。本文介绍了光子晶体的发展,总结了光子晶体的研究现状,应用领域和设计制作。光子晶体的许多应用都是基于“光子禁带”特性。本文直接推导得出了周期性结构中光子禁带产生的数学依据。最终得出了一维周期结构的数学解的限制条件,证明了一维周期结构必然产生非连续解,该非连续部分即是光子禁带;且该非连续解解与介电常数比和填充比有关。本文分别运用平面波传输法和时域有限差分法对不同结构的光子禁带进行了分析,分析两种算法结果存在的差异。提出要减小设计与实际制作之间的差异,有必要在理论设计时将两种方法结合起来,对于禁带范围的确定,应尽量以两种方法的禁带的重合区域的中心作为实际禁带区域中心考虑。运用平面波展开法对各种情况下的禁带进行了仿真计算。结果表明:不同的晶格结构、介电常数比、填充比和柱体形状对禁带都会产生影响。特别是介电常数与填充比在一定范围内与禁带宽度成正比关系;柱体形状的微小差异也会引起禁带的明显改变。这些特性对光子晶体的设计具有明显的指导意义。采用了微带线方法来实现光子晶体结构。设计了微带PBG结构的周期尺寸,对影响禁带的各个因素进行了计算。通过对S参数仿真结果观察,发现微波波段的光子禁带同样受到第四章中各种规律的影响。选用了5周期结构的正方单元结构,制作成为微带光子晶体结构,进行了测量并分析了测量结果。测量结果与仿真结果符合较好,证明了仿真结果的正确性。更多还原

【Abstract】 Photonic Crystals are new-style optical materials. It was composed by permittivity with periodic structure in one、two or three dimension. Because of the characteristic theory of the Photonic Crystals, People are interested in the theoretical analyse and laboratorial research of Photonic Crystals. Presently, the photonic band gap is one of hotspot in research.The development of Photonic Crystal is introduced first, and then the author summarizes the status , applications and factures of the Photonic Crystal.The most applications of the Photonic Crystal base on the photonic band gap (PBG). One-dimensional Photonic Crystal are discussed and one-dimensional PBG’s existence are directly proved by mathematical way. Finally the restrictive condition of the mathematical answer were got, that is why the one-dimensional periodic structure can make the PBG and PBG related to the permittivity contrast and the filling contrast.The plane-wave expansion method (PWE) and the time-domain finite difference method (FDTD) are used to analyse the different structures’PBG .The difference of the answers are discussed. In order to reduce the difference between the design and and the product, it’s necessary to combine the two method and choose the superposition of two method’s band-gap as the center band-gap.By the plane-wave expansion method, PBG’s rules are found by changing the Photonic Crystal structures, permittivity and filling contrast. The permittivity and filling contrast are direct ratio to the band-gap in some rage; the nuance of the column can make the visible change of the band-gap. These properties are important to design. Photonic Crystals are realized in micro-strip. The periodic size are calculated. The different structures’S-parameter are presented and analyzed. The simulated result are good agreement in our result in chapter 4. At last, considering the stop-band range and S parameter, a five-period structure are choosed to realize and test it. The testing result agree with the calculate answer.更多还原