一维光子晶体的禁带宽度分析

闽江学院

本科毕业论文(设计)

题目一维光子晶体的禁带宽度分析

学生姓名

学号

系别电子系

年级03

专业电子科学与技术

指导教师

职称副教授

完成日期2007.05.16

目录

摘要 (2)

ABSTRACT (3)

第一章绪论 (4)

1.1什么是光子晶体？ (4)

1.2光子晶体理论计算方法 (5)

1.3光子晶体的应用 (8)

第二章一维光子晶体基本理论 (9)

2.1光子禁带的产生 (9)

2.2一维光子晶体的特征矩阵 (11)

第三章一维光子晶体带隙变化规律的研究 (13)

3.1带隙随厚度比的变化 (13)

3.2带隙随折射率差的变化 (16)

3.3带隙随角度的变化 (19)

3.4厚度比与折射率差同时变化下的最大带隙 (22)

总结 (24)

参考文献 (25)

摘要

光子晶体的研究领域非常广泛，涉及到光学的方方面面。由于它所具有的特殊的性质，故被称为光的半导体，足见它对光学领域的影响力。虽然这个领域的工作也才刚开始10年多一点，但是进展非常地快。通过对这个领域的深入研究.不仅对光子晶体研究本身有意义，而且对光学领域的理论发展也具有重要的价值。使得人们对光的理解更加深入。

介绍了一维光子晶体的基本概念和原理系统综述了对一维光子晶体的研究进展和应用前景。

作为一维光子晶体的应用基础,一维光子晶体的禁带是研究的重点。一维光子晶体的带隙决定了工作频率范围，因此研究其带隙变化规律是其应用的关键，通过改变各种参数确定带隙的依赖因素及其定量关系。

通过传输矩阵的方法分析了一维光子晶体禁带的特性,讨论了影响带宽的因素，说明了相对带宽对光子晶体设计的重要性。在这个基础上讨论了扩展一维光子晶体带宽的方法,：1、使各层介质的厚度d微微变化，形成规则递增，达到展宽禁带的目的。2、角度 逐渐变化，使晶体在角度域化互相叠加，达到扩展带宽的目的。3、使晶体的折射率n1逐渐变化（n2＝4.6），达到扩展带宽的目的。通过画出改变各种参数的情况下的带隙曲线图，得到带隙随各参数变化的规律，从而达到对一维光子晶体带隙变化规律的分析。

关键词:光子晶体;光子禁带;相对带宽;展宽。

ABSTRACT

The research field of photonic crystal is very abroad,it comes down to each aspect of optics.It is called photic semiconductor,due to its special property,which shows its influence to optical doman.The research of this doman develops quite quickly,although it has just begun for only 10 years.The further study for the doman not only make sense of the research of the photonic crystal,but also have important value to the theoretic development of optical doman.It makes humankind’s further comprehension of photics.

This article introduces the basic conceptions and principles of one_dimensional photonic crystal,and summarizes the research development and application foreground.

As the applied basement of one_dimensional photonic crystal,the forbidden band of one_dimensional photonic crystal is the emphasis of the research. The frequancy range is decided by the forbidden band of one_dimensional photonic crystal,so investigation over its mutative rule is the key of its application.In this article we will change each parameter to fix the reliant factors of the forbidden band and its quantitative relation.

By using a transfer matrix method,we will analyse the characteristic of the forbidden band of one_dimensional photonic crystal,and discuss factors which influence the forbidden band,which shows the importance of relative bandwidth for photonic crystals.Basing on what has being studied,we discussed the method to enlarge the bandwidth:first, change the thickness(d) slightly, regularly increase,in order to enlarge the bandwidth;second, change the angle( )slightly,make the crystals overlapps each other in angle region so as to enlarge the bandwidth;third,change the refractive index(n

) slightly,n1=4.6,which can also enlarge the bandwidth.By 2

drawing the forbidden band graphs,we will find the regulation so that we can analyse the changing regulation of the forbidden band of one_dimensional photonic crystal.

Key words: photonic crystal, photonic forbidden band, relative bandwidth, expand.