摘要
超常材料(metamaterial)是近几年提出的一种新型人工材料。它具有和传统的天然材料不一样的电磁性质,通过特殊的微结构设计,超常材料可以具备负的介电常数或者负的磁导率,甚至能做到两者皆为负值。当材料的介电常数和磁导率中有一个为负值时,我们称这样的材料为单负材料。单负材料又可分为两种:若磁导率为负值,介电常数为正值,此单负材料称为磁负材料;反之,若介电常数为负值,磁导率为正值,则此单负材料称为电负材料。近几年来由于单负材料自身的一些特殊性质,它们受到了越来越多的关注。
本文重点研究了由单负材料组成的一维光子晶体的光学与电磁波传输特性以及线性与非线性的古斯-汉欣位移。文章主要内容为:
一、含单负材料的一维光子晶体的缺陷模特性
我们首先利用传输矩阵方法研究了由单负材料构成的一维光子晶体中包含缺陷时的电磁波传输性质。指出了在零有效相移光子禁带中,缺陷模的数量可以通过调节缺陷层本身的厚度或者层数来控制。数值结果还表明,在该带隙中的缺陷模基本不受入射光角度和极化模式的影响,并且对光子晶体自身结构尺度和无序效应也表现出弱敏感性。最后,我们推广有效媒质理论来对体系进行简化,从而得到了缺陷模频率的近似计算公式。利用该公式,我们可以很好的给出缺陷模出现的频率位置。
二、含单负材料一维光子晶体的古斯—汉欣效应我们研究由单负材料构成的光子晶体中的古斯—汉欣位移。发现在零有效相移带隙中,固定两种材料的厚度比时,改变入射光极化模式,可以得到可正可负的古斯—汉欣位移,而固定入射光的极化模式时,改变两材料厚度比也可以使古斯—汉欣位移由一个方向转变的另一个方向。同时我们还发现当材料的厚度比或者周期数达到一个临界点时,古斯—汉欣位移的大小将保持恒定不变。根据这个特性,我们结合有效媒质理论定性的讨论了产生古斯—汉欣位移正负转变的原因。最后,我们研究了在单负周期性结构中嵌入正常材料缺陷层时的古斯—汉欣位移,发现在缺陷模频率附近,古斯—汉欣位移可以得到大幅度的增强,并且随着入射角的增大,古斯—汉欣位移的幅度会增加但是突变处的频率位置基本保持不变。
三、含非线性缺陷的单负一维光子晶体的古斯-汉欣效应
我们主要研究了在由单负材料组成的一维光子晶体中嵌入非线性材料缺陷时的古斯—汉欣效应。我们发现,在零有效相移带隙和布拉格带隙的缺陷模频率附近,体系的古斯—汉欣位移同透射谱一样都展现出双稳特性。在零有效相移带隙中,当入射波分别为横电波(TE)和横磁波(TM)时,可表现出正和负的双稳变化。且在不同入射角时,古斯—汉欣位移的峰值位置比较稳定。而在布拉格带隙中,没有正负的变换并且古斯-汉欣的峰值受角度变化的影响比较大。随后,我们进一步研究了相位同入射角之间的关系,发现在不同的入射光强下,同角度的相位会在阈值附近出现跃迁变化,而在其他位置的变化相对比较平稳。同时,TE极化模式的古斯—汉欣位移随角度变化的影响比较小,而TM模式下的古斯—汉欣位移在两个阈值附近变化比较明显。
Metamaterial is a new kind of artificial material which is widely studied by many people.Different from nature material,metamaterial has many especial electromagnetic properties.By some special microstructure designs,it can be made to have negative permittivity(ε)or negative permeability(μ),or even double negative of bothεandμ. When the material has only one negative index,it is called single-negative material.The single-material has two different kinds:one is epsilon-negative(ENG)media withε＜0 butμ＞0 and another is mu-negative(MNG)withμ＜0 butε＞0.Recently,the single-negative material has attracted a great deal of attention due to its unusual electromagnetic properties.
In this thesis,we investigate the optical and electromagnetic properties of the one dimensional structure consisting of single-negative materials.The main contents are organized as follows:
Ⅰ.Characterization for defect modes of one-dimensional photonic crystals containing metamaterials.
Transmission studies for one-dimensional photonic crystals containing single-negative materials inserted with multiple defects are presented.We find that the numbers and positions of the defect modes inside the zero-φ_(eff)gap can be adjusted by changing the thicknesses or numbers of the defect layers.Then we study the characterization of the defect modes in different conditions.Numerical results show that these kinds of defect modes are nearly independent on incident angles and polarization,and almost insensitive to the scaling and disorder.In addition,we obtain the frequency equation for the defect modes based on the effective medium theory.Numerical results are in good agreement with those based on the transfer matrix method.
Ⅱ.Goos-H(?)chen effect in the gap of photonic crystals containing single-negative materials
Goos-H(?)chen effects for one-dimensional photonic crystals containing single-negative materials are investigated.Positive or negative GH shifts will appear alternatively in the zero-φ_(eff)gap by changing the polarization of the incident wave or the ratios of the thicknesses of the two different single-negative materials.When the numbers of the periods arrive some critical points,the GH shifts will be a constant.We theoretically explain these phenomena within the framework of the effective medium theory.When a defect layer is inserted,the both positive and negative GH shifts are enhanced at the defect modes.And the giant lateral shifts are almost insensitive to the incident angle.
Ⅲ.The Goos-H(?)chen shifts of the nonlinear defect in the one-dimensional structure composed of single negative materials
We investigate the GH shifts in the one-dimensional crystals containing single-negative when a nonlinear defect layer is inserted.It is found that both in the the zero-φ_(eff)gap and in the Bragg gap,the GH shifts in such structure can exhibits bistable behavior.More specially,in the zero-φ_(eff)gap,both the negative and positive bistability lateral shifts will occur with changing the polarization of the incident waves.And the peak of the GH shifts is almost invariant to the incident angle.But in the Bragg gap,they are seriously affected by the incident angle.By studying the relation of the phase(φ)and the incident angle(θ),we find that theφwill have a jumping-variation near the switch-up and switch-down threshold values.
引文
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