光子晶体的光学传输特性研究

【作者】 石宗华；

【导师】 闫珂柱；

【作者基本信息】 曲阜师范大学 ， 理论物理， 2006， 硕士

【摘要】 近几年来,光子晶体已成为国内外的研究热点之一。本文的工作主要集中在光子晶体的反常折射,含负折射率材料的光子晶体,以及光子晶体光纤三个方面: 1.对于一维光子晶体反常折射的研究大都基于光子晶体的色散关系解析解,本文认为,在光线非正入射时上述方法是不适用的,有必要使用更加合适的方法对一维光子晶体的折射规律加以系统研究,从而对一维光子晶体器件的设计起到些指导作用。文章将一维光子晶体作为二维问题来考察,使用数值方法（平面波展开法）来计算光线在光子晶体中沿各个方向传播时的色散关系,进而得到了折射角与入射角和频率的关系。结果表明:对于一维光子晶体,考查在第一能带范围内的频率,当频率越接近能带边,且入射角越接近敏感区时,折射角对入射角和频率的变化越敏感。而且,敏感区随频率的增大有向小角度移动的趋势。 2.采用光学传输矩阵方法,研究了由正折射率材料和负折射率材料交替组成的一维光子晶体中带有缺陷层时的光学传输特性。计算了含有普通电介质插层和有吸收的介质插层两种情况下的透射谱。结果表明,在正入射时,对于普通电介质插层,随插层厚度的增大,缺陷模的个数增多;对于有吸收特性的介质插层,随插层厚度的增大和吸收特性的增强,缺陷模式并没有出现,而是表现为对透射峰的明显增益。 3.利用已有文献对光子晶体光纤色散特性的计算结果,分析了色散随光子晶体光纤结构参数变化的趋势,并利用有效折射率方法基于标量近似理论对光子晶体光纤色散特性进行了有目的性的数值模拟,发现通过独立调整纤芯大小,可以在光通信波段实现非常接近零色散的色散平坦光子晶体光纤,其色散系数D的绝对值在1.3～2.0μm波长范围小于1.5ps·km^-1·nm^-1。更多还原

【Abstract】 Recently, photonic crystal has become one of the focuses of researchers all over the world. The paper is about the three aspects followed: abnormal refraction of photonic crystal, photonic crystal containing negative refraction materials, and photonic crystal fibers.1. With plane wave method, the relation between the incident angle and refraction angle and frequency in one-dimensional photonic crystals are investigated. It is found, when frequency is near the edge of band and incident angle is near the sensitive domain, the varition of refracton angle is sensitive;while frequency increase, the sensitive domain moves to small angles.2. By "means of transfer matrix method, the transmission properties of one-dimensional photonic crystals containing negative refraction materials （with a defect layer in it） were investigated. The transmittance were calculated, which include two kinds of conditions: normal dielectric layer and absorbing dielectric layer. It is shown that, on normal incidence, for the normal dielectric layer, the number of the defect modes increase with the increase of width of the layer;for the absorbing dielectric layer, with the increase of width and absorbing of layer, the defect mode will not emerge, instead, the peak of transmission were increased.3. Using the results of printed papers, the trend of the dispersion with different structures is analyzed. Based on scalar approximation the dispersion property of photonic crystal fibers are investigated by an effective index approach in this paper. It is found that the photonic crystal fiber with closing to zero and flattened chromatic dispersion is obtained by changing the core diameter independently. Which has absolute value less than 1.5 ps ? km^-1 ? nm^-1 in dispersion coefficient D at the wavelengths from 1.3μ m to 2.0 μm.更多还原