基于介质环形柱结构的二维光子晶体中狄拉克点的实现

发布时间：2018-04-24 14:27

本文选题：环形柱结构光子晶体 + 狄拉克点　；参考：《中国矿业大学》2016年硕士论文

【摘要】：单层石墨烯在有限温度下的成功获取,使得物理学以及材料学领域的发展掀开了一页新的篇章。而随后跟进的对类石墨烯光子晶体的研究,使光颤动、赝散射以及特殊边界效应等一系列奇特的物理性质得以发现,同时在类石墨烯光子晶体中利用偶然简并获得的零折射率材料在隐身方面的应用,使类石墨烯光子晶体成为当下光学材料研究领域的一大热点。本文在二维正方格子介质环形柱结构光子晶体中通过偶然简并成功地实现了狄拉克点,并对狄拉克点的具体实现过程进行了系统的探究,而探究过程中所用到的理论计算方法主要是平面波展开法。首先,本文在构建环形光子晶体模型后,对在环形光子晶体中实现狄拉克点的一般过程进行了探究。研究结果表明:在介质环折射率固定不变的情况下,当选取合适的介质环内外半径值时,在二维正方格子介质环形柱结构光子晶体的布里渊区中心可利用偶然简并来实现狄拉克点。同时通过研究还得到了在狄拉克点实现过程中晶体的第二、三、四能带的变化规律,并在随后的章节中对其进行了物理机理上的理论解释。其次,在固定环形光子晶体背景为空气不变的情况下,利用控制变量法,依次分别探究介质环内、外半径以及折射率这三个变量对实现狄拉克点的影响。研究结果表明,对于二维正方格子介质环形柱结构光子晶体,在一定的外径RO范围内(0.37aRO0.5a),当狄拉克点存在时(n1.4),介质环内径RI与外径RO满足一个不随介质环折射率n变化的恒定关系式。同时,狄拉克点对应的光子约化频率f随折射率n及外径RO的增大而减小。再次,基于狄拉克点处的光子约化频率f与外径RO之间在不同介质环折射率n时的统一表达式、(RO,RI)=(0.45a,0.26a)时的f-n函数关系式以及RI与RO之间的恒定关系式,在n取[2.8,4]范围内任一特定值时,实现对目标二维正方格子介质环形柱结构光子晶体的多个参数的预判,具体参数包括介质环内、外半径以及狄拉克点处的光子约化频率等,而预判结果的最大误差为4%。最后,本文就围绕狄拉克点在环形光子晶体中的实现所做的工作进行了总结,并对相关研究结果的潜在应用价值进行了展望。
[Abstract]:The successful acquisition of monolayer graphene at finite temperatures opens a new chapter in the development of physics and materials science. The subsequent studies of graphene like photonic crystals have led to the discovery of a series of peculiar physical properties, such as light tremor, pseudo-scattering and special boundary effects. At the same time, the application of zero-refractive index materials obtained by chance in graphene photonic crystals makes graphene photonic crystals become a hot spot in the field of optical materials. In this paper, the Dirac point is successfully realized by chance degeneracy in the two-dimensional square lattice dielectric annular cylindrical photonic crystal, and the concrete realization process of the Dirac point is studied systematically. The theoretical calculation method used in the process of exploration is mainly plane wave expansion method. Firstly, after constructing the ring photonic crystal model, the general process of realizing Dirac point in ring photonic crystal is discussed. The results show that when the refractive index of the dielectric ring is fixed, when the appropriate radius of the inner and outer dielectric ring is selected, In the center of Brillouin zone of two-dimensional photonic crystal with circular cylindrical structure in square lattice, the Dirac point can be realized by accidental degeneracy. At the same time, the second, third and fourth energy bands of the crystal are obtained in the process of Dirac point realization, and the theoretical explanation of the physical mechanism is given in the following chapters. Secondly, under the condition that the background of the ring photonic crystal is constant, the influence of three variables, the radius inside the ring, the outer radius and the refractive index of the ring, on the realization of Dirac point is studied by using the control variable method. The results show that for two-dimensional square lattice dielectric annular cylindrical photonic crystals, When the Dirac point exists, the internal diameter RI and the outer diameter RO of the dielectric ring satisfy a constant relation which does not change with the refractive index n of the dielectric ring. At the same time, the photon reduction frequency f of Dirac point decreases with the increase of refractive index n and outer diameter RO. Thirdly, based on the unified expression of the photonic reduction frequency f at the Dirac point and the outer diameter RO at the refractive index n of different dielectric rings, the f-n function relation and the constant relation between RI and RO are obtained. In the case of any particular value in the range of [2.8N4], the prediction of multiple parameters of the target two-dimensional square lattice dielectric ring structure photonic crystal is realized, including the inner and outer radius of the dielectric ring and the photon reduction frequency at the Dirac point, etc. The maximum error of the predicted result is 4. Finally, this paper summarizes the implementation of Dirac point in ring photonic crystals, and prospects the potential application value of related research results.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TQ127.11;O734

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