基于有限元方法的二维光子带隙几何形状和参数优化

发布时间：2019-04-19 05:41

【摘要】：光子带隙是光子晶体的基本特性,带隙频率范围内的电磁波在光子晶体中传播会被禁止。本文基于电磁场理论和数值算法主要研究了二维光子晶体的带隙优化设计问题。在TE模和TM模偏振模式下,考虑影响二维方形晶格光子晶体带隙结构的几何和参数因素,包括对称、旋转、半径大小和折射率等因素。本文通过数值模拟的方法,对影响二维方形晶格光子晶体带隙结构主要几何和参数因素进行了分析研究。电磁波在光子晶体中的传播主要是由Maxwell方程组决定,在TE模或TM模偏振模式下,该问题可以转化为周期边界条件的Helmholtz方程系统。对于该微分方程系统,本文分别采取平面波展开法和有限元方法进行数值求解。首先,本文用平面波法对较简单二维结构进行初始探究和优化,分析了 “方形介质”、“圆形介质”和新设计“方形环介质”等基本结构的能带,得到了“初步推断破坏对称性有助于产生宽带隙和改变几何形状的过程具有渐近稳定性”的结论。进一步,用精度更高的有限元法进一步分析了复杂二维结构,如新设计的椭圆和45°斜椭圆结构等,得到了“破坏几何对称性和旋转介质可以增大带隙”的结论。本文进行了大量的数值模拟实验,实验结果不仅设计了若干优化的光子晶体结构,还展示了新的设计方案在优化带隙中的效果。通过对在MATLAB和COMSOL软件上设计的实验结果分析可见,文中新设计的“方形环介质”结构和“从圆形到椭圆再到45°斜椭圆的变化结构”过程,带隙均有所改善,达到了优化的目的。实验结果表明本文的算法设计和优化过程是行之有效的。
[Abstract]:Photonic band gap is the basic characteristic of photonic crystal. The propagation of electromagnetic wave in photonic crystal will be forbidden in the band gap frequency range. Based on the electromagnetic field theory and numerical algorithm, the band gap optimization design of two-dimensional photonic crystals is studied in this paper. In the polarization modes of TE mode and TM mode, the geometric and parametric factors affecting the band gap structure of two-dimensional square lattice photonic crystals are considered, including symmetry, rotation, radius and refractive index. In this paper, the main geometric and parametric factors affecting the band gap structure of two-dimensional square lattice photonic crystals are studied by numerical simulation. The propagation of electromagnetic wave in photonic crystals is mainly determined by Maxwell equations. In the polarization mode of TE mode or TM mode, the problem can be transformed into a Helmholtz equation system with periodic boundary conditions. In this paper, the plane wave expansion method and the finite element method are used to solve the differential equation. Firstly, in this paper, the plane wave method is used to explore and optimize the simple two-dimensional structure, and the energy bands of the basic structures such as "square medium", "circular medium" and "square ring medium" are analyzed. A conclusion is obtained that "the process of destroying symmetry is conducive to the generation of wide band gap and the asymptotic stability of the process of changing geometric shape". Furthermore, the complex two-dimensional structures, such as the newly designed ellipse and the 45 掳oblique ellipse structure, are further analyzed by the more accurate finite element method, and the conclusion that "the destruction of geometric symmetry and rotating medium can increase the band gap" is obtained. In this paper, a large number of numerical simulation experiments are carried out. The experimental results not only design several optimized photonic crystal structures, but also show the effectiveness of the new design scheme in the optimization of band gaps. Through the analysis of the experimental results designed on MATLAB and COMSOL software, it can be seen that the new design of the "square ring medium" structure and the "changing structure from circle to ellipse to 45 掳oblique ellipse" have improved the band gap and achieved the goal of optimization. The experimental results show that the algorithm design and optimization process in this paper is effective.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O734

【相似文献】