基于COMSOL弱形式方程求解色散光子晶体能带
Band Diagram Calculations of Dispersive Photonic Crystals Based on COMSOL Weak Form Equation
DOI: 10.12677/APP.2017.75021, PDF, HTML, XML, 下载: 4,258  浏览: 9,350  国家自然科学基金支持
作者: 徐云飞*, 杭志宏：苏州大学物理与光电?能源学部，苏州纳米科技协同创新中心，江苏 苏州
关键词: 数值求解；弱形式；光子晶体；能带结构；Numerical Methods； Weak Form； Photonic Crystals； Band Diagram
摘要: 为了研究光子晶体复杂色散关系，基于有限元数值仿真软件COMSOL Multiphysics, 我们发展了一套基于COMSOL弱形式方程光子晶体能带的计算方法。通过频率求解波矢k的本征值，将传统方法很难求解的色散能带问题转化为简单线性的本征值问题。利用这一新的数值工具，我们首先对比分析了无色散简单正方晶格光子晶体的体能带结构，弱形式方法与现有方法得到完全一致的能带结果，验证了这种计算方法的正确性。利用这种求解方法能快速求解光子晶体的等频率曲线(equi-frequency contour), 我们也验证了我们研究的正方晶格光子晶体具有类狄拉克锥能带结构。我们将这种方法应用于具有色散负介电常数背景下类石墨烯蜂巢晶格光子晶体的能带结构计算，这是传统光子晶体能带计算方法难以求解的结构。我们发现，在这种光子晶体的胡须状(Bearded)和锯齿状(Zigzag)界面都存在光子界面态。
Abstract: In order to study dispersive photonic crystals (PCs), we introduce a numerical finite element method based on weak form equation in COMSOL, which transforms the complex band diagram problem into a simple eigenvalue problem by solving the eigenvalue with respective to wave vector k by frequency. The advantages of the method are illustrated by two examples. The equi-fre- quency contours close to the Dirac-like cone dispersion of a square-lattice PC can be calculated with much less time than traditional methods. We also succeeded in obtained the edge states on the bearded edge and the zigzag edge of a honeycomb PC with a dispersive negative background medium which is numerical unstable for traditional methods.
文章引用：徐云飞, 杭志宏. 基于COMSOL弱形式方程求解色散光子晶体能带[J]. 应用物理, 2017, 7(5): 149-158. https://doi.org/10.12677/APP.2017.75021

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