二维光子晶体负折射率的数值分析  

Numerical Simulation for Negative Refractive Index of Two-dimensional Photonic Crystals

作　　者：朱璇笛 袁健华[1] Zhu Xuandi;Yuan Jianhua(School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]北京邮电大学理学院,北京100876

出　　处：《激光与光电子学进展》2021年第21期108-115,共8页Laser & Optoelectronics Progress

基　　金：国家自然科学基金(11671052,11871115)。

摘　　要：为了研究光子晶体负折射率所在的频率范围,基于有限元算法分析数值来求解二维光子晶体的带隙结构,这一过程涉及如何设计数学和物理模型,设计有限元算法的求解方程,对数值结果进行物理分析。首先使用有限元算法将布里渊区域内所有相关频率上波矢空间中的点都计算出来以绘制等频率面,然后绘制不同空气孔半径下的等频率面,最后在等频率面的结构上找到群速度为负的方向就能得到负折射率所在的频率区间。同时,比较不同空气孔半径对光子晶体负折射所在频率区间的影响,可为光子晶体器件的制备提供支撑。In order to study the frequency range of the negative refractive index of the photonic crystal,the band gap structure of the two-dimensional photonic crystal is solved by analyzing the numerical value based on the finite element algorithm.This process involves how to design the mathematical and physical models,design the solving equation of the finite element algorithm,and the numerical results were physically analyzed.First,the finite element algorithm is used to calculate the points in the wave vector space of all relevant frequencies in the Brillouin region to plot the isofrequency surface.Then,the isofrequency surface under different air hole radii is drawn.Finally,the frequency interval between the negative refractive index can be obtained by finding the direction with negative group velocity on the structure of the isofrequency surface.At the same time,comparing the influence of different air hole radii on the frequency range of the negative refraction of photonic crystals can provide support for the preparation of photonic crystal devices.

关 键 词：几何光学 光子晶体 负折射材料 等频率面 数值模拟 

分 类 号：O242.21[理学—计算数学]