任意形状二维介质光子晶体带结构计算

用数值积分和蒙特卡罗的方法分别求解了介电常数分布函数的傅立叶展开系数,用平面波展开法计算了任意形状光子晶体的带隙结构。本方法结果与CST(Computer Simulation Technology)仿真模拟结果以及参考文献3]中的计算结果分别进行了对比,结果显示,计算结果吻合良好;并分析了禁带随光子晶体排列结构、填充比f和介电常数变化的关系。当光子晶体填充区域的介电常数较小,背景材料填充区域的介电常数较大时,H极化波在f=0.65左右时的带隙最宽,E极化波也开始出现禁带;而光子晶体填充区域的介电常数较大,背景材料填充区域的介电常数较小时,E极化波在f较小时出现了比较宽的禁带;光子晶体填充区域与背景材料填充区域的介电常数越悬殊,禁带的宽度越宽,归一化频率有下降趋势。

A Method of Calculating PBG Band Structures of Arbitrary Two-Dimension Dielectric Photonic Crystals

This paper calculates the expanded Fourier expansion coefficient of dielectric distributed function of arbitrary two-dimension photonic crystals and structures by methods of numerical integration and Monte Carlo and analyzed the PBG band structures of arbitrary two-dimension photonic crystals by PWM (Plane Wave Expansion Method). The results by the methods of this paper are accorded with the results of CST (Computer Simulation Technology) and Ref 3] very well. The obtained band-structures of the three photonic crystals structures in this paper demonstrate some rules when the dielectric constant of filling area is small and the dielectric constant of background area is large, the PBG-bands of the H polarization are extraordinary wide and the PBG bands of E polarization appear when the filling ratio is 0.65. When the dielectric constant of filling area is large and the dielectric constant of background area is small, the obtained PBG-bands of the E polarization are comparatively wide when filling ratio is small.