Luo Ma, Liu Qing Huo
Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA.
J Opt Soc Am A Opt Image Sci Vis. 2010 Aug 1;27(8):1878-84. doi: 10.1364/JOSAA.27.001878.
The goal of this work is to analyze three-dimensional dispersive metallic photonic crystals (PCs) and to find a structure that can provide a bandgap and a high cutoff frequency. The determination of the band structure of a PC with dispersive materials is an expensive nonlinear eigenvalue problem; in this work we propose a rational-polynomial method to convert such a nonlinear eigenvalue problem into a linear eigenvalue problem. The spectral element method is extended to rapidly calculate the band structure of three-dimensional PCs consisting of realistic dispersive materials modeled by Drude and Drude-Lorentz models. Exponential convergence is observed in the numerical experiments. Numerical results show that, at the low frequency limit, metallic materials are similar to a perfect electric conductor, where the simulation results tend to be the same as perfect electric conductor PCs. Band structures of the scaffold structure and semi-woodpile structure metallic PCs are investigated. It is found that band structures of semi-woodpile PCs have a very high cutoff frequency as well as a bandgap between the lowest two bands and the higher bands.
这项工作的目标是分析三维色散金属光子晶体（PCs），并找到一种能够提供带隙和高截止频率的结构。确定具有色散材料的光子晶体的能带结构是一个昂贵的非线性特征值问题；在这项工作中，我们提出一种有理多项式方法，将这样的非线性特征值问题转化为线性特征值问题。谱元法被扩展用于快速计算由德鲁德模型和德鲁德 - 洛伦兹模型建模的实际色散材料组成的三维光子晶体的能带结构。在数值实验中观察到指数收敛。数值结果表明，在低频极限下，金属材料类似于理想导体，此时模拟结果趋于与理想导体光子晶体相同。研究了支架结构和半木堆结构金属光子晶体的能带结构。发现半木堆光子晶体的能带结构具有非常高的截止频率，以及最低的两个能带与较高能带之间的带隙。
