Fietz Chris, Urzhumov Yaroslav, Shvets Gennady
Dept. of Physics, The University of Texas at Austin, Austin, Texas 78712, USA.
Opt Express. 2011 Sep 26;19(20):19027-41. doi: 10.1364/OE.19.019027.
A finite element method (FEM) for solving a complex valued k(ω) vs. ω dispersion curve of a 3D metamaterial/photonic crystal system is presented. This 3D method is a generalization of a previously reported 2D eigenvalue method [Opt. Express 15, 9681 (2007)]. This method is particularly convenient for analyzing periodic systems containing dispersive (e.g., plasmonic) materials, for computing isofrequency surfaces in the k-space, and for calculating the decay length of the evanescent waves. Two specific examples are considered: a photonic crystal comprised of dielectric spheres and a plasmonic fishnet structure. Hybridization and avoided crossings between Mie resonances and propagating modes are numerically demonstrated. Negative index propagation of four electromagnetic modes distinguished by their symmetry is predicted for the plasmonic fishnets. By calculating the isofrequency contours, we also demonstrate that the fishnet structure is a hyperbolic medium.
提出了一种用于求解三维超材料/光子晶体系统复值k(ω)与ω色散曲线的有限元方法（FEM）。这种三维方法是先前报道的二维特征值方法[《光学快报》15, 9681 (2007)]的推广。该方法对于分析包含色散（如等离子体）材料的周期系统、计算k空间中的等频面以及计算倏逝波的衰减长度特别方便。考虑了两个具体例子：由介质球组成的光子晶体和等离子体渔网结构。通过数值演示了米氏共振与传播模式之间的杂化和避免交叉。预测了等离子体渔网中由对称性区分的四种电磁模式的负折射率传播。通过计算等频轮廓，我们还证明了渔网结构是一种双曲介质。
