Bao Huaguang, Kang Lei, Campbell Sawyer D, Werner Douglas H
Opt Express. 2019 Apr 29;27(9):13116-13128. doi: 10.1364/OE.27.013116.
An efficient discontinuous Galerkin time domain (DGTD) method with a generalized dispersive material (GDM) model and periodic boundary conditions (PBCs), hereto referred to as DGTD-GDM-PBCs, is proposed to analyze the electromagnetic scattering from dispersive periodic nanostructures. The GDM model is utilized to achieve a robust and accurate universal model for arbitrary dispersive materials. Using a transformed field variable technique, PBCs are introduced to efficiently truncate the computational domain in the periodic directions for both normally and obliquely incident illumination cases. Based on the transformed Maxwell's equations with PBCs, the formulation of the DGTD method with a GDM model is derived. Furthermore, a Runge-Kutta time-stepping scheme is proposed to update the semi-discrete transformed Maxwell's equations and auxiliary differential equations (ADEs) with high order accuracy. Numerical examples for periodic nanostructures with dispersive elements, such as reflection and transmission of a thin film, surface plasmon at the interfaces of a metallic hole array structure, and absorption properties of a dual-band infrared absorber are presented to demonstrate the accuracy and capability of the proposed method.
提出了一种具有广义色散材料（GDM）模型和周期性边界条件（PBC）的高效时域间断伽辽金（DGTD）方法，在此简称为DGTD-GDM-PBC，用于分析色散周期性纳米结构的电磁散射。利用GDM模型为任意色散材料建立了一个稳健且准确的通用模型。采用变换场变量技术，引入PBC以在周期性方向上有效地截断计算域，适用于垂直入射和斜入射照明情况。基于带有PBC的变换麦克斯韦方程组，推导了具有GDM模型的DGTD方法的公式。此外，提出了一种龙格-库塔时间步进格式，以高精度更新半离散变换麦克斯韦方程组和辅助微分方程（ADE）。给出了具有色散元件的周期性纳米结构的数值例子，如薄膜的反射和透射、金属孔阵列结构界面处的表面等离子体以及双波段红外吸收器的吸收特性，以证明所提方法的准确性和能力。
