Discontinuous Galerkin time domain analysis of electromagnetic scattering from dispersive periodic nanostructures at oblique incidence.

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.