Contents I. Introduction
Nanophotonics is concerned with the study of the behavior of light at the nanometer scale in interaction with sub-wavelength particles or devices. The numerical study of electromagnetic wave propagation in interaction with nanostructures generally relies on the solution of the system of time-domain Maxwell's equations and taking into account an appropriate physical dispersion model, such as the Drude or Drude-Lorentz models, for characterizing the material properties of the involved nanostructures at optical frequencies [1]. For the numerical solution of the time-domain Maxwell's equations, plenty of methods are developed, such as finite difference time domain (FDTD) methods, finite element time domain (FETD) methods. The FDTD methods are very popular because of their simplicity and their non-dissipative nature. While for realistic nanophotonic applications, the FDTD methods suffer from several important limitations, essentially due to the use of a cartesian discretization grid [2]. Although the FETD methods are more flexible for capturing complex geometric structures, they have to solve linear systems of equations within each time step, which is very expensive in realistic problems. In the last ten years, the Discontinuous-Galerkin Time-Domain (DGTD) methods [3] gain more and more attentions in the purpose of simulating complex realistic problems. DGTD methods accommodate elements of various types and shapes, irregular non-matching grids, and even locally varying polynomial order, and hence offer great flexibility for modeling complex problems. Thus the DGTD methods are very promising for modeling complex problems like the nanophotonic applications. In this work, an interior penalty discontinuous galerkin time domain (IPDGTD) [4] method is developed for solving time-domain Maxwell's equations in Drude-like media.
