3D Simulations of Spatially Dispersive Metals with a Finite Element Time Domain Method

We present recent advances in the development of a Finite Element Time Domain (Discontinuous Galerkin) solver for computational nanophotonics. Throughout this contribution a particular focus is put on metallic nano... [ view full abstract ]

We present recent advances in the development of a Finite Element Time Domain (Discontinuous Galerkin)

solver for computational nanophotonics. Throughout this contribution a particular focus is put on metallic nano structures of sizes between 1 nm and 15 nm. Metal structures at these sizes are well known to show spatial dispersion which can be modeled by a nonlocal dispersion model for the electron gas. Taking such a nonlocal model into account leads to a hydrodynamic fluid equation for the free electrons in the metal. While Maxwell's equations describe the evolution of the electromagnetic fields, the additional fluid equation accounts for the material response and is strongly coupled to Maxwell's equations by means of a source current.

Numerically speaking, the considered 3D finite element time domain method benefits from high-order polynomial solutions on very flexible unstructured tetrahedral meshes. Additionally, working in time domain gives access to broad band frequency solution within a single simulation run due to short pulses. Exploiting distributed memory parallelism eventually allows large computational domains and hence realistic nanophotonic setups.

We assess the performance of our numerical method on multiple nanophotonic scenarios like spherical dimer systems (simulation_mesh_dimer.png) and nanocubes (simulation_mesh_nanocube.png). We emphasize the importance of highly accurate numerical schemes that guarantee a powerful resolution of surface effects, which is especially indispensable for plasmonic applications since most physics happen in the vicinity of the metal surface. 

Moreover, we show the importance of high-order numerical methods including curvilinear tetrahedral meshes in order to properly approximate material interfaces if roundings are of concern.