Nanoscale electromagnetism with the boundary element method
Ulrich Hohenester, Gerhard Unger
Abstract
In Yang et al. [Nature 576, 248 (2019)], the authors introduced a general theoretical framework for nanoscale electromagnetism based on Feibelman parameters. Here quantum effects of the optically excited electrons at the interface between two materials are lumped into two complex-valued and frequency-dependent parameters which can be incorporated into modified boundary conditions for Maxwell's equations, the so-called mesoscopic boundary conditions. These modifications can, in principle, be implemented in any Maxwell solver, although the technicalities can be subtle and depend on the chosen computational approach. In this paper, we show how to implement mesoscopic boundary conditions in a boundary element method approach based on a Galerkin scheme with Raviart-Thomas shape elements for the representation of the tangential electromagnetic fields at the boundary. We demonstrate that the results of our simulations are in perfect agreement with Mie theory, including Feibelman parameters, and that for typical simulation scenarios the computational overhead is usually small.