Nanoscale electromagnetism with the boundary element method

TL;DR

This paper presents a boundary element method implementation for nanoscale electromagnetism incorporating Feibelman parameters, enabling accurate simulations of quantum interface effects with minimal computational overhead.

Contribution

It introduces a practical implementation of mesoscopic boundary conditions in a boundary element method for nanoscale electromagnetism.

Findings

Simulation results match Mie theory with Feibelman parameters.

Computational overhead remains small for typical scenarios.

Method effectively captures quantum interface effects.

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 implemeted 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 the 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.