Theoretical and numerical analysis of a non-local dispersion model for light interaction with metallic nanostructures

In this paper, we discuss the time-domain Maxwell’s equations coupled to another partial differential equation, which arises from modeling of light and structure interaction at the nanoscale. One major contribution of this paper is that the well-posedness is rigorously justified for the first time. Then we propose a fully-discrete finite element method to solve this model. It is interesting to note that we need use curl conforming, divergence conforming, and L2L2 finite elements for this model. Numerical stability and optimal error estimate of the scheme are proved. Numerical results justifying our theoretical convergence rate are presented.