Comparison of Numerical Methods for the Analysis of Plasmonic Structures

Numerical simulations of plasmonic structures are very demanding and expensive in terms of memory and CPU time, making the selection of a suitable numerical method for the field computation important. To examine this problem, we applied several numerical methods to a group of 2D plasmonic nanowire problems. In particular, we examine the Finite Element Method (FEM) and the Finite Difference Time-Domain (FDTD) method from the family of domain-discretization methods. We also look at the Multiple Multipole Program (MMP), the Method of Auxiliary Sources (MAS), and the Mesh-less Boundary Integral Equation (BIE) method from the family of boundary-discretization methods. We quantitatively compare several results generated from each method to make some conclusions about their applicability and accuracy for plasmonic simulations. Domain-discretization methods (FEM and FDTD) can reach a high level of accuracy only with a high discretization. This is affordable on modern computer hardware in 2D. Recommendations for improving this are provided. The boundary-discretization techniques have a clear advantage in terms of speed, matrix size, and accuracy in 2D. This advantage may disappear in the full 3D analysis of geometrically complicated structures. This happens because matrices become denser or more ill-conditioned. Therefore the most efficient method depends on the problem dimension and complexity.