A large-scale nonlinear eigensolver for the analysis of dispersive nanostructures

Abstract

We introduce the electromagnetic eigenmodal solver code FemaxxNano for the numerical analysis of nanometer structured optical systems, a scientific field generally know as nanooptics. FemaxxNano solves the electric field vector wave equation and calculates the electromagnetic eigenmodes of nearly arbitrary 3-dimensional resonators, embedded either in free-space, vacuum or a background medium. Here, the study of the interaction between nanometer sized metallic structures and light is at the heart of the physical problem. Since metals in the optical region of the electromagnetic spectrum are highly dispersive and, thus, dissipative, dielectric media, we eventually obtain a nonlinear eigenvalue problem. We discretize the electromagnetic eigenvalue problem with the finite element method (FEM) in 3-dimensional space and on unstructured tetrahedral grids. We introduce a fully iterative scheme to solve the nonlinear problem for complex coefficient matrices that depend on wavelength. We investigate the properties of the algorithm in detail and demonstrate its performance by analyzing a nanometer sized optical dimer structure, a specific type of optical antenna, on distributed-memory parallel computers.