On the convergence and accuracy of the FDTD method for nanoplasmonics

Abstract

Use of the Finite-Difference Time-Domain (FDTD) method to model nanoplasmonic structures continues to rise - more than 2700 papers have been published in 2014 on FDTD simulations of surface plasmons. However, a comprehensive study on the convergence and accuracy of the method for nanoplasmonic structures has yet to be reported. Although the method may be well-established in other areas of electromagnetics, the peculiarities of nanoplasmonic problems are such that a targeted study on convergence and accuracy is required. The availability of a high-performance computing system (a massively parallel IBM Blue Gene/Q) allows us to do this for the first time. We consider gold and silver at optical wavelengths along with three "standard" nanoplasmonic structures: a metal sphere, a metal dipole antenna and a metal bowtie antenna - for the first structure comparisons with the analytical extinction, scattering, and absorption coefficients based on Mie theory are possible. We consider different ways to set-up the simulation domain, we vary the mesh size to very small dimensions, we compare the simple Drude model with the Drude model augmented with two critical points correction, we compare single-precision to double-precision arithmetic, and we compare two staircase meshing techniques, per-component and uniform. We find that the Drude model with two critical points correction (at least) must be used in general. Double-precision arithmetic is needed to avoid round-off errors if highly converged results are sought. Per-component meshing increases the accuracy when complex geometries are modeled, but the uniform mesh works better for structures completely fillable by the Yee cell (e.g., rectangular structures). Generally, a mesh size of 0.25 nm is required to achieve convergence of results to ∼ 1%. We determine how to optimally setup the simulation domain, and in so doing we find that performing scattering calculations within the near-field does not necessarily produces large errors but reduces the computational resources required.

Laser-induced plasmonic colours on metals

“…We used in-house 3D-FDTD parallel code4647 on an IBM BlueGene/Q supercomputer (64k cores) part of the Southern Ontario Smart Computing Innovation Platform (SOSCIP). In the model, metal NPs were arranged in the xz plane, as inspired by SEM images of irradiated surfaces and the corresponding statistics of the metal NP distributions, and the system was excited by a z -polarized plane wave.…”

Surface Plasmon Enhanced Schottky Detectors

“…On resonance, the electric field near the particle (in the dielectric) is strongly enhanced compared to the illuminating field. Resonant features appear in the measured extinction and scattering spectra of metal nanoparticles, in correlation with the plasmon resonances that are excited thereon [22].…”

Vectorial control of nonlinear emission via chiral butterfly nanoantennas: generation of pure high order nonlinear vortex beams

“…The simulations are performed using an in-house parallel 3D-FDTD code [47]. We model the dispersion of gold by the Drude model plus two critical points (Drude+2CP), implemented in FDTD by the auxiliary differential equation (ADE) technique.…”