Abstract
As nanofabrication techniques become more precise, with ever smaller feature sizes, the ability to model nonlocal effects in plasmonics becomes increasingly important. While nonlocal models based on hydrodynamics have been implemented using various computational electromagnetics techniques, the finite-difference time-domain (FDTD) version has remained elusive. Here we present a comprehensive FDTD implementation of nonlocal hydrodynamics, including for parallel computing. As a sub-nanometer step size is required to resolve nonlocal effects, a parallel implementation makes the computational cost of nonlocal FDTD more affordable. We first validate our algorithms for small spherical metallic particles, and find that nonlocality smears out staircasing artifacts at metal surfaces, increasing the accuracy over local models. We find this also for a larger nanostructure with sharp extrusions. The large size of this simulation, where nonlocal effects are clearly present, highlights the importance and impact of a parallel implementation in FDTD.
Highlights
F ABRICATING objects with nanoscale precision is possible due to significant progress in nanofabrication techniques over the last few decades [1]
We find the same trend as presented in Ref. [13], showing that generalized nonlocal optical response (GNOR) finite-difference time-domain (FDTD) is consistent with experimental measurements and calculations using quantum-based permittivities, with quantitative agreement down to 10 nm diameter, and qualitative agreement to 2 nm
We have introduced a parallel FDTD implementation for modeling nonlocality in plasmonics
Summary
F ABRICATING objects with nanoscale precision is possible due to significant progress in nanofabrication techniques over the last few decades [1]. Nonlocal hydrodynamic models have been implemented using several computational electromagnetic methods including the finite element method [21], the discontinuous Galerkin time-domain (DGTD) method [22], and the boundary element method [23] Due to their inhomogeneous mesh, finite element methods, including DGTD, offer computationally efficient calculations for systems containing sharp features, or complex geometry, especially when compared to finite difference methods. BAXTER et al.: PARALLEL FDTD MODELING OF NONLOCALITY IN PLASMONICS important for simulating nonlocality, as the grid cell size needs to be smaller than the Fermi wavelength λF ∼ 0.5 nm to capture the spread of electron density [30] This can require a large amount of memory and can present a prohibitive computational load.
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