A hybridizable discontinuous Galerkin method for computing nonlocal electromagnetic effects in three-dimensional metallic nanostructures

TL;DR

This paper introduces a hybridizable discontinuous Galerkin method for simulating nonlocal electromagnetic effects in 3D metallic nanostructures, improving accuracy and efficiency in modeling plasmonic resonances.

Contribution

The paper develops a novel HDG method combined with a hydrodynamic model to accurately simulate nonlocal electron interactions in nanostructures, including a new postprocessing scheme.

Findings

The HDG method converges for 2D and 3D nanostructure simulations.

Nonlocal effects significantly differ from local models at the nanoscale.

The method efficiently captures plasmonic resonances in complex geometries.

Abstract

The interaction of light with metallic nanostructures produces a collective excitation of electrons at the metal surface, also known as surface plasmons. These collective excitations lead to resonances that enable the confinement of light in deep-subwavelength regions, thereby leading to large near-field enhancements. The simulation of plasmon resonances presents notable challenges. From the modeling perspective, the realistic behavior of conduction-band electrons in metallic nanostructures is not captured by Maxwell's equations, thus requiring additional modeling. From the simulation perspective, the disparity in length scales stemming from the extreme field localization demands efficient and accurate numerical methods. In this paper, we develop the hybridizable discontinuous Galerkin (HDG) method to solve Maxwell's equations augmented with the hydrodynamic model for the conduction-band electrons in noble metals. This method enables the efficient simulation of plasmonic nanostructures while accounting for the nonlocal interactions between electrons and the incident light. We introduce a novel postprocessing scheme to recover superconvergent solutions and demonstrate the convergence of the proposed HDG method for the simulation of a 2D gold nanowire and a 3D periodic annular nanogap structure. The results of the hydrodynamic model are compared to those of a simplified local response model, showing that differences between them can be significant at the nanoscale.