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

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.

arXiv comment27 pages, 8 figures

References in corpus (7)

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• Nonlocal optical response in metallic nanostructures
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Cited by in corpus (12)

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• Impact of surface roughness in nanogap plasmonic systems
• HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB
• Computing parametrized solutions for plasmonic nanogap structures
• Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
• A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures
• Numerical simulation of a coupled system of Maxwell equations and a gas dynamic model
• Mathematical and numerical analysis of a nonlocal Drude model in nanoplasmonics
• A posteriori error estimates for finite element discretizations of time-harmonic Maxwell's equations coupled with a non-local hydrodynamic Drude model
• The Uniqueness Theorem for Nonlocal Hydrodynamic Media
• Efficient multiscale algorithms for simulating nonlocal optical response of metallic nanostructure arrays
• A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs