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

F. Vidal-Codina, N. C. Nguyen, S. H. Oh, J. Peraire

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14 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)548-565
Number of pages18
JournalJournal of Computational Physics
StatePublished - Feb 15 2018

Bibliographical note

Funding Information:
F. V.-C., N. C. N and J. P. acknowledge support from the AFOSR Grant No. FA9550-11-1-0141 and the AFOSR Grant No. FA9550-12-0357 . S.-H. O. acknowledges support from the NSF Grant No. ECCS 1610333 and the Seagate Technology University Project. The authors thank Prof. Luis Martín-Moreno and Dr. Cristian Ciracì for their valuable suggestions, comments and inputs.

Publisher Copyright:
© 2017 Elsevier Inc.


  • Hybridizable discontinuous Galerkin method
  • Hydrodynamic model for metals
  • Maxwell's equations
  • Nonlocal electrodynamics
  • Plasmonics
  • Terahertz nonlocality


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