Adaptive finite element simulations of waveguide configurations involving parallel 2D material sheets

Jung Heon Song, Matthias Maier, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We discuss analytically and numerically the propagation and energy transmission of electromagnetic waves caused by the coupling of surface plasmon polaritons (SPPs) between two spatially separated layers of 2D materials, such as graphene, at subwavelength distances. We construct an adaptive finite-element method to compute the ratio of energy transmitted within these waveguide structures reliably and efficiently. At its heart, the method is built upon a goal-oriented a posteriori error estimation with the dual-weighted residual method (DWR). Furthermore, we derive analytic solutions of the two-layer system, compare those to (known) single-layer configurations, and compare and validate our numerical findings by comparing numerical and analytical values for optimal spacing of the two-layer configuration. Additional aspects of our numerical treatment, such as local grid refinement, and the utilization of perfectly matched layers (PMLs) are examined in detail.

Original languageEnglish (US)
Pages (from-to)20-34
Number of pages15
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Jul 1 2019

Bibliographical note

Funding Information:
We wish to thank Professor Dionisios Margetis for useful discussions. We acknowledge support by ARO MURI Award W911NF-14-0247 .

Publisher Copyright:
© 2019 Elsevier B.V.


  • Adaptive finite-element methods
  • Surface plasmon–polariton
  • Time-harmonic Maxwell's equations
  • Waveguide configurations

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