Homogenization of plasmonic crystals: Seeking the epsilon-near-zero effect

M. Maier, M. Mattheakis, E. Kaxiras, M. Luskin, D. Margetis

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Abstract

By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell's equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic dielectric host. This structure is motivated by the need to design plasmonic crystals that enable the propagation of electromagnetic waves with no phase delay (epsilon-near-zero effect). Our microscopic model incorporates the surface conductivity of the two-dimensional (2D) material of each sheet and a corresponding line charge density through a line conductivity along possible edges of the sheets. Our analysis generalizes averaging principles inherent in previous Bloch-wave approaches. We investigate physical implications of our findings. In particular, we emphasize the role of the vector-valued corrector field, which expresses microscopic modes of surface waves on the 2D material. We demonstrate how our homogenization procedure may set the foundation for computational investigations of: effective optical responses of reasonably general geometries, and complicated design problems in the plasmonics of 2D materials.

Original languageEnglish (US)
Article number20190220
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume475
Issue number2230
DOIs
StatePublished - 2019

Bibliographical note

Funding Information:
We acknowledge support by ARO MURI award no. W911NF-14-1-0247 (M.Mai., M.Mat., E.K., M.L. and D.M.); EFRI 2-DARE NSF grant no. 1542807 (M.Mat.); as well as NSF DMS grant nos 1412769 (D.M.) and 1912847 (M.Mai). The last author (D.M.) acknowledges the support by a research and scholarship award from the graduate school, University of Maryland, in the spring of 2019.

Funding Information:
Data accessibility. Detailed analytical derivations accompanying the discussion in this paper have been made available as part of the supplementary material. Source code and configuration files of all computations have been made available at https://doi.org/10.5281/zenodo.3383328, and https://github.com/tamiko/ rspa-2019. Authors’ contributions. M.Mai., D.M. and M.L. developed the analysis. M.Mat. and E.K. contributed the physical interpretation. Numerical computations were carried out by M.Mai. and M.Mat. M.Mai., M.Mat. and D.M. wrote the manuscript. All authors discussed the results and contributed to the final manuscript. Competing interests. We declare we have no competing interests. Funding. We acknowledge support by ARO MURI award no. W911NF-14-1-0247 (M.Mai., M.Mat., E.K., M.L. and D.M.); EFRI 2-DARE NSF grant no. 1542807 (M.Mat.); as well as NSF DMS grant nos 1412769 (D.M.) and 1912847 (M.Mai). The last author (D.M.) acknowledges the support by a research and scholarship award from the graduate school, University of Maryland, in the spring of 2019.

Publisher Copyright:
© 2019 The Author(s) Published by the Royal Society. All rights reserved.

Keywords

  • Asymptotic analysis
  • Graphene
  • Homogenization
  • Maxwell's equations
  • Plasmonic crystals
  • Surface plasmon-polariton

PubMed: MeSH publication types

  • Journal Article

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