Mathematical analysis of plasmonic resonances for nanoparticles: The full Maxwell equations

Habib Ammari, Matias Ruiz, Sanghyeon Yu, Hai Zhang

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


In this paper we use the full Maxwell equations for light propagation in order to analyze plasmonic resonances for nanoparticles. We mathematically define the notion of plasmonic resonance and analyze its shift and broadening with respect to changes in size, shape, and arrangement of the nanoparticles, using the layer potential techniques associated with the full Maxwell equations. We present an effective medium theory for resonant plasmonic systems and derive a condition on the volume fraction under which the Maxwell–Garnett theory is valid at plasmonic resonances.

Original languageEnglish
Pages (from-to)3615-3669
Number of pages55
JournalJournal of Differential Equations
Issue number6
Publication statusPublished - 2016 Sept 15
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.


  • Maxwell equations
  • Maxwell–Garnett theory
  • Nanoparticle
  • Neumann–Poincaré operator
  • Plasmonic resonance
  • Scattering and absorption enhancements

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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