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

by H. Ammari and M. Ruiz and S. Yu and H. Zhang

(Report number 2015-34)

Abstract
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.

Keywords: plasmonic resonance, Neumann-Poincare operator, nanoparticle, scattering and absorption enhancements, Maxwell equations, Maxwell-Garnett theory

@Techreport{ARYZ15_624,
  author = {H. Ammari and M. Ruiz and S. Yu and H. Zhang},
  title = {Mathematical analysis of plasmonic resonances for nanoparticles: the full Maxwell equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2015-34},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-34.pdf },
  year = {2015}
}

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