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Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Case

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Abstract

Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light scattering and an enhancement of the local electromagnetic fields. This paper is devoted to the mathematical modeling of plasmonic nanoparticles. Its aim is fourfold: (1) to mathematically define the notion of plasmonic resonance and to analyze the shift and broadening of the plasmon resonance with changes in size and shape of the nanoparticles; (2) to study the scattering and absorption enhancements by plasmon resonant nanoparticles and express them in terms of the polarization tensor of the nanoparticle; (3) to derive optimal bounds on the enhancement factors; (4) to show, by analyzing the imaginary part of the Green function, that one can achieve super-resolution and super-focusing using plasmonic nanoparticles. For simplicity, the Helmholtz equation is used to model electromagnetic wave propagation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland

    Habib Ammari

  2. EPFL SB MATHAA CAMA, Station 8, 1015, Lausanne, Switzerland

    Pierre Millien

  3. Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005, Paris, France

    Matias Ruiz

  4. Department of Mathematics, HKUST, Clear Water Bay, Kowloon, Hong Kong

    Hai Zhang

Authors
  1. Habib Ammari
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  2. Pierre Millien
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  3. Matias Ruiz
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  4. Hai Zhang
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Corresponding author

Correspondence to Habib Ammari.

Additional information

Communicated by P. Rabinowitz

This work was supported by the ERC Advanced Grant Project MULTIMOD–267184. Hai Zhang was supported by Hong Kong RGC grant 26301016 and an initiation Grant IGN15SC05 from HKUST.

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Ammari, H., Millien, P., Ruiz, M. et al. Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Case. Arch Rational Mech Anal 224, 597–658 (2017). https://doi.org/10.1007/s00205-017-1084-5

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  • DOI: https://doi.org/10.1007/s00205-017-1084-5

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