pp 1–12 | Cite as

Localized Surface Plasmon Resonances of Simple Tunable Plasmonic Nanostructures

  • Luke C. UgwuokeEmail author
  • Tomáš Mančal
  • Tjaart P. J. Krüger


We derive and present systematic relationships between the analytical formulas for calculation of the localized surface plasmon resonances (LSPR) of some plasmonic nanostructures which we have categorized as simple. These relationships, including some new formulas, are summarized in a tree diagram which highlights the core-shell plasmons as the generators of solid and cavity plasmons. In addition, we show that the LSPR of complex structures can be reduced to that of simpler ones, using the LSPR of a nanorice as a case study, in the dipole limit. All the formulas were derived using a combination of the Drude model, the Rayleigh approximation, and the Fröhlich condition. The formulas are handy and they are in good agreement with the results of the plasmon hybridization theory. The formulas also account for dielectric effects, which provide versatility in the tuning of the LSPR of the nanostructures. A simplified model of plasmon hybridization is presented, allowing us to investigate the weak-coupling regimes of solid and cavity plasmons in the core-shell nanostructures we have studied.


Gold Localized surface plasmons (LSP) Local response approximation (LRA) Localized surface plasmon resonance (LSPR) Electrostatic polarizability Symmetrization Anti-symmetrization Dielectric reversal Geometric reduction Plasmon hybridization 



We wish to thank Vincenzo Giannini for his advice on the manuscript.

Funding Information

L. C. U. was sponsored by the National Research Foundation (NRF) and the University of Pretoria. T. M. was supported by the Czech Science Foundation (GACR) grant no. 17-22160S. T. P. J. K. was supported by the NRF project nos. 109302 and 112085.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

Supplementary material

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of PretoriaHatfieldSouth Africa
  2. 2.Faculty of Mathematics and PhysicsCharles UniversityPrague 2Czech Republic

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