Mathematical analysis of plasmonic nanoparticles: the scalar case

Habib Ammari, Pierre Millien, Matias Ruiz, Hai Zhang

Research output: Contribution to journalArticlepeer-review


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 threefold: (i) 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; (ii) to study the scattering and absorption enhancements by plasmon resonant nanoparticles and express them in terms of the polarization tensor of the nanoparticle. Optimal bounds on the enhancement factors are also derived; (iii) 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.
Original languageEnglish
Pages (from-to)597–658
Number of pages62
JournalArchive for Rational Mechanics and Analysis
Issue number2
Early online date2 Feb 2017
Publication statusPublished - 31 May 2017


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