Shape reconstruction of nanoparticles from their associated plasmonic resonances

TL;DR

This paper demonstrates how plasmonic resonances can be used to classify nanoparticle shapes with algebraic boundaries and to reconstruct the distance between nearly touching nanoparticles, supported by explicit spectral computations and numerical results.

Contribution

It introduces a method to classify nanoparticle shapes and measure inter-particle distances using spectral analysis of plasmonic resonances, with explicit computations for specific geometries.

Findings

Spectral decompositions of Neumann-Poincaré operators are explicitly computed for certain domains.

Plasmonic resonances can classify shapes with algebraic boundaries.

Resonance measurements can determine separation distances between nanoparticles.

Abstract

We prove by means of a couple of examples that plasmonic resonances can be used on one hand to classify shapes of nanoparticles with real algebraic boundaries and on the other hand to reconstruct the separation distance between two nanoparticles from measurements of their first collective plasmonic resonances. To this end, we explicitly compute the spectral decompositions of the Neumann-Poincar\'{e} operators associated with a class of quadrature domains and two nearly touching disks. Numerical results are included in support of our main findings.