Shape reconstruction of nanoparticles from their associated plasmonic resonances

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.