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

Shape reconstruction of nanoparticles from their associated plasmonic resonances