Heat generation of plasmonic nanoparticles

In this paper we use layer potentials and asymptotic analysis techniques to analyze the heat generation due to nanoparticles when illuminated at their plasmonic resonance. We consider arbitrary-shaped particles and the cases of both a single and multiple particles. We clarify the strong dependency of the heat generation on the geometry of the particles as it depends on the eigenvalues of the associated Neumann--Poincaré operator. For close-to-touching nanoparticles, we show that the temperature field deviates significantly from the one generated by two single nanoparticles. The results of this paper formally explain experimental results reported in the nanomedical literature. They open a door for solving the challenging problems of detecting plasmonic nanoparticles in biological media and monitoring temperature elevation in tissue generated by nanoparticle heating.