Resonance in metallic nanoparticles: a rigorous formulation of the dipolar approximation

In classical electromagnetism, the interaction of light with matter is introduced through the polarizability of a dipole subject to the local field of nearby atoms, leading to the Clausius–Mossotti rule. The dipolar model is also used to introduce plasmonics and fluorescence to undergraduates in electromagnetism courses: the scattering, absorption and extinction of light by spherical particles are examples of analytical solutions in spherical coordinates. The possible resonance of the interaction between light and metallic nanoparticles is commonly described in terms of the infinite limit of the dipole when its relative permittivity tends towards −2. However, this divergence is physically disruptive and therefore a mathematically sustainable approach is required to describe the resonance that occurs in the interaction between light and a metallic spherical particle. The proposed method removes infinity, enabling a rigorous discussion of the resonance.

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