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Relative magnitude of dipolar and quadrupolar contriubutions to the second harmonic generation from small gold metallic nanoparticles

The optical second harmonic response from small gold metallic particles with a diameter ranging between 20 and 100 nm is investigated with the technique of Hyper Rayleigh Scattering. The analysis is performed as a function of the polarization state of the incoming fundamental beam. For the particles with the smallest diameters, the nonlinear optical response is purely dipolar, arising from the surface of the particles owing to the breaking of the centrosymmetry of the particles. For larger diameter particles, the retardation effects cannot be neglected anymore, the response exhibiting a clear quadrupolar pattern. A general framework is proposed to discuss the experimental data, based on a a weighing parameter allowing the quanitfication of the relative magnitude of the dipolar and quadrupoloar contributions.