Multipolar second harmonic generation from metallic nanoparticles

A general framework is given to describe the multipolar Second Harmonic (SH) response from small metallic particles the size of which ranges between a few ten of nanometers and 150 nm. A particular emphasis is given to the input polarization dependence of the SH intensity and the separation of its different mechanisms. The nonlinear polarization is here reduced as a surface polarization term only, the latter stemming from the local breaking of the centrosymmetry at the surface of the particle. The results are applied to the experimental case of the incoherent scattering of the second harmonic light, i.e. hyper Rayleigh scattering, for non-interacting metallic particles dispersed in solution.