Multipolar second harmonic generation from metallic nanoparticles

We describe the multipolar Second Harmonic (SH) response from metallic particles with sizes up to 150 nm. A particular emphasis is given to the light polarization and size dependence of the SH intensity collected to identify the different field mechanisms involved and quantify the different sources to the nonlinear polarization. It is shown that the dipolar, quadrupolar and octupolar modes can be observed depending on the input fundamental and output harmonic polarization configurations chosen and the size of the particles. We furthermore develop a careful analysis of the experimental results obtained for the largest size of particles investigated, e.g. 150 nm diameter gold particles, in conjunction with finite element simulations to compute the different sources to the nonlinear polarization, namely the surface local and the bulk nonlocal contributions. It is then shown that their relative weight can be determined. These results are recast within the general model initially proposed by Rudnick and Stern (J. Rudnick and E. A. Stern, Phys. Rev. B, 4 (1971) 4274).