Effective medium multipolar tensor analysis of second-harmonic generation from metal nanoparticles

We present a detailed multipolar tensor analysis of second-harmonic (SH) generation from arrays of L-shaped gold nanoparticles. We define three effective nonlinear tensors, which include electric dipoles only (A(eee)) and lowest-order magnetic (and quadrupole) effects at the fundamental (A(eem)) and the SH (A(mee)) frequency. The components of the various tensors are distinguished through their different transformations as the experimental geometry is varied. The response is dominated by electric-dipole effects. However, the higher multipoles also play a significant role and are more important at the fundamental frequency than at the SH frequency. The results correlate well with the particles' plasmonic resonances and symmetry rules.