Second harmonic generation from 3D nanoantennas: on the surface and bulk contributions by far-field pattern analysis

We numerically study second harmonic generation from dipole gold nanoantennas by analyzing the different contributions of bulk and surface nonlinear terms. We focus our attention to the properties of the emitted field related to the different functional expressions of the two terms. The second harmonic field exhibits different far and near field patterns if both nonlinear contributions are taken into account or if only one of them is considered. This effect persists despite of the model used to estimate the parameters of the nonlinear sources and it is strictly related to the resonant behavior of the plasmonic nanostructure at the fundamental frequency field and to its linear properties at the second harmonic frequency. We show that the excitation of localized surface plasmon polaritons in these structures can remarkably modify the nonlinear response of the system by enhancing surface and/or bulk contributions, creating regimes where bulk nonlinear terms dominate over surface linear terms and vice versa. Finally, the results of our calculations suggest a method that could be implemented to experimentally extract information on the relevance of bulk and surface contributions by measuring and analyzing the generated far field second harmonic patterns in metal nanoantennas and, more in general, in plasmonic nanostructures.