Wave-mixing origin and optimization in single and compact aluminum nanoantennas

The outstanding optical properties for plasmon resonances in noble metal nanoparticles enable the observation of non-linear optical processes such as second-harmonic generation (SHG) at the nanoscale. Here, we investigate the SHG process in single rectangular aluminum nanoantennas and demonstrate that i) a doubly resonant regime can be achieved in very compact nanostructures, yielding a 7.5 enhancement compared to singly resonant structures and ii) the $\chi_{\perp\perp\perp}$ local surface and $\gamma_{bulk}$ nonlocal bulk contributions can be separated while imaging resonant nanostructures excited by a tightly focused beam, provided the $\chi_{\perp\parallel\parallel}$ local surface is assumed to be zero, as it is the case in all existing models for metals. Thanks to the quantitative agreement between experimental and simulated far-field SHG maps, taking into account the real experimental configuration (focusing and substrate), we identify the physical origin of the SHG in aluminum nanoantennas as arising mainly from $\chi_{\perp\perp\perp}$ local surface sources.