  We investigate the process of the second harmonic generation by plasmonic
nano-antennas that exhibit Fano-like resonances. A rigorous fully vectorial
Maxwell-hydrodynamics approach is employed to directly calculate the second
order susceptibilities as function of the pump frequency, considering a
periodic array of nanodolmens comprised of three Au nanorods. The results of
the numerical simulations demonstrate noticeable enhancement of the second
harmonic efficiency by the antisymmetric mode. Additionally, a simple
analytical model based on two coupled nonlinear oscillators is proposed. It is
shown that the second order optical response can be significantly enhanced at
the frequency of the antisymmetric normal mode thus supporting our numerical
results.
