  Second harmonic generation is enhanced at the surface lattice resonance in
plasmonic nanoparticle arrays. We carried out a parametric investigation on
two-dimensional lattices composed of gold nanobars where the centrosymmetry is
broken at oblique incidence. We study the influence of the periodicity, the
incidence angle and the direction of the linear input polarization on the
second harmonic generation. Excitation of the surface lattice resonance either
at the fundamental or second harmonic wavelength, achieved by varying the
incidence angle, enhance the conversion efficiency. As a special case, we
demonstrate that both the wavelengths can be simultaneously in resonance for a
specific period of the lattice. In this double resonant case, maximum second
harmonic power is achieved.
