Nonlinear Surface Lattice Resonance in Plasmonic Nanoparticle Arrays

We study experimentally second-harmonic generation from arrays of split-ring resonators at oblique incidence and find conditions of more than 30-fold enhancement of the emitted second harmonic with respect to normal incidence. We show that these conditions agree well with a nonlinear Rayleigh-Wood anomaly relation and the existence of a surface lattice resonance at the second harmonic. The existence of a nonlinear surface lattice resonance is theoretically confirmed by extending the coupled dipole approximation to the nonlinear case. We further show that the localized surface plasmon modes that collectively contribute to the surface lattice resonance are inherently dark modes that become highly bright due to the collective interaction.