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The optical responses of metal nanoparticles are associated with their localized surface-plasmon resonances. Such resonances give rise to strong local fields near the particles, which are particularly advantageous for nonlinear interactions. Here, we present an overview of our results on second-harmonic generation (SHG) from metasurfaces consisting of metal nanoparticles and discuss factors that affect its efficiency. Our metasurfaces consist mainly of ordered arrays of nanoparticles. L or T shaped particle appear non-centrosymmetric also at normal incidence, a requirement for SHG. The quality of the particles is crucial for homogeneous plasmon resonances and high overall SHG efficiency. Beyond this, subtle details of sample structure strongly influence the response. Furthermore, the response from SHG-active non-centrosymmetric particles can be enhanced by SHG-passive centrosymmetric particles. Both effects arise from lattice interactions between the members of the array. By extending these concepts further, we have shown the importance of surface lattice resonances for SHG efficiency, allowing the response to be enhanced even for reduced particle density. The nonlinear responses are assumed to depend mainly on the resonance at the fundamental wavelength. However, this is not sufficient as such, because the details of the local-field distributions, which are closely associated with particle geometry, are also crucial. We have also extended our work to random metal nanoisland films, where a dielectric overlayer shifts the plasmon resonance away from the resonance at the SHG wavelength. Rather surprisingly, the SHG response is enhanced because of strongly enhanced local fields at the fundamental wavelength as the dielectric loading is increased.
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