Direct and cascaded collective third-harmonic generation in metasurfaces

We use collective interactions in plasmonic metasurfaces to manipulate the interplay between direct and cascaded third-harmonic generation. We implement a simple case where in contrast to the direct contribution, which is mainly enhanced by the local plasmonic resonances, the cascaded contribution enhancement may be manipulated using the metasurface’s geometry, in addition to the single nanoparticle’s electrical response, by enabling the proper nonlocal interactions at the second-harmonic frequency. In addition, an anomalous phase relation of the single nanoparticle’s linear polarizability at the second-harmonic region affects the relative phase between the direct and cascaded contributions, which results in a Fano-like asymmetrical line shape of the third-harmonic generation. We demonstrate that this can be used to enhance or contrarily completely eliminate third-harmonic generation from metasurfaces over a very narrow bandwidth. Such a unique fundamental observation of the interplay between direct and cascaded third-harmonic generation in periodic resonant systems may find new applications in sensing and to control nonlinear optical phenomena.