  Collective responses of localized surface plasmon resonances, known as
surface lattice resonances (SLRs) in metal nanoparticle arrays, can lead to
high quality factors (~100), large local-field enhancements and strong
light-matter interactions. SLRs have found many applications in linear optics,
but little work of the influence of SLRs on nonlinear optics has been reported.
Here we show how SLRs could be utilized to enhance nonlinear optical
interactions. We devote special attention to the sum-frequency,
difference-frequency, and third-harmonic generation processes because of their
potential for the realization of novel sources of light. We also demonstrate
how such arrays could be engineered to enhance higher-order nonlinear optical
interactions through cascaded nonlinear processes. In particular, we
demonstrate how the efficiency of third-harmonic generation could be engineered
via cascaded second-order responses.
