摘要： Nonlinear optical processes are important in many fields of photonics, ranging from biomedical imaging to ultrafast spectroscopy. Thanks to recent progress in nanophotonics and metamaterials, there is a growing demand for smaller and more efficient nonlinear optical components. Unfortunately, it is very challenging to satisfy this demand by using traditional materials, which motivates the search for alternative approaches. Nonlinear plasmonics has recently emerged as a potential solution for enabling more efficient nanoscale nonlinear optics. However, it is not yet clear how nonlinear responses of metamaterials can be enhanced sufficiently to enable practical nonlinear applications. Recent attempts to find the solution to this issue have been focused on two enhancement strategies, which are both based on resonance engineering. First, nanoparticle arrays associated with collective and narrow plasmon resonances with relatively high quality factors (Q-factors) known as surface lattice resonances (SLRs) have been utilized. Second, multiply-resonant nanostructures have been investigated where the resonance enhancement occurring both at the input and output wavelengths results in strong nonlinear response. Here, we combine these two concepts to enable even higher overall enhancement. We numerically study the enhancement of second-harmonic generation (SHG) in multiply-resonant plasmonic metasurfaces consisting of L-shaped aluminium nanoparticles. The array is designed to support two simultaneous high-Q SLRs, termed SLR(cid:90) and SLR2(cid:90), peaking at the fundamental and SHG wavelengths, respectively. The Q-factors of SLR(cid:90) and SLR2(cid:90) were estimated to be 800 and 250, respectively. We perform SHG simulations using an approach based on the nonlinear discrete-dipole approximation, and predict an enhancement of over six orders-of-magnitude of the emitted SHG intensity at doubly-resonant conditions.