We investigate optical second-harmonic generation (SHG) from metasurfaces where noncentrosymmetric V-shaped gold nanoparticles are ordered into regular array configurations. In contrast to expectations, a substantial enhancement of the SHG signal is observed when the number density of the particles in the array is reduced. More specifically, by halving the number density, we obtain over 5-fold enhancement in SHG intensity. This striking result is attributed to favorable interparticle interactions mediated by the lattice, where surface-lattice resonances lead to spectral narrowing of the plasmon resonances. Importantly, however, the results cannot be explained by the improved quality of the plasmon resonance alone. Instead, the lattice interactions also lead to further enhancement of the local fields at the particles. The experimental observations agree very well with results obtained from numerical simulations including lattice interactions.

We investigate the role of surface-lattice resonances (SLRs) in second-harmonic generation (SHG) from arrays of metal nanoparticles. The SLRs affect the generated signal when the sample is rotated away from normal incidence. The adjustment of the incident angle tunes the SLRs to the fundamental wavelength for SHG and improves the quality of the resonance for better resonance enhancement of SHG. Compared to normal incidence, an enhancement by a factor of 10 is observed. However, at certain incident angles, the enhancement is interrupted by diffraction anomalies, which redirect light into the substrate, increasing radiation damping and compromising the quality of the resonance.

Plasmonic metasurfaces are promising as enablers of nanoscale nonlinear optics and flat nonlinear optical components. Nonlinear optical responses of such metasurfaces are determined by the nonlinear optical properties of individual plasmonic meta-atoms. Unfortunately, no simple methods exist to determine the nonlinear optical properties (hyperpolarizabilities) of the meta-atoms hindering the design of nonlinear metasurfaces. Here, we develop the equivalent RLC circuit (resistor, inductor, capacitor) model of such metaatoms to estimate their second-order nonlinear optical properties, that is, the first-order hyperpolarizability in the optical spectral range. In parallel, we extract from second-harmonic generation experiments the first-order hyperpolarizabilities of individual meta-atoms consisting of asymmetrically shaped (elongated) plasmonic nanoprisms, verified with detailed calculations using both nonlinear hydrodynamic-FDTD and nonlinear scattering theory. All three approaches, analytical, experimental, and computational, yield results that agree very well. Our empirical RLC model can thus be used as a simple tool to enable an efficient design of nonlinear plasmonic metasurfaces.

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Here, we experimentally determine the order-of-magnitude value of the 1st-order hyperpolarizability of plasmonic meta-atoms in metasurfaces. This result will prove useful in designing nonlinear metasurfaces for a variety of applications.