Hyperpolarizability of plasmonic meta-atoms in metasurfaces

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 nanostructured plasmonic meta-atoms, which are the building blocks of the metasurfaces. Unfortunately, no simple methods exist to determine the nonlinear coefficients (hyperpolarizabilities) of the meta-atoms hindering designing of nonlinear metasurfaces. Here, we develop the equivalent RLC circuit model of such meta-atoms to estimate their second-order nonlinear optical parameter i.e. the first-order hyperpolarizability in the optical spectral range. In parallel, we extract from second-harmonic generation experiments the spectrum of the 1st-order hyperpolarizabilities of individual meta-atoms consisting of asymmetrically shaped (elongated) plasmonic nanoprisms. Moreover, we verify our results using nonlinear hydrodynamic-FDTD and with calculations based on 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 efficient design of nonlinear plasmonic metasurfaces.