Hyperpolarizability is a measure of the nonlinear optical characteristics of natural or meta-atoms describing how the atoms become nonlinearly polarized by the induced local-field. However, determining hyperpolarizability in the case of structured plasmonic meta-atoms is not straightforward due to their relatively larger sizes, unique shapes, and the index of refraction of the surrounding dielectric medium. Also, the order-of-magnitude of hyperpolarizability may vary with the frequency of light especially when inter-band transitions in metals become dominant. Here, we experimentally and theoretically estimated the order-of-magnitude of the 1st-order hyperpolarizability of gold meta-atoms that can be used in designing nonlinear metasurfaces.
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