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We employed both theoretical calculations and experiments to study the nonlinear responses in optical metamaterials. The spectra of second-harmonic generations measured on a fishnet metamaterial are in quantitative agreements with calculations based on full-wave numerical simulations combined with field integrations, both exhibiting ~80 times enhancements at the magnetic resonance frequency. Our calculations explained several interesting features observed experimentally, and suggested an optimal metamaterial structure to yield the strongest nonlinear signals.

Metamaterials; Nonlinear optics; Resonance