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We present a study of the second-order nonlinear optical properties of metal-based metamaterials. A hydrodynamic model for electronic response is used, in which nonlinear surface contributions are expressed in terms of the bulk polarization. The model is in good agreement with published experimental results, and clarifies the mechanisms contributing to the nonlinear response. In particular, we show that the reported enhancement of the second harmonic in split-ring resonator based media is driven by the electric rather than the magnetic properties of the structure.
Ciracì et al. (Tue,) studied this question.