Modal analysis method to describe weak nonlinear effects in metamaterials

We apply a rigorous eigenmode analysis to study the electromagnetic properties of linear and weakly nonlinear metamaterials. The nonlinear response can be totally described by the linear eigenmodes when weak nonlinearities are attributed to metamaterials. We use this theory to interpret intrinsic second-harmonic spectroscopy on metallic metamaterials. Our study indicates that metamaterial eigenmodes play a critical role in optimizing a nonlinear metamaterial response to the extent that a poorly optimized modal pattern overwhelms the widely recognized benefits of plasmonic resonant field enhancements.