A modal analysis method to describe weak nonlinear effects in metamaterials

TL;DR

This paper introduces a modal analysis approach to characterize weak nonlinear effects in metamaterials, showing that linear eigenmodes can describe nonlinear responses and influence optimization of nonlinear properties.

Contribution

It presents a rigorous eigenmode analysis framework for weakly nonlinear metamaterials, linking linear eigenmodes to nonlinear responses and guiding design improvements.

Findings

Eigenmodes can fully describe weak nonlinear responses.

Modal patterns significantly impact nonlinear metamaterial optimization.

Eigenmode analysis aids in interpreting second-harmonic spectroscopy.

Abstract

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.