Nonlinear magnetoelectric metamaterials: Analysis and homogenization via a microscopic coupled-mode theory

Artificially structured metamaterials hybridized with elements that respond nonlinearly to incident electromagnetic fields can, from a macroscopic perspective, support nonlinear responses that cannot be described by purely electric or magnetic interactions. To investigate the mechanisms and behaviors of such interactions, termed nonlinear magnetoelectric coupling, we develop a set of coupled-mode equations for describing three-wave mixing in a metamaterial, using Bloch modes as the basis. By equating these coupled-mode equations to those of a homogenized system, we derive closed-form expressions for the macroscopic nonlinear susceptibilities. From these expressions, a great deal can be inferred about the nature and construction of magnetoelectric nonlinearities in metamaterials. As an example, we apply this method in the analysis of a prototypical nonlinear magnetoelectric metamaterial. In particular, we show that independent control of the eight second-order susceptibility tensors encompasses a massive parameter space from which new realms of nonlinear interference and wave manipulation can be accessed.